24 game/Solve: Difference between revisions
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[8, 7, 9, 7] : No solution found |
[8, 7, 9, 7] : No solution found |
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[9, 4, 4, 5] : No solution found</pre> |
[9, 4, 4, 5] : No solution found</pre> |
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===Python: using tkinter=== |
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<lang python> |
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''' Python 3.6.5 code using Tkinter graphical user interface. |
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Combination of '24 game' and '24 game/Solve' |
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allowing user or random selection of 4-digit number |
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and user or computer solution. |
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Note that all computer solutions are displayed''' |
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from tkinter import * |
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from tkinter import messagebox |
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from tkinter.scrolledtext import ScrolledText |
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# 'from tkinter import scrolledtext' in later versions? |
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import random |
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import itertools |
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# ************************************************ |
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class Game: |
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def __init__(self, gw): |
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self.window = gw |
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self.digits = '0000' |
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a1 = "(Enter '4 Digits' & click 'My Digits'" |
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a2 = "or click 'Random Digits')" |
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self.msga = a1 + '\n' + a2 |
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b1 = "(Enter 'Solution' & click 'Check Solution'" |
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b2 = "or click 'Show Solutions')" |
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self.msgb = b1 + '\n' + b2 |
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# top frame: |
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self.top_fr = Frame(gw, |
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width=600, |
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height=100, |
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bg='dodger blue') |
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self.top_fr.pack(fill=X) |
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self.hdg = Label(self.top_fr, |
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text=' 21 Game ', |
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font='arial 22 bold', |
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fg='navy', |
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bg='lemon chiffon') |
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self.hdg.place(relx=0.5, rely=0.5, |
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anchor=CENTER) |
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self.close_btn = Button(self.top_fr, |
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text='Quit', |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.close_window) |
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self.close_btn.place(relx=0.07, rely=0.5, |
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anchor=W) |
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self.clear_btn = Button(self.top_fr, |
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text='Clear', |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.clear_screen) |
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self.clear_btn.place(relx=0.92, rely=0.5, |
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anchor=E) |
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# bottom frame: |
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self.btm_fr = Frame(gw, |
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width=600, |
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height=500, |
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bg='lemon chiffon') |
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self.btm_fr.pack(fill=X) |
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self.msg = Label(self.btm_fr, |
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text=self.msga, |
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font='arial 16 bold', |
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fg='navy', |
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bg='lemon chiffon') |
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self.msg.place(relx=0.5, rely=0.1, |
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anchor=CENTER) |
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self.user_dgt_btn = Button(self.btm_fr, |
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text='My Digits', |
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width=12, |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.get_digits) |
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self.user_dgt_btn.place(relx=0.07, rely=0.2, |
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anchor=W) |
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self.rdm_dgt_btn = Button(self.btm_fr, |
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text='Random Digits', |
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width=12, |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.gen_digits) |
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self.rdm_dgt_btn.place(relx=0.92, rely=0.2, |
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anchor=E) |
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self.dgt_fr = LabelFrame(self.btm_fr, |
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text=' 4 Digits ', |
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bg='dodger blue', |
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fg='navy', |
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bd=4, |
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relief=RIDGE, |
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font='arial 12 bold') |
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self.dgt_fr.place(relx=0.5, rely=0.27, |
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anchor=CENTER) |
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self.digit_ent = Entry(self.dgt_fr, |
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justify='center', |
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font='arial 16 bold', |
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fg='navy', |
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disabledforeground='navy', |
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bg='lemon chiffon', |
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disabledbackground='lemon chiffon', |
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bd=4, |
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width=6) |
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self.digit_ent.grid(row=0, column=0, |
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padx=(8,8), |
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pady=(8,8)) |
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self.chk_soln_btn = Button(self.btm_fr, |
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text='Check Solution', |
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state='disabled', |
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width=14, |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.check_soln) |
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self.chk_soln_btn.place(relx=0.07, rely=.42, |
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anchor=W) |
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self.show_soln_btn = Button(self.btm_fr, |
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text='Show Solutions', |
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state='disabled', |
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width=14, |
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bd=5, |
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bg='navy', |
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fg='lemon chiffon', |
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font='arial 12 bold', |
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command=self.show_soln) |
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self.show_soln_btn.place(relx=0.92, rely=.42, |
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anchor=E) |
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self.soln_fr = LabelFrame(self.btm_fr, |
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text=' Solution ', |
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bg='dodger blue', |
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fg='navy', |
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bd=4, |
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relief=RIDGE, |
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font='arial 12 bold') |
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self.soln_fr.place(relx=0.07, rely=0.58, |
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anchor=W) |
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self.soln_ent = Entry(self.soln_fr, |
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justify='center', |
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font='arial 16 bold', |
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fg='navy', |
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disabledforeground='navy', |
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bg='lemon chiffon', |
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disabledbackground='lemon chiffon', |
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state='disabled', |
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bd=4, |
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width=15) |
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self.soln_ent.grid(row=0, column=0, |
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padx=(8,8), pady=(8,8)) |
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self.solns_fr = LabelFrame(self.btm_fr, |
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text=' Solutions ', |
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bg='dodger blue', |
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fg='navy', |
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bd=4, |
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relief=RIDGE, |
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font='arial 12 bold') |
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self.solns_fr.place(relx=0.92, rely=0.5, |
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anchor='ne') |
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self.solns_all = ScrolledText(self.solns_fr, |
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font='courier 14 bold', |
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state='disabled', |
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fg='navy', |
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bg='lemon chiffon', |
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height=8, |
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width=14) |
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self.solns_all.grid(row=0, column=0, |
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padx=(8,8), pady=(8,8)) |
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# validate '4 Digits' entry. |
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# save if valid and switch screen to solution mode. |
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def get_digits(self): |
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txt = self.digit_ent.get() |
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if not(len(txt) == 4 and txt.isdigit()): |
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self.err_msg('Please enter 4 digits (eg 1357)') |
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return |
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self.digits = txt # save |
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self.reset_one() # to solution mode |
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return |
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# generate 4 random digits, display them, |
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# save them, and switch screen to solution mode. |
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def gen_digits(self): |
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self.digit_ent.delete(0, 'end') |
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self.digits = ''.join([random.choice('123456789') |
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for i in range(4)]) |
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self.digit_ent.insert(0, self.digits) # display |
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self.reset_one() # to solution mode |
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return |
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# switch screen from get digits to solution mode: |
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def reset_one(self): |
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self.digit_ent.config(state='disabled') |
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self.user_dgt_btn.config(state='disabled') |
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self.rdm_dgt_btn.config(state='disabled') |
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self.msg.config(text=self.msgb) |
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self.chk_soln_btn.config(state='normal') |
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self.show_soln_btn.config(state='normal') |
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self.soln_ent.config(state='normal') |
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return |
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# edit user's solution: |
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def check_soln(self): |
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txt = self.soln_ent.get() # user's expression |
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d = '' # save digits in expression |
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dgt_op = 'd' # expecting d:digit or o:operation |
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for t in txt: |
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if t not in '123456789+-*/() ': |
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self.err_msg('Invalid character found: ' + t) |
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return |
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if t.isdigit(): |
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if dgt_op == 'd': |
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d += t |
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dgt_op = 'o' |
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else: |
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self.err_msg('Need operator between digits') |
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return |
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if t in '+-*/': |
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if dgt_op == 'o': |
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dgt_op = 'd' |
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else: |
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self.err_msg('Need digit befor operator') |
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return |
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if sorted(d) != sorted(self.digits): |
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self.err_msg("Use each digit in '4 Digits' once") |
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return |
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try: |
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# round covers up Python's |
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# representation of floats |
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if round(eval(txt),5) == 24: |
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messagebox.showinfo( |
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'Success', |
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'YOUR SOLUTION IS VADLID!') |
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self.show_soln() # show all solutions |
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return |
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except: |
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self.err_msg('Invalid arithmetic expression') |
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return |
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messagebox.showinfo( |
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'Failure', |
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'Your expression does not yield 24') |
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return |
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# show all solutions: |
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def show_soln(self): |
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# get all sets of 3 operands: ('+', '+', '*'), ...) |
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ops = ['+-*/', '+-*/', '+-*/'] |
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combs = [p for p in itertools.product(*ops)] |
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# get unique permutations for requested 4 digits: |
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d = self.digits |
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perms = set([''.join(p) for p in itertools.permutations(d)]) |
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# list of all (hopefully) expressions for |
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# 4 operands and 3 operations: |
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formats = ['Aop1Bop2Cop3D', |
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'(Aop1Bop2C)op3D', |
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'((Aop1B)op2C)op3D', |
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'(Aop1(Bop2C))op3D', |
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'Aop1Bop2(Cop3D)', |
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'Aop1(Bop2C)op3D', |
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'(Aop1B)op2Cop3D', |
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'(Aop1B)op2(Cop3D)', |
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'Aop1(Bop2Cop3D)', |
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'Aop1((Bop2C)op3D)', |
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'Aop1(Bop2(Cop3D))'] |
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lox = [] # list of valid expressions |
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for fm in formats: # pick a format |
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for c in combs: # plug in 3 ops |
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f = fm.replace('op1', c[0]) |
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f = f.replace('op2', c[1]) |
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f = f.replace('op3', c[2]) |
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for A, B, C, D in perms: # plug in 4 digits |
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x = f.replace('A', A) |
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x = x.replace('B', B) |
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x = x.replace('C', C) |
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x = x.replace('D', D) |
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try: # evaluate expression |
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# round covers up Python's |
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# representation of floats |
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if round(eval(x),5) == 24: |
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lox.append(' ' + x) |
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except ZeroDivisionError: # can ignore these |
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continue |
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if lox: |
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txt = '\n'.join(x for x in lox) |
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else: |
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txt =' No Solution' |
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self.solns_all.config(state='normal') |
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self.solns_all.insert('end', txt) # show solutions |
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self.solns_all.config(state='disabled') |
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self.chk_soln_btn.config(state='disabled') |
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self.show_soln_btn.config(state='disabled') |
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self.soln_ent.config(state='disabled') |
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return |
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def err_msg(self, msg): |
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messagebox.showerror('Error Message', msg) |
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return |
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# restore screen to it's 'initial' state: |
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def clear_screen(self): |
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self.digits = '' |
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self.digit_ent.config(state='normal') |
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self.user_dgt_btn.config(state='normal') |
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self.rdm_dgt_btn.config(state='normal') |
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self.digit_ent.delete(0, 'end') |
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self.chk_soln_btn.config(state='disabled') |
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self.show_soln_btn.config(state='disabled') |
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self.soln_ent.config(state='normal') |
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self.soln_ent.delete(0, 'end') |
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self.soln_ent.config(state='disabled') |
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self.msg.config(text=self.msga) |
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self.clear_solns_all() |
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return |
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# clear the 'Solutions' frame. |
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# note: state must be 'normal' to change data |
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def clear_solns_all(self): |
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self.solns_all.config(state='normal') |
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self.solns_all.delete(1.0, 'end') |
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self.solns_all.config(state='disabled') |
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return |
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def close_window(self): |
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self.window.destroy() |
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# ************************************************ |
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root = Tk() |
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root.title('24 Game') |
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root.geometry('600x600+100+50') |
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root.resizable(False, False) |
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g = Game(root) |
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root.mainloop() |
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</lang> |
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=={{header|R}}== |
=={{header|R}}== |
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Revision as of 01:08, 27 December 2020
You are encouraged to solve this task according to the task description, using any language you may know.
- task
Write a program that takes four digits, either from user input or by random generation, and computes arithmetic expressions following the rules of the 24 game.
Show examples of solutions generated by the program.
- Related task
AArch64 Assembly
<lang AArch64 Assembly> /* ARM assembly AARCH64 Raspberry PI 3B */ /* program game24Solvex64.s */
/*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "../includeConstantesARM64.inc"
.equ NBDIGITS, 4 // digits number .equ TOTAL, 24 .equ BUFFERSIZE, 80
/*********************************/ /* Initialized data */ /*********************************/ .data szMessRules: .ascii "24 Game\n"
.ascii "The program will display four randomly-generated \n"
.asciz "single-digit numbers and search a solution for a total to 24\n\n"
szMessDigits: .asciz "The four digits are @ @ @ @ and the score is 24. \n" szMessOK: .asciz "Solution : \n" szMessNotOK: .asciz "No solution for this problem !! \n" szMessNewGame: .asciz "New game (y/n) ? \n" szMessErrOper: .asciz "Error opérator in display result !!!" szCarriageReturn: .asciz "\n" .align 4 qGraine: .quad 123456 /*********************************/ /* UnInitialized data */ /*********************************/ .bss .align 4 sZoneConv: .skip 24 sBuffer: .skip BUFFERSIZE qTabDigit: .skip 8 * NBDIGITS // digits table qTabOperand1: .skip 8 * NBDIGITS // operand 1 table qTabOperand2: .skip 8 * NBDIGITS // operand 2 table qTabOperation: .skip 8 * NBDIGITS // operator table /*********************************/ /* code section */ /*********************************/ .text .global main main: // entry of program
ldr x0,qAdrszMessRules // display rules bl affichageMess
1:
mov x3,#0 ldr x12,qAdrqTabDigit ldr x5,qAdrszMessDigits
2: // loop generate random digits
mov x0,#8 bl genereraleas add x0,x0,#1 str x0,[x12,x3,lsl 3] // store in table ldr x1,qAdrsZoneConv bl conversion10 // call decimal conversion mov x0,x5 ldr x1,qAdrsZoneConv // insert conversion in message bl strInsertAtCharInc mov x5,x0 add x3,x3,#1 cmp x3,#NBDIGITS // end ? blt 2b // no -> loop mov x0,x5 bl affichageMess mov x0,#0 // start leval mov x1,x12 // address digits table bl searchSoluce cmp x0,#-1 // solution ? bne 3f // no ldr x0,qAdrszMessOK bl affichageMess bl writeSoluce // yes -> write solution in buffer ldr x0,qAdrsBuffer // and display buffer bl affichageMess b 10f
3: // display message no solution
ldr x0,qAdrszMessNotOK bl affichageMess
10: // display new game ?
ldr x0,qAdrszCarriageReturn bl affichageMess ldr x0,qAdrszMessNewGame bl affichageMess bl saisie cmp x0,#'y' beq 1b cmp x0,#'Y' beq 1b
100: // standard end of the program
mov x0,0 // return code mov x8,EXIT // request to exit program svc 0 // perform the system call
qAdrszCarriageReturn: .quad szCarriageReturn qAdrszMessRules: .quad szMessRules qAdrszMessDigits: .quad szMessDigits qAdrszMessNotOK: .quad szMessNotOK qAdrszMessOK: .quad szMessOK qAdrszMessNewGame: .quad szMessNewGame qAdrsZoneConv: .quad sZoneConv qAdrqTabDigit: .quad qTabDigit /******************************************************************/ /* recherche solution */ /******************************************************************/ /* x0 level */ /* x1 table value address */ /* x0 return -1 if ok */ searchSoluce:
stp x1,lr,[sp,-16]! // save registres stp x2,x3,[sp,-16]! // save registres stp x4,x5,[sp,-16]! // save registres stp x6,x7,[sp,-16]! // save registres stp x8,x9,[sp,-16]! // save registres stp x10,x11,[sp,-16]! // save registres stp x12,fp,[sp,-16]! // save registres sub sp,sp,#8* NBDIGITS // reserve size new digits table mov fp,sp // frame pointer = address stack mov x10,x1 // save table add x9,x0,#1 // new level mov x13,#NBDIGITS sub x3,x13,x9 // last element digits table ldr x4,[x1,x3,lsl 3] // load last element cmp x4,#TOTAL // equal to total to search ? bne 0f // no cmp x9,#NBDIGITS // all digits are used ? bne 0f // no mov x0,#-1 // yes -> it is ok -> end b 100f
0:
mov x5,#0 // indice loop 1
1: // begin loop 1
cmp x5,x3 bge 9f ldr x4,[x10,x5,lsl 3] // load first operand ldr x8,qAdrqTabOperand1 str x4,[x8,x9,lsl 3] // and store in operand1 table add x6,x5,#1 // indice loop 2
2: // begin loop 2
cmp x6,x3 bgt 8f ldr x12,[x10,x6,lsl 3] // load second operand ldr x8,qAdrqTabOperand2 str x12,[x8,x9,lsl 3] // and store in operand2 table mov x7,#0 // k mov x8,#0 // n
3:
cmp x7,x5 beq 4f cmp x7,x6 beq 4f ldr x0,[x10,x7,lsl 3] // copy other digits in new table on stack str x0,[fp,x8,lsl 3] add x8,x8,#1
4:
add x7,x7,#1 cmp x7,x3 ble 3b
add x7,x4,x12 // addition test
str x7,[fp,x8,lsl 3] // store result of addition
mov x7,#'+'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3] // store operator
mov x0,x9 // pass new level
mov x1,fp // pass new table address on stack
bl searchSoluce
cmp x0,#0
blt 100f
// soustraction test
sub x13,x4,x12
sub x14,x12,x4
cmp x4,x12
csel x7,x13,x14,gt
str x7,[fp,x8,lsl 3]
mov x7,#'-'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
cmp x0,#0
blt 100f
mul x7,x4,x12 // multiplication test
str x7,[fp,x8,lsl 3]
mov x7,#'*'
ldr x0,qAdrqTabOperation
str x7,[x0,x9,lsl 3]
mov x0,x9
mov x1,fp
bl searchSoluce
cmp x0,#0
blt 100f
5: // division test
udiv x13,x4,x12 msub x14,x13,x12,x4 cmp x14,#0 bne 6f str x13,[fp,x8,lsl 3] mov x7,#'/' ldr x0,qAdrqTabOperation str x7,[x0,x9,lsl 3] mov x0,x9 mov x1,fp bl searchSoluce b 7f
6:
udiv x13,x12,x4 msub x14,x13,x4,x12 cmp x14,#0 bne 7f str x13,[fp,x8,lsl 3] mov x7,#'/' ldr x0,qAdrqTabOperation str x7,[x0,x9,lsl 3] mov x0,x9 mov x1,fp bl searchSoluce
7:
cmp x0,#0 blt 100f add x6,x6,#1 // increment indice loop 2 b 2b
8:
add x5,x5,#1 // increment indice loop 1 b 1b
9:
100:
add sp,sp,8* NBDIGITS // stack alignement ldp x12,fp,[sp],16 // restaur des 2 registres ldp x10,x11,[sp],16 // restaur des 2 registres ldp x8,x9,[sp],16 // restaur des 2 registres ldp x6,x7,[sp],16 // restaur des 2 registres ldp x4,x5,[sp],16 // restaur des 2 registres ldp x2,x3,[sp],16 // restaur des 2 registres ldp x1,lr,[sp],16 // restaur des 2 registres ret
qAdrqTabOperand1: .quad qTabOperand1 qAdrqTabOperand2: .quad qTabOperand2 qAdrqTabOperation: .quad qTabOperation /******************************************************************/ /* write solution */ /******************************************************************/ writeSoluce:
stp x1,lr,[sp,-16]! // save registres stp x2,x3,[sp,-16]! // save registres stp x4,x5,[sp,-16]! // save registres stp x6,x7,[sp,-16]! // save registres stp x8,x9,[sp,-16]! // save registres stp x10,x11,[sp,-16]! // save registres stp x12,fp,[sp,-16]! // save registres ldr x6,qAdrqTabOperand1 ldr x7,qAdrqTabOperand2 ldr x8,qAdrqTabOperation ldr x10,qAdrsBuffer mov x4,#0 // buffer indice mov x9,#1
1:
ldr x13,[x6,x9,lsl 3] // operand 1 ldr x11,[x7,x9,lsl 3] // operand 2 ldr x12,[x8,x9,lsl 3] // operator cmp x12,#'-' beq 2f cmp x12,#'/' beq 2f b 3f
2: // if division or soustraction
cmp x13,x11 // reverse operand if operand 1 is < operand 2 bge 3f mov x2,x13 mov x13,x11 mov x11,x2
3: // conversion operand 1 = x13
mov x1,#10 udiv x2,x13,x1 msub x3,x1,x2,x13 cmp x2,#0 beq 31f add x2,x2,#0x30 strb w2,[x10,x4] add x4,x4,#1
31:
add x3,x3,#0x30 strb w3,[x10,x4] add x4,x4,#1 ldr x2,[x7,x9,lsl 3]
strb w12,[x10,x4] // operator add x4,x4,#1 mov x1,#10 // conversion operand 2 = x11 udiv x2,x11,x1 msub x3,x2,x1,x11 cmp x2,#0 beq 32f add x2,x2,#0x30 strb w2,[x10,x4] add x4,x4,#1
32:
add x3,x3,#0x30 strb w3,[x10,x4] add x4,x4,#1 mov x0,#'=' strb w0,[x10,x4] // compute sous total add x4,x4,#1 cmp x12,'+' // addition bne 33f add x0,x13,x11 b 37f
33:
cmp x12,'-' // soustraction bne 34f sub x0,x13,x11 b 37f
34:
cmp x12,'*' // multiplication bne 35f mul x0,x13,x11 b 37f
35:
cmp x12,'/' // division bne 36f udiv x0,x13,x11 b 37f
36: // error
ldr x0,qAdrszMessErrOper bl affichageMess b 100f
37: // and conversion ascii
mov x1,#10 udiv x2,x0,x1 msub x3,x2,x1,x0 cmp x2,#0 beq 36f add x2,x2,#0x30 strb w2,[x10,x4] add x4,x4,#1
36:
add x3,x3,#0x30 strb w3,[x10,x4] add x4,x4,#1 mov x0,#'\n' strb w0,[x10,x4] add x4,x4,#1 add x9,x9,1 cmp x9,#NBDIGITS blt 1b mov x1,#0 strb w1,[x10,x4] // store 0 final
100:
ldp x12,fp,[sp],16 // restaur des 2 registres ldp x10,x11,[sp],16 // restaur des 2 registres ldp x8,x9,[sp],16 // restaur des 2 registres ldp x6,x7,[sp],16 // restaur des 2 registres ldp x4,x5,[sp],16 // restaur des 2 registres ldp x2,x3,[sp],16 // restaur des 2 registres ldp x1,lr,[sp],16 // restaur des 2 registres ret
qAdrsBuffer: .quad sBuffer qAdrszMessErrOper: .quad szMessErrOper /******************************************************************/ /* string entry */ /******************************************************************/ /* x0 return the first character of human entry */ saisie:
stp x1,lr,[sp,-16]! // save registres stp x2,x8,[sp,-16]! // save registres mov x0,#STDIN // Linux input console ldr x1,qAdrsBuffer // buffer address mov x2,#BUFFERSIZE // buffer size mov x8,#READ // request to read datas svc 0 // call system ldr x1,qAdrsBuffer // buffer address ldrb w0,[x1] // load first character
100:
ldp x2,x8,[sp],16 // restaur des 2 registres ldp x1,lr,[sp],16 // restaur des 2 registres ret
/***************************************************/ /* Generation random number */ /***************************************************/ /* x0 contains limit */ genereraleas:
stp x1,lr,[sp,-16]! // save registres stp x2,x3,[sp,-16]! // save registres stp x4,x5,[sp,-16]! // save registres ldr x4,qAdrqGraine ldr x2,[x4] ldr x3,qNbDep1 mul x2,x3,x2 ldr x3,qNbDep2 add x2,x2,x3 str x2,[x4] // maj de la graine pour l appel suivant cmp x0,#0 beq 100f add x1,x0,#1 // divisor mov x0,x2 // dividende udiv x3,x2,x1 msub x0,x3,x1,x0 // résult = remainder
100: // end function
ldp x4,x5,[sp],16 // restaur des 2 registres ldp x2,x3,[sp],16 // restaur des 2 registres ldp x1,lr,[sp],16 // restaur des 2 registres ret
/*****************************************************/ qAdrqGraine: .quad qGraine qNbDep1: .quad 0x0019660d qNbDep2: .quad 0x3c6ef35f /********************************************************/ /* File Include fonctions */ /********************************************************/ /* for this file see task include a file in language AArch64 assembly */ .include "../includeARM64.inc" </lang>
- Output:
The four digits are 6 8 3 1 and the score is 24. Solution : 6*8=48 3-1=2 48/2=24 New game (y/n) ? y The four digits are 8 6 6 5 and the score is 24. Solution : 8-5=3 6*3=18 6+18=24 New game (y/n) ?
ABAP
Will generate all possible solutions of any given four numbers according to the rules of the 24 game.
Note: the permute function was locally from here <lang ABAP>data: lv_flag type c,
lv_number type i,
lt_numbers type table of i.
constants: c_no_val type i value 9999.
append 1 to lt_numbers. append 1 to lt_numbers. append 2 to lt_numbers. append 7 to lt_numbers.
write 'Evaluating 24 with the following input: '. loop at lt_numbers into lv_number.
write lv_number.
endloop. perform solve_24 using lt_numbers.
form eval_formula using iv_eval type string changing ev_out type i.
call function 'EVAL_FORMULA' "analysis of a syntactically correct formula
exporting
formula = iv_eval
importing
value = ev_out
exceptions
others = 1.
if sy-subrc <> 0. ev_out = -1. endif.
endform.
" Solve a 24 puzzle. form solve_24 using it_numbers like lt_numbers.
data: lv_flag type c,
lv_op1 type c,
lv_op2 type c,
lv_op3 type c,
lv_var1 type c,
lv_var2 type c,
lv_var3 type c,
lv_var4 type c,
lv_eval type string,
lv_result type i,
lv_var type i.
define retrieve_var. read table it_numbers index &1 into lv_var. &2 = lv_var. end-of-definition.
define retrieve_val.
perform eval_formula using lv_eval changing lv_result.
if lv_result = 24.
write / lv_eval.
endif.
end-of-definition.
" Loop through all the possible number permutations.
do.
" Init. the operations table.
retrieve_var: 1 lv_var1, 2 lv_var2, 3 lv_var3, 4 lv_var4.
do 4 times.
case sy-index.
when 1.
lv_op1 = '+'.
when 2.
lv_op1 = '*'.
when 3.
lv_op1 = '-'.
when 4.
lv_op1 = '/'.
endcase.
do 4 times.
case sy-index.
when 1.
lv_op2 = '+'.
when 2.
lv_op2 = '*'.
when 3.
lv_op2 = '-'.
when 4.
lv_op2 = '/'.
endcase.
do 4 times.
case sy-index.
when 1.
lv_op3 = '+'.
when 2.
lv_op3 = '*'.
when 3.
lv_op3 = '-'.
when 4.
lv_op3 = '/'.
endcase.
concatenate '(' '(' lv_var1 lv_op1 lv_var2 ')' lv_op2 lv_var3 ')' lv_op3 lv_var4 into lv_eval separated by space.
retrieve_val.
concatenate '(' lv_var1 lv_op1 lv_var2 ')' lv_op2 '(' lv_var3 lv_op3 lv_var4 ')' into lv_eval separated by space.
retrieve_val.
concatenate '(' lv_var1 lv_op1 '(' lv_var2 lv_op2 lv_var3 ')' ')' lv_op3 lv_var4 into lv_eval separated by space.
retrieve_val.
concatenate lv_var1 lv_op1 '(' '(' lv_var2 lv_op2 lv_var3 ')' lv_op3 lv_var4 ')' into lv_eval separated by space.
retrieve_val.
concatenate lv_var1 lv_op1 '(' lv_var2 lv_op2 '(' lv_var3 lv_op3 lv_var4 ')' ')' into lv_eval separated by space.
retrieve_val.
enddo.
enddo.
enddo.
" Once we've reached the last permutation -> Exit.
perform permute using it_numbers changing lv_flag.
if lv_flag = 'X'.
exit.
endif.
enddo.
endform.
" Permutation function - this is used to permute:
" A = {A1...AN} -> Set of supplied variables.
" B = {B1...BN - 1} -> Set of operators.
" Can be used for an unbounded size set. Relies
" on lexicographic ordering of the set.
form permute using iv_set like lt_numbers
changing ev_last type c.
data: lv_len type i,
lv_first type i,
lv_third type i,
lv_count type i,
lv_temp type i,
lv_temp_2 type i,
lv_second type i,
lv_changed type c,
lv_perm type i.
describe table iv_set lines lv_len.
lv_perm = lv_len - 1.
lv_changed = ' '.
" Loop backwards through the table, attempting to find elements which
" can be permuted. If we find one, break out of the table and set the
" flag indicating a switch.
do.
if lv_perm <= 0.
exit.
endif.
" Read the elements.
read table iv_set index lv_perm into lv_first.
add 1 to lv_perm.
read table iv_set index lv_perm into lv_second.
subtract 1 from lv_perm.
if lv_first < lv_second.
lv_changed = 'X'.
exit.
endif.
subtract 1 from lv_perm.
enddo.
" Last permutation. if lv_changed <> 'X'. ev_last = 'X'. exit. endif.
" Swap tail decresing to get a tail increasing.
lv_count = lv_perm + 1.
do.
lv_first = lv_len + lv_perm - lv_count + 1.
if lv_count >= lv_first.
exit.
endif.
read table iv_set index lv_count into lv_temp. read table iv_set index lv_first into lv_temp_2. modify iv_set index lv_count from lv_temp_2. modify iv_set index lv_first from lv_temp. add 1 to lv_count. enddo.
lv_count = lv_len - 1.
do.
if lv_count <= lv_perm.
exit.
endif.
read table iv_set index lv_count into lv_first.
read table iv_set index lv_perm into lv_second.
read table iv_set index lv_len into lv_third.
if ( lv_first < lv_third ) and ( lv_first > lv_second ).
lv_len = lv_count.
endif.
subtract 1 from lv_count. enddo.
read table iv_set index lv_perm into lv_temp. read table iv_set index lv_len into lv_temp_2. modify iv_set index lv_perm from lv_temp_2. modify iv_set index lv_len from lv_temp.
endform.</lang>
Sample Runs:
Evaluating 24 with the following input: 1 1 2 7 ( 1 + 2 ) * ( 1 + 7 ) ( 1 + 2 ) * ( 7 + 1 ) ( 1 + 7 ) * ( 1 + 2 ) ( 1 + 7 ) * ( 2 + 1 ) ( 2 + 1 ) * ( 1 + 7 ) ( 2 + 1 ) * ( 7 + 1 ) ( 7 + 1 ) * ( 1 + 2 ) ( 7 + 1 ) * ( 2 + 1 ) Evaluating 24 with the following input: 1 ( ( 1 + 2 ) + 3 ) * 4 ( 1 + ( 2 + 3 ) ) * 4 ( ( 1 * 2 ) * 3 ) * 4 ( 1 * 2 ) * ( 3 * 4 ) ( 1 * ( 2 * 3 ) ) * 4 1 * ( ( 2 * 3 ) * 4 ) 1 * ( 2 * ( 3 * 4 ) ) ( ( 1 * 2 ) * 4 ) * 3 ( 1 * 2 ) * ( 4 * 3 ) ( 1 * ( 2 * 4 ) ) * 3 1 * ( ( 2 * 4 ) * 3 ) 1 * ( 2 * ( 4 * 3 ) ) ( ( 1 + 3 ) + 2 ) * 4 ( 1 + ( 3 + 2 ) ) * 4 ( 1 + 3 ) * ( 2 + 4 ) ( ( 1 * 3 ) * 2 ) * 4 ( 1 * 3 ) * ( 2 * 4 ) ( 1 * ( 3 * 2 ) ) * 4 1 * ( ( 3 * 2 ) * 4 ) 1 * ( 3 * ( 2 * 4 ) ) ( 1 + 3 ) * ( 4 + 2 ) ( ( 1 * 3 ) * 4 ) * 2 ( 1 * 3 ) * ( 4 * 2 ) ( 1 * ( 3 * 4 ) ) * 2 1 * ( ( 3 * 4 ) * 2 ) 1 * ( 3 * ( 4 * 2 ) ) ( ( 1 * 4 ) * 2 ) * 3 ( 1 * 4 ) * ( 2 * 3 ) ( 1 * ( 4 * 2 ) ) * 3 1 * ( ( 4 * 2 ) * 3 ) 1 * ( 4 * ( 2 * 3 ) ) ( ( 1 * 4 ) * 3 ) * 2 ( 1 * 4 ) * ( 3 * 2 ) ( 1 * ( 4 * 3 ) ) * 2 1 * ( ( 4 * 3 ) * 2 ) 1 * ( 4 * ( 3 * 2 ) ) ( ( 2 + 1 ) + 3 ) * 4 ( 2 + ( 1 + 3 ) ) * 4 ( ( 2 * 1 ) * 3 ) * 4 ( 2 * 1 ) * ( 3 * 4 ) ( 2 * ( 1 * 3 ) ) * 4 2 * ( ( 1 * 3 ) * 4 ) 2 * ( 1 * ( 3 * 4 ) ) ( ( 2 / 1 ) * 3 ) * 4 ( 2 / 1 ) * ( 3 * 4 ) ( 2 / ( 1 / 3 ) ) * 4 2 / ( 1 / ( 3 * 4 ) ) 2 / ( ( 1 / 3 ) / 4 ) ( ( 2 * 1 ) * 4 ) * 3 ( 2 * 1 ) * ( 4 * 3 ) ( 2 * ( 1 * 4 ) ) * 3 2 * ( ( 1 * 4 ) * 3 ) 2 * ( 1 * ( 4 * 3 ) ) ( ( 2 / 1 ) * 4 ) * 3 ( 2 / 1 ) * ( 4 * 3 ) ( 2 / ( 1 / 4 ) ) * 3 2 / ( 1 / ( 4 * 3 ) ) 2 / ( ( 1 / 4 ) / 3 ) ( ( 2 + 3 ) + 1 ) * 4 ( 2 + ( 3 + 1 ) ) * 4 ( ( 2 * 3 ) * 1 ) * 4 ( 2 * 3 ) * ( 1 * 4 ) ( 2 * ( 3 * 1 ) ) * 4 2 * ( ( 3 * 1 ) * 4 ) 2 * ( 3 * ( 1 * 4 ) ) ( ( 2 * 3 ) / 1 ) * 4 ( 2 * ( 3 / 1 ) ) * 4 2 * ( ( 3 / 1 ) * 4 ) ( 2 * 3 ) / ( 1 / 4 ) 2 * ( 3 / ( 1 / 4 ) ) ( ( 2 * 3 ) * 4 ) * 1 ( 2 * 3 ) * ( 4 * 1 ) ( 2 * ( 3 * 4 ) ) * 1 2 * ( ( 3 * 4 ) * 1 ) 2 * ( 3 * ( 4 * 1 ) ) ( ( 2 * 3 ) * 4 ) / 1 ( 2 * 3 ) * ( 4 / 1 ) ( 2 * ( 3 * 4 ) ) / 1 2 * ( ( 3 * 4 ) / 1 ) 2 * ( 3 * ( 4 / 1 ) ) ( 2 + 4 ) * ( 1 + 3 ) ( ( 2 * 4 ) * 1 ) * 3 ( 2 * 4 ) * ( 1 * 3 ) ( 2 * ( 4 * 1 ) ) * 3 2 * ( ( 4 * 1 ) * 3 ) 2 * ( 4 * ( 1 * 3 ) ) ( ( 2 * 4 ) / 1 ) * 3 ( 2 * ( 4 / 1 ) ) * 3 2 * ( ( 4 / 1 ) * 3 ) ( 2 * 4 ) / ( 1 / 3 ) 2 * ( 4 / ( 1 / 3 ) ) ( 2 + 4 ) * ( 3 + 1 ) ( ( 2 * 4 ) * 3 ) * 1 ( 2 * 4 ) * ( 3 * 1 ) ( 2 * ( 4 * 3 ) ) * 1 2 * ( ( 4 * 3 ) * 1 ) 2 * ( 4 * ( 3 * 1 ) ) ( ( 2 * 4 ) * 3 ) / 1 ( 2 * 4 ) * ( 3 / 1 ) ( 2 * ( 4 * 3 ) ) / 1 2 * ( ( 4 * 3 ) / 1 ) 2 * ( 4 * ( 3 / 1 ) ) ( ( 3 + 1 ) + 2 ) * 4 ( 3 + ( 1 + 2 ) ) * 4 ( 3 + 1 ) * ( 2 + 4 ) ( ( 3 * 1 ) * 2 ) * 4 ( 3 * 1 ) * ( 2 * 4 ) ( 3 * ( 1 * 2 ) ) * 4 3 * ( ( 1 * 2 ) * 4 ) 3 * ( 1 * ( 2 * 4 ) ) ( ( 3 / 1 ) * 2 ) * 4 ( 3 / 1 ) * ( 2 * 4 ) ( 3 / ( 1 / 2 ) ) * 4 3 / ( 1 / ( 2 * 4 ) ) 3 / ( ( 1 / 2 ) / 4 ) ( 3 + 1 ) * ( 4 + 2 ) ( ( 3 * 1 ) * 4 ) * 2 ( 3 * 1 ) * ( 4 * 2 ) ( 3 * ( 1 * 4 ) ) * 2 3 * ( ( 1 * 4 ) * 2 ) 3 * ( 1 * ( 4 * 2 ) ) ( ( 3 / 1 ) * 4 ) * 2 ( 3 / 1 ) * ( 4 * 2 ) ( 3 / ( 1 / 4 ) ) * 2 3 / ( 1 / ( 4 * 2 ) ) 3 / ( ( 1 / 4 ) / 2 ) ( ( 3 + 2 ) + 1 ) * 4 ( 3 + ( 2 + 1 ) ) * 4 ( ( 3 * 2 ) * 1 ) * 4 ( 3 * 2 ) * ( 1 * 4 ) ( 3 * ( 2 * 1 ) ) * 4 3 * ( ( 2 * 1 ) * 4 ) 3 * ( 2 * ( 1 * 4 ) ) ( ( 3 * 2 ) / 1 ) * 4 ( 3 * ( 2 / 1 ) ) * 4 3 * ( ( 2 / 1 ) * 4 ) ( 3 * 2 ) / ( 1 / 4 ) 3 * ( 2 / ( 1 / 4 ) ) ( ( 3 * 2 ) * 4 ) * 1 ( 3 * 2 ) * ( 4 * 1 ) ( 3 * ( 2 * 4 ) ) * 1 3 * ( ( 2 * 4 ) * 1 ) 3 * ( 2 * ( 4 * 1 ) ) ( ( 3 * 2 ) * 4 ) / 1 ( 3 * 2 ) * ( 4 / 1 ) ( 3 * ( 2 * 4 ) ) / 1 3 * ( ( 2 * 4 ) / 1 ) 3 * ( 2 * ( 4 / 1 ) ) ( ( 3 * 4 ) * 1 ) * 2 ( 3 * 4 ) * ( 1 * 2 ) ( 3 * ( 4 * 1 ) ) * 2 3 * ( ( 4 * 1 ) * 2 ) 3 * ( 4 * ( 1 * 2 ) ) ( ( 3 * 4 ) / 1 ) * 2 ( 3 * ( 4 / 1 ) ) * 2 3 * ( ( 4 / 1 ) * 2 ) ( 3 * 4 ) / ( 1 / 2 ) 3 * ( 4 / ( 1 / 2 ) ) ( ( 3 * 4 ) * 2 ) * 1 ( 3 * 4 ) * ( 2 * 1 ) ( 3 * ( 4 * 2 ) ) * 1 3 * ( ( 4 * 2 ) * 1 ) 3 * ( 4 * ( 2 * 1 ) ) ( ( 3 * 4 ) * 2 ) / 1 ( 3 * 4 ) * ( 2 / 1 ) ( 3 * ( 4 * 2 ) ) / 1 3 * ( ( 4 * 2 ) / 1 ) 3 * ( 4 * ( 2 / 1 ) ) 4 * ( ( 1 + 2 ) + 3 ) 4 * ( 1 + ( 2 + 3 ) ) ( ( 4 * 1 ) * 2 ) * 3 ( 4 * 1 ) * ( 2 * 3 ) ( 4 * ( 1 * 2 ) ) * 3 4 * ( ( 1 * 2 ) * 3 ) 4 * ( 1 * ( 2 * 3 ) ) ( ( 4 / 1 ) * 2 ) * 3 ( 4 / 1 ) * ( 2 * 3 ) ( 4 / ( 1 / 2 ) ) * 3 4 / ( 1 / ( 2 * 3 ) ) 4 / ( ( 1 / 2 ) / 3 ) 4 * ( ( 1 + 3 ) + 2 ) 4 * ( 1 + ( 3 + 2 ) ) ( ( 4 * 1 ) * 3 ) * 2 ( 4 * 1 ) * ( 3 * 2 ) ( 4 * ( 1 * 3 ) ) * 2 4 * ( ( 1 * 3 ) * 2 ) 4 * ( 1 * ( 3 * 2 ) ) ( ( 4 / 1 ) * 3 ) * 2 ( 4 / 1 ) * ( 3 * 2 ) ( 4 / ( 1 / 3 ) ) * 2 4 / ( 1 / ( 3 * 2 ) ) 4 / ( ( 1 / 3 ) / 2 ) ( 4 + 2 ) * ( 1 + 3 ) 4 * ( ( 2 + 1 ) + 3 ) 4 * ( 2 + ( 1 + 3 ) ) ( ( 4 * 2 ) * 1 ) * 3 ( 4 * 2 ) * ( 1 * 3 ) ( 4 * ( 2 * 1 ) ) * 3 4 * ( ( 2 * 1 ) * 3 ) 4 * ( 2 * ( 1 * 3 ) ) ( ( 4 * 2 ) / 1 ) * 3 ( 4 * ( 2 / 1 ) ) * 3 4 * ( ( 2 / 1 ) * 3 ) ( 4 * 2 ) / ( 1 / 3 ) 4 * ( 2 / ( 1 / 3 ) ) ( 4 + 2 ) * ( 3 + 1 ) 4 * ( ( 2 + 3 ) + 1 ) 4 * ( 2 + ( 3 + 1 ) ) ( ( 4 * 2 ) * 3 ) * 1 ( 4 * 2 ) * ( 3 * 1 ) ( 4 * ( 2 * 3 ) ) * 1 4 * ( ( 2 * 3 ) * 1 ) 4 * ( 2 * ( 3 * 1 ) ) ( ( 4 * 2 ) * 3 ) / 1 ( 4 * 2 ) * ( 3 / 1 ) ( 4 * ( 2 * 3 ) ) / 1 4 * ( ( 2 * 3 ) / 1 ) 4 * ( 2 * ( 3 / 1 ) ) 4 * ( ( 3 + 1 ) + 2 ) 4 * ( 3 + ( 1 + 2 ) ) ( ( 4 * 3 ) * 1 ) * 2 ( 4 * 3 ) * ( 1 * 2 ) ( 4 * ( 3 * 1 ) ) * 2 4 * ( ( 3 * 1 ) * 2 ) 4 * ( 3 * ( 1 * 2 ) ) ( ( 4 * 3 ) / 1 ) * 2 ( 4 * ( 3 / 1 ) ) * 2 4 * ( ( 3 / 1 ) * 2 ) ( 4 * 3 ) / ( 1 / 2 ) 4 * ( 3 / ( 1 / 2 ) ) 4 * ( ( 3 + 2 ) + 1 ) 4 * ( 3 + ( 2 + 1 ) ) ( ( 4 * 3 ) * 2 ) * 1 ( 4 * 3 ) * ( 2 * 1 ) ( 4 * ( 3 * 2 ) ) * 1 4 * ( ( 3 * 2 ) * 1 ) 4 * ( 3 * ( 2 * 1 ) ) ( ( 4 * 3 ) * 2 ) / 1 ( 4 * 3 ) * ( 2 / 1 ) ( 4 * ( 3 * 2 ) ) / 1 4 * ( ( 3 * 2 ) / 1 ) 4 * ( 3 * ( 2 / 1 ) ) Evaluating 24 with the following input: 5 6 7 8 5 * ( 6 - ( 8 / 7 ) ) ( 5 + 7 ) * ( 8 - 6 ) ( ( 5 + 7 ) - 8 ) * 6 ( 5 + ( 7 - 8 ) ) * 6 ( ( 5 - 8 ) + 7 ) * 6 ( 5 - ( 8 - 7 ) ) * 6 6 * ( ( 5 + 7 ) - 8 ) 6 * ( 5 + ( 7 - 8 ) ) 6 * ( ( 5 - 8 ) + 7 ) 6 * ( 5 - ( 8 - 7 ) ) 6 * ( ( 7 + 5 ) - 8 ) 6 * ( 7 + ( 5 - 8 ) ) ( 6 / ( 7 - 5 ) ) * 8 6 / ( ( 7 - 5 ) / 8 ) 6 * ( ( 7 - 8 ) + 5 ) 6 * ( 7 - ( 8 - 5 ) ) ( 6 * 8 ) / ( 7 - 5 ) 6 * ( 8 / ( 7 - 5 ) ) ( 6 - ( 8 / 7 ) ) * 5 ( 7 + 5 ) * ( 8 - 6 ) ( ( 7 + 5 ) - 8 ) * 6 ( 7 + ( 5 - 8 ) ) * 6 ( ( 7 - 8 ) + 5 ) * 6 ( 7 - ( 8 - 5 ) ) * 6 ( 8 - 6 ) * ( 5 + 7 ) ( 8 * 6 ) / ( 7 - 5 ) 8 * ( 6 / ( 7 - 5 ) ) ( 8 - 6 ) * ( 7 + 5 ) ( 8 / ( 7 - 5 ) ) * 6 8 / ( ( 7 - 5 ) / 6 )
Argile
<lang Argile>die "Please give 4 digits as argument 1\n" if argc < 2
print a function that given four digits argv[1] subject to the rules of \ the _24_ game, computes an expression to solve the game if possible.
use std, array
let digits be an array of 4 byte let operators be an array of 4 byte (: reordered arrays :) let (type of digits) rdigits let (type of operators) roperators
.: a function that given four digits <text digits> subject to
the rules of the _24_ game, computes an expression to solve
the game if possible. :. -> text
if #digits != 4 {return "[error: need exactly 4 digits]"}
operators[0] = '+' ; operators[1] = '-'
operators[2] = '*' ; operators[3] = '/'
for each (val int d) from 0 to 3
if (digits[d] < '1') || (digits[d] > '9')
return "[error: non-digit character given]"
(super digits)[d] = digits[d]
let expr = for each operand order stuff
return "" if expr is nil
expr
.:for each operand order stuff:. -> text
for each (val int a) from 0 to 3
for each (val int b) from 0 to 3
next if (b == a)
for each (val int c) from 0 to 3
next if (c == b) or (c == a)
for each (val int d) from 0 to 3 next if (d == c) or (d == b) or (d == a) rdigits[0] = digits[a] ; rdigits[1] = digits[b] rdigits[2] = digits[c] ; rdigits[3] = digits[d] let found = for each operator order stuff return found unless found is nil
nil
.:for each operator order stuff:. -> text
for each (val int i) from 0 to 3
for each (val int j) from 0 to 3
for each (val int k) from 0 to 3
roperators[0] = operators[i]
roperators[1] = operators[j] roperators[2] = operators[k] let found = for each RPN pattern stuff return found if found isn't nil
nil
our (raw array of text) RPN_patterns = Cdata
"xx.x.x." "xx.xx.." "xxx..x." "xxx.x.." "xxxx..."
our (raw array of text) formats = Cdata
"((%c%c%c)%c%c)%c%c" "(%c%c%c)%c(%c%c%c)" "(%c%c(%c%c%c))%c%c" "%c%c((%c%c%c)%c%c)" "%c%c(%c%c(%c%c%c))"
our (raw array of array of 3 int) rrop = Cdata
{0;1;2}; {0;2;1}; {1;0;2}; {2;0;1}; {2;1;0}
.:for each RPN pattern stuff:. -> text
let RPN_stack be an array of 4 real
for each (val int rpn) from 0 to 4
let (nat) sp=0, op=0, dg=0.
let text p
for (p = RPN_patterns[rpn]) (*p != 0) (p++)
if *p == 'x'
if sp >= 4 {die "RPN stack overflow\n"}
if dg > 3 {die "RPN digits overflow\n"} RPN_stack[sp++] = (rdigits[dg++] - '0') as real
if *p == '.'
if sp < 2 {die "RPN stack underflow\n"}
if op > 2 {die "RPN operators overflow\n"} sp -= 2 let x = RPN_stack[sp] let y = RPN_stack[sp + 1] switch roperators[op++] case '+' {x += y} case '-' {x -= y} case '*' {x *= y} case '/' {x /= y} default {die "RPN operator unknown\n"} RPN_stack[sp++] = x
if RPN_stack[0] == 24.0
our array of 12 byte buffer (: 4 paren + 3 ops + 4 digits + null :)
snprintf (buffer as text) (size of buffer) (formats[rpn]) \
(rdigits[0]) (roperators[(rrop[rpn][0])]) (rdigits[1]) \
(roperators[(rrop[rpn][1])]) (rdigits[2]) \
(roperators[(rrop[rpn][2])]) (rdigits[3]);
return buffer as text
nil</lang>
Examples:
$ arc 24_game_solve.arg -o 24_game_solve.c $ gcc -Wall 24_game_solve.c -o 24_game_solve $ ./24_game_solve 1234 ((1+2)+3)*4 $ ./24_game_solve 9999 $ ./24_game_solve 5678 ((5+7)-8)*6 $ ./24_game_solve 1127 (1+2)*(1+7)
ARM Assembly
<lang ARM Assembly> /* ARM assembly Raspberry PI */ /* program game24Solver.s */
/* REMARK 1 : this program use routines in a include file
see task Include a file language arm assembly for the routine affichageMess conversion10 see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */ /************************************/ /* Constantes */ /************************************/ .include "../constantes.inc" .equ STDIN, 0 @ Linux input console .equ READ, 3 @ Linux syscall .equ NBDIGITS, 4 @ digits number .equ TOTAL, 24 .equ BUFFERSIZE, 80
/*********************************/ /* Initialized data */ /*********************************/ .data szMessRules: .ascii "24 Game\n"
.ascii "The program will display four randomly-generated \n"
.asciz "single-digit numbers and search a solution for a total to 24\n\n"
szMessDigits: .asciz "The four digits are @ @ @ @ and the score is 24. \n" szMessOK: .asciz "Solution : \n" szMessNotOK: .asciz "No solution for this problem !! \n" szMessNewGame: .asciz "New game (y/n) ? \n" szCarriageReturn: .asciz "\n" .align 4 iGraine: .int 123456 /*********************************/ /* UnInitialized data */ /*********************************/ .bss .align 4 sZoneConv: .skip 24 sBuffer: .skip BUFFERSIZE iTabDigit: .skip 4 * NBDIGITS @ digits table iTabOperand1: .skip 4 * NBDIGITS @ operand 1 table iTabOperand2: .skip 4 * NBDIGITS @ operand 2 table iTabOperation: .skip 4 * NBDIGITS @ operator table /*********************************/ /* code section */ /*********************************/ .text .global main main: @ entry of program
ldr r0,iAdrszMessRules @ display rules bl affichageMess
1:
mov r3,#0 ldr r12,iAdriTabDigit ldr r5,iAdrszMessDigits
2: @ loop generate random digits
mov r0,#8 bl genereraleas add r0,r0,#1 str r0,[r12,r3,lsl #2] @ store in table ldr r1,iAdrsZoneConv bl conversion10 @ call decimal conversion mov r2,#0 strb r2,[r1,r0] @ reduce size display area with zéro final mov r0,r5 ldr r1,iAdrsZoneConv @ insert conversion in message bl strInsertAtCharInc mov r5,r0 add r3,r3,#1 cmp r3,#NBDIGITS @ end ? blt 2b @ no -> loop mov r0,r5 bl affichageMess mov r0,#0 @ start leval mov r1,r12 @ address digits table bl searchSoluce cmp r0,#-1 @ solution ? bne 3f @ no ldr r0,iAdrszMessOK bl affichageMess bl writeSoluce @ yes -> write solution in buffer ldr r0,iAdrsBuffer @ and display buffer bl affichageMess b 10f
3: @ display message no solution
ldr r0,iAdrszMessNotOK bl affichageMess
10: @ display new game ?
ldr r0,iAdrszCarriageReturn bl affichageMess ldr r0,iAdrszMessNewGame bl affichageMess bl saisie cmp r0,#'y' beq 1b cmp r0,#'Y' beq 1b
100: @ standard end of the program
mov r0, #0 @ return code mov r7, #EXIT @ request to exit program svc #0 @ perform the system call
iAdrszCarriageReturn: .int szCarriageReturn iAdrszMessRules: .int szMessRules iAdrszMessDigits: .int szMessDigits iAdrszMessNotOK: .int szMessNotOK iAdrszMessOK: .int szMessOK iAdrszMessNewGame: .int szMessNewGame iAdrsZoneConv: .int sZoneConv iAdriTabDigit: .int iTabDigit /******************************************************************/ /* recherche solution */ /******************************************************************/ /* r0 level */ /* r1 table value address */ /* r0 return -1 if ok */ searchSoluce:
push {r1-r12,lr} @ save registers
sub sp,#4* NBDIGITS @ reserve size new digits table
mov fp,sp @ frame pointer = address stack
mov r10,r1 @ save table
add r9,r0,#1 @ new level
rsb r3,r9,#NBDIGITS @ last element digits table
ldr r4,[r1,r3,lsl #2] @ load last element
cmp r4,#TOTAL @ equal to total to search ?
bne 0f @ no
cmp r9,#NBDIGITS @ all digits are used ?
bne 0f @ no
mov r0,#-1 @ yes -> it is ok -> end
b 100f
0:
mov r5,#0 @ indice loop 1
1: @ begin loop 1
cmp r5,r3 bge 9f ldr r4,[r10,r5,lsl #2] @ load first operand ldr r8,iAdriTabOperand1 str r4,[r8,r9,lsl #2] @ and store in operand1 table add r6,r5,#1 @ indice loop 2
2: @ begin loop 2
cmp r6,r3 bgt 8f ldr r12,[r10,r6,lsl #2] @ load second operand ldr r8,iAdriTabOperand2 str r12,[r8,r9,lsl #2] @ and store in operand2 table mov r7,#0 @ k mov r8,#0 @ n
3:
cmp r7,r5 beq 4f cmp r7,r6 beq 4f ldr r0,[r10,r7,lsl #2] @ copy other digits in new table on stack str r0,[fp,r8,lsl #2] add r8,r8,#1
4:
add r7,r7,#1 cmp r7,r3 ble 3b
add r7,r4,r12 @ addition test
str r7,[fp,r8,lsl #2] @ store result of addition
mov r7,#'+'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2] @ store operator
mov r0,r9 @ pass new level
mov r1,fp @ pass new table address on stack
bl searchSoluce
cmp r0,#0
blt 100f
@ soustraction test
cmp r4,r12
subgt r7,r4,r12
suble r7,r12,r4
str r7,[fp,r8,lsl #2]
mov r7,#'-'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
cmp r0,#0
blt 100f
mul r7,r4,r12 @ multiplication test
str r7,[fp,r8,lsl #2]
mov r7,#'*'
//vidregtit mult
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
cmp r0,#0
blt 100f
5: @ division test
push {r1-r3}
mov r0,r4
mov r1,r12
bl division
// mov r7,r9
cmp r3,#0
bne 6f
str r2,[fp,r8,lsl #2]
mov r7,#'/'
ldr r0,iAdriTabOperation
str r7,[r0,r9,lsl #2]
mov r0,r9
mov r1,fp
bl searchSoluce
b 7f
6:
mov r0,r12 mov r1,r4 bl division cmp r3,#0 bne 7f str r2,[fp,r8,lsl #2] mov r7,#'/' ldr r0,iAdriTabOperation str r7,[r0,r9,lsl #2] mov r0,r9 mov r1,fp bl searchSoluce
7:
pop {r1-r3}
cmp r0,#0
blt 100f
add r6,r6,#1 @ increment indice loop 2
b 2b
8:
add r5,r5,#1 @ increment indice loop 1 b 1b
9:
100:
add sp,#4* NBDIGITS @ stack alignement
pop {r1-r12,lr}
bx lr @ return
iAdriTabOperand1: .int iTabOperand1 iAdriTabOperand2: .int iTabOperand2 iAdriTabOperation: .int iTabOperation /******************************************************************/ /* write solution */ /******************************************************************/ writeSoluce:
push {r1-r12,lr} @ save registers
ldr r6,iAdriTabOperand1
ldr r7,iAdriTabOperand2
ldr r8,iAdriTabOperation
ldr r10,iAdrsBuffer
mov r4,#0 @ buffer indice
mov r9,#1
1:
ldr r5,[r6,r9,lsl #2] @ operand 1 ldr r11,[r7,r9,lsl #2] @ operand 2 ldr r12,[r8,r9,lsl #2] @ operator cmp r12,#'-' beq 2f cmp r12,#'/' beq 2f b 3f
2: @ if division or soustraction
cmp r5,r11 @ reverse operand if operand 1 is < operand 2 movlt r2,r5 movlt r5,r11 movlt r11,r2
3: @ conversion operand 1 = r0
mov r0,r5 mov r1,#10 bl division cmp r2,#0 addne r2,r2,#0x30 strneb r2,[r10,r4] addne r4,r4,#1 add r3,r3,#0x30 strb r3,[r10,r4] add r4,r4,#1 ldr r2,[r7,r9,lsl #2]
strb r12,[r10,r4] @ operator add r4,r4,#1 mov r0,r11 @ conversion operand 2 mov r1,#10 bl division cmp r2,#0 addne r2,r2,#0x30 strneb r2,[r10,r4] addne r4,r4,#1 add r3,r3,#0x30 strb r3,[r10,r4] add r4,r4,#1 mov r0,#'=' str r0,[r10,r4] @ conversion sous total add r4,r4,#1 cmp r12,#'+' addeq r0,r5,r11 cmp r12,#'-' subeq r0,r5,r11 cmp r12,#'*' muleq r0,r5,r11 cmp r12,#'/' udiveq r0,r5,r11
mov r1,#10 bl division cmp r2,#0 addne r2,r2,#0x30 strneb r2,[r10,r4] addne r4,r4,#1 add r3,r3,#0x30 strb r3,[r10,r4] add r4,r4,#1 mov r0,#'\n' str r0,[r10,r4] add r4,r4,#1 add r9,#1 cmp r9,#NBDIGITS blt 1b mov r1,#0 strb r1,[r10,r4] @ store 0 final
100:
pop {r1-r12,lr}
bx lr @ return
iAdrsBuffer: .int sBuffer
/******************************************************************/ /* string entry */ /******************************************************************/ /* r0 return the first character of human entry */ saisie:
push {r1-r7,lr} @ save registers
mov r0,#STDIN @ Linux input console
ldr r1,iAdrsBuffer @ buffer address
mov r2,#BUFFERSIZE @ buffer size
mov r7,#READ @ request to read datas
svc 0 @ call system
ldr r1,iAdrsBuffer @ buffer address
ldrb r0,[r1] @ load first character
100:
pop {r1-r7,lr}
bx lr @ return
/***************************************************/ /* Generation random number */ /***************************************************/ /* r0 contains limit */ genereraleas:
push {r1-r4,lr} @ save registers
ldr r4,iAdriGraine
ldr r2,[r4]
ldr r3,iNbDep1
mul r2,r3,r2
ldr r3,iNbDep2
add r2,r2,r3
str r2,[r4] @ maj de la graine pour l appel suivant
cmp r0,#0
beq 100f
add r1,r0,#1 @ divisor
mov r0,r2 @ dividende
bl division
mov r0,r3 @ résult = remainder
100: @ end function
pop {r1-r4,lr} @ restaur registers
bx lr @ return
/*****************************************************/ iAdriGraine: .int iGraine iNbDep1: .int 0x343FD iNbDep2: .int 0x269EC3 /***************************************************/ /* ROUTINES INCLUDE */ /***************************************************/ .include "../affichage.inc"
</lang>
- Output:
New game (y/n) ? y The four digits are 8 3 9 1 and the score is 24. Solution : 8*9=72 3*1=3 72/3=24 New game (y/n) ? y The four digits are 7 7 9 4 and the score is 24. No solution for this problem !! New game (y/n) ? y The four digits are 3 5 8 9 and the score is 24. Solution : 3*9=27 8-5=3 27-3=24 New game (y/n) ?
AutoHotkey
Output is in RPN. <lang AHK>#NoEnv InputBox, NNNN ; user input 4 digits NNNN := RegExReplace(NNNN, "(\d)(?=\d)", "$1,") ; separate with commas for the sort command sort NNNN, d`, ; sort in ascending order for the permutations to work StringReplace NNNN, NNNN, `,, , All ; remove comma separators after sorting
ops := "+-*/" patterns := [ "x x.x.x." ,"x x.x x.." ,"x x x..x." ,"x x x.x.." ,"x x x x..." ]
- build bruteforce operator list ("+++, ++-, ++* ... ///")
a := b := c := 0 While (++a<5){
While (++b<5){
While (++c<5){
l := SubStr(ops, a, 1) . SubStr(ops, b, 1) . SubStr(ops, c, 1)
; build bruteforce template ("x x+x+x+, x x+x x++ ... x x x x///")
For each, pattern in patterns
{
Loop 3
StringReplace, pattern, pattern, ., % SubStr(l, A_Index, 1)
pat .= pattern "`n"
}
}c := 0
}b := 0
} StringTrimRight, pat, pat, 1 ; remove trailing newline
- permutate input. As the lexicographic algorithm is used, each permutation generated is unique
While NNNN { StringSplit, N, NNNN ; substitute numbers in for x's and evaluate Loop Parse, pat, `n { eval := A_LoopField ; current line Loop 4 StringReplace, eval, eval, x, % N%A_Index% ; substitute number for "x" If Round(evalRPN(eval), 4) = 24 final .= eval "`n" } NNNN := perm_next(NNNN) ; next lexicographic permutation of user's digits } MsgBox % final ? clipboard := final : "No solution"
- simple stack-based evaluation. Integers only. Whitespace is used to push a value.
evalRPN(s){ stack := [] Loop Parse, s If A_LoopField is number t .= A_LoopField else { If t stack.Insert(t), t := "" If InStr("+-/*", l := A_LoopField) { a := stack.Remove(), b := stack.Remove() stack.Insert( l = "+" ? b + a :l = "-" ? b - a :l = "*" ? b * a :l = "/" ? b / a :0 ) } } return stack.Remove() }
perm_Next(str){ p := 0, sLen := StrLen(str) Loop % sLen { If A_Index=1 continue t := SubStr(str, sLen+1-A_Index, 1) n := SubStr(str, sLen+2-A_Index, 1) If ( t < n ) { p := sLen+1-A_Index, pC := SubStr(str, p, 1) break } } If !p return false Loop { t := SubStr(str, sLen+1-A_Index, 1) If ( t > pC ) { n := sLen+1-A_Index, nC := SubStr(str, n, 1) break } } return SubStr(str, 1, p-1) . nC . Reverse(SubStr(str, p+1, n-p-1) . pC . SubStr(str, n+1)) }
Reverse(s){ Loop Parse, s o := A_LoopField o return o }</lang>
- Output:
for 1127
1 2+1 7+* 1 2+7 1+* 1 7+1 2+* 1 7+2 1+* 2 1+1 7+* 2 1+7 1+* 7 1+1 2+* 7 1+2 1+*
And for 8338:
8 3 8 3/-/
BBC BASIC
<lang bbcbasic>
PROCsolve24("1234")
PROCsolve24("6789")
PROCsolve24("1127")
PROCsolve24("5566")
END
DEF PROCsolve24(s$)
LOCAL F%, I%, J%, K%, L%, P%, T%, X$, o$(), p$(), t$()
DIM o$(4), p$(24,4), t$(11)
o$() = "", "+", "-", "*", "/"
RESTORE
FOR T% = 1 TO 11
READ t$(T%)
NEXT
DATA "abcdefg", "(abc)defg", "ab(cde)fg", "abcd(efg)", "(abc)d(efg)", "(abcde)fg"
DATA "ab(cdefg)", "((abc)de)fg", "(ab(cde))fg", "ab((cde)fg)", "ab(cd(efg))"
FOR I% = 1 TO 4
FOR J% = 1 TO 4
FOR K% = 1 TO 4
FOR L% = 1 TO 4
IF I%<>J% IF J%<>K% IF K%<>L% IF I%<>K% IF J%<>L% IF I%<>L% THEN
P% += 1
p$(P%,1) = MID$(s$,I%,1)
p$(P%,2) = MID$(s$,J%,1)
p$(P%,3) = MID$(s$,K%,1)
p$(P%,4) = MID$(s$,L%,1)
ENDIF
NEXT
NEXT
NEXT
NEXT
FOR I% = 1 TO 4
FOR J% = 1 TO 4
FOR K% = 1 TO 4
FOR T% = 1 TO 11
FOR P% = 1 TO 24
X$ = t$(T%)
MID$(X$, INSTR(X$,"a"), 1) = p$(P%,1)
MID$(X$, INSTR(X$,"b"), 1) = o$(I%)
MID$(X$, INSTR(X$,"c"), 1) = p$(P%,2)
MID$(X$, INSTR(X$,"d"), 1) = o$(J%)
MID$(X$, INSTR(X$,"e"), 1) = p$(P%,3)
MID$(X$, INSTR(X$,"f"), 1) = o$(K%)
MID$(X$, INSTR(X$,"g"), 1) = p$(P%,4)
F% = TRUE : ON ERROR LOCAL F% = FALSE
IF F% IF EVAL(X$) = 24 THEN PRINT X$ : EXIT FOR I%
RESTORE ERROR
NEXT
NEXT
NEXT
NEXT
NEXT
IF I% > 4 PRINT "No solution found"
ENDPROC
</lang>
- Output:
(1+2+3)*4 6*8/(9-7) (1+2)*(1+7) (5+5-6)*6
C++
This code may be extended to work with more than 4 numbers, goals other than 24, or different digit ranges. Operations have been manually determined for these parameters, with the belief they are complete.
<lang cpp>
- include <iostream>
- include <ratio>
- include <array>
- include <algorithm>
- include <random>
typedef short int Digit; // Typedef for the digits data type.
constexpr Digit nDigits{4}; // Amount of digits that are taken into the game. constexpr Digit maximumDigit{9}; // Maximum digit that may be taken into the game. constexpr short int gameGoal{24}; // Desired result.
typedef std::array<Digit, nDigits> digitSet; // Typedef for the set of digits in the game. digitSet d;
void printTrivialOperation(std::string operation) { // Prints a commutative operation taking all the digits. bool printOperation(false); for(const Digit& number : d) { if(printOperation) std::cout << operation; else printOperation = true; std::cout << number; } std::cout << std::endl; }
void printOperation(std::string prefix, std::string operation1, std::string operation2, std::string operation3, std::string suffix = "") { std::cout << prefix << d[0] << operation1 << d[1] << operation2 << d[2] << operation3 << d[3] << suffix << std::endl; }
int main() { std::mt19937_64 randomGenerator; std::uniform_int_distribution<Digit> digitDistro{1, maximumDigit}; // Let us set up a number of trials: for(int trial{10}; trial; --trial) { for(Digit& digit : d) { digit = digitDistro(randomGenerator); std::cout << digit << " "; } std::cout << std::endl; std::sort(d.begin(), d.end()); // We start with the most trivial, commutative operations: if(std::accumulate(d.cbegin(), d.cend(), 0) == gameGoal) printTrivialOperation(" + "); if(std::accumulate(d.cbegin(), d.cend(), 1, std::multiplies<Digit>{}) == gameGoal) printTrivialOperation(" * "); // Now let's start working on every permutation of the digits. do { // Operations with 2 symbols + and one symbol -: if(d[0] + d[1] + d[2] - d[3] == gameGoal) printOperation("", " + ", " + ", " - "); // If gameGoal is ever changed to a smaller value, consider adding more operations in this category. // Operations with 2 symbols + and one symbol *: if(d[0] * d[1] + d[2] + d[3] == gameGoal) printOperation("", " * ", " + ", " + "); if(d[0] * (d[1] + d[2]) + d[3] == gameGoal) printOperation("", " * ( ", " + ", " ) + "); if(d[0] * (d[1] + d[2] + d[3]) == gameGoal) printOperation("", " * ( ", " + ", " + ", " )"); // Operations with one symbol + and 2 symbols *: if((d[0] * d[1] * d[2]) + d[3] == gameGoal) printOperation("( ", " * ", " * ", " ) + "); if(d[0] * d[1] * (d[2] + d[3]) == gameGoal) printOperation("( ", " * ", " * ( ", " + ", " )"); if((d[0] * d[1]) + (d[2] * d[3]) == gameGoal) printOperation("( ", " * ", " ) + ( ", " * ", " )"); // Operations with one symbol - and 2 symbols *: if((d[0] * d[1] * d[2]) - d[3] == gameGoal) printOperation("( ", " * ", " * ", " ) - "); if(d[0] * d[1] * (d[2] - d[3]) == gameGoal) printOperation("( ", " * ", " * ( ", " - ", " )"); if((d[0] * d[1]) - (d[2] * d[3]) == gameGoal) printOperation("( ", " * ", " ) - ( ", " * ", " )"); // Operations with one symbol +, one symbol *, and one symbol -: if(d[0] * d[1] + d[2] - d[3] == gameGoal) printOperation("", " * ", " + ", " - "); if(d[0] * (d[1] + d[2]) - d[3] == gameGoal) printOperation("", " * ( ", " + ", " ) - "); if(d[0] * (d[1] - d[2]) + d[3] == gameGoal) printOperation("", " * ( ", " - ", " ) + "); if(d[0] * (d[1] + d[2] - d[3]) == gameGoal) printOperation("", " * ( ", " + ", " - ", " )"); if(d[0] * d[1] - (d[2] + d[3]) == gameGoal) printOperation("", " * ", " - ( ", " + ", " )"); // Operations with one symbol *, one symbol /, one symbol +: if(d[0] * d[1] == (gameGoal - d[3]) * d[2]) printOperation("( ", " * ", " / ", " ) + "); if(((d[0] * d[1]) + d[2]) == gameGoal * d[3]) printOperation("(( ", " * ", " ) + ", " ) / "); if((d[0] + d[1]) * d[2] == gameGoal * d[3]) printOperation("(( ", " + ", " ) * ", " ) / "); if(d[0] * d[1] == gameGoal * (d[2] + d[3])) printOperation("( ", " * ", " ) / ( ", " + ", " )"); // Operations with one symbol *, one symbol /, one symbol -: if(d[0] * d[1] == (gameGoal + d[3]) * d[2]) printOperation("( ", " * ", " / ", " ) - "); if(((d[0] * d[1]) - d[2]) == gameGoal * d[3]) printOperation("(( ", " * ", " ) - ", " ) / "); if((d[0] - d[1]) * d[2] == gameGoal * d[3]) printOperation("(( ", " - ", " ) * ", " ) / "); if(d[0] * d[1] == gameGoal * (d[2] - d[3])) printOperation("( ", " * ", " ) / ( ", " - ", " )"); // Operations with 2 symbols *, one symbol /: if(d[0] * d[1] * d[2] == gameGoal * d[3]) printOperation("", " * ", " * ", " / "); if(d[0] * d[1] == gameGoal * d[2] * d[3]) printOperation("", " * ", " / ( ", " * ", " )"); // Operations with 2 symbols /, one symbol -: if(d[0] * d[3] == gameGoal * (d[1] * d[3] - d[2])) printOperation("", " / ( ", " - ", " / ", " )"); // Operations with 2 symbols /, one symbol *: if(d[0] * d[1] == gameGoal * d[2] * d[3]) printOperation("( ", " * ", " / ", " ) / ", ""); } while(std::next_permutation(d.begin(), d.end())); // All operations are repeated for all possible permutations of the numbers. } return 0; } </lang>
- Output:
8 3 7 9 3 * ( 7 + 9 - 8 ) 3 * ( 9 + 7 - 8 ) 1 4 3 1 ( 3 * 4 * ( 1 + 1 ) ( 4 * 3 * ( 1 + 1 ) 5 4 3 6 6 * ( 3 + 5 - 4 ) 6 * ( 5 + 3 - 4 ) 2 5 5 8 5 4 7 3 3 * 4 + 5 + 7 3 * 4 + 7 + 5 ( 3 * 4 * ( 7 - 5 ) 3 * ( 5 + 7 - 4 ) 3 * ( 7 + 5 - 4 ) 4 * 3 + 5 + 7 4 * 3 + 7 + 5 ( 4 * 3 * ( 7 - 5 ) 4 * 5 + 7 - 3 5 * 4 + 7 - 3 5 * ( 7 - 3 ) + 4 3 3 9 2 2 * 9 + 3 + 3 3 * ( 2 + 3 ) + 9 3 * ( 2 + 9 - 3 ) 3 * ( 3 + 2 ) + 9 3 * ( 9 - 2 ) + 3 3 * ( 9 + 2 - 3 ) 9 * 2 + 3 + 3 3 2 7 9 3 * ( 7 - 2 ) + 9 (( 7 + 9 ) * 3 ) / 2 (( 9 + 7 ) * 3 ) / 2 7 1 5 3 7 6 9 4 (( 7 + 9 ) * 6 ) / 4 (( 9 + 7 ) * 6 ) / 4 3 5 3 1 ( 1 * 3 * ( 3 + 5 ) ( 1 * 3 * ( 5 + 3 ) ( 3 * 1 * ( 3 + 5 ) ( 3 * 1 * ( 5 + 3 ) (( 3 + 5 ) * 3 ) / 1 (( 5 + 3 ) * 3 ) / 1
C#
Generate binary trees -> generate permutations -> create expression -> evaluate expression
This works with other targets and more numbers but it will of course become slower.
Redundant expressions are filtered out (based on https://www.4nums.com/theory/) but I'm not sure I caught them all.
<lang csharp>using System; using System.Collections.Generic; using static System.Linq.Enumerable;
public static class Solve24Game {
public static void Main2() {
var testCases = new [] {
new [] { 1,1,2,7 },
new [] { 1,2,3,4 },
new [] { 1,2,4,5 },
new [] { 1,2,7,7 },
new [] { 1,4,5,6 },
new [] { 3,3,8,8 },
new [] { 4,4,5,9 },
new [] { 5,5,5,5 },
new [] { 5,6,7,8 },
new [] { 6,6,6,6 },
new [] { 6,7,8,9 },
};
foreach (var t in testCases) Test(24, t);
Test(100, 9,9,9,9,9,9);
static void Test(int target, params int[] numbers) {
foreach (var eq in GenerateEquations(target, numbers)) Console.WriteLine(eq);
Console.WriteLine();
}
}
static readonly char[] ops = { '*', '/', '+', '-' };
public static IEnumerable<string> GenerateEquations(int target, params int[] numbers) {
var operators = Repeat(ops, numbers.Length - 1).CartesianProduct().Select(e => e.ToArray()).ToList();
return (
from pattern in Patterns(numbers.Length)
let expression = CreateExpression(pattern)
from ops in operators
where expression.WithOperators(ops).HasPreferredTree()
from permutation in Permutations(numbers)
let expr = expression.WithValues(permutation)
where expr.Value == target && expr.HasPreferredValues()
select $"{expr.ToString()} = {target}")
.Distinct()
.DefaultIfEmpty($"Cannot make {target} with {string.Join(", ", numbers)}");
}
///<summary>Generates postfix expression trees where 1's represent operators and 0's represent numbers.</summary>
static IEnumerable<int> Patterns(int length) {
if (length == 1) yield return 0; //0
if (length == 2) yield return 1; //001
if (length < 3) yield break;
//Of each tree, the first 2 bits must always be 0 and the last bit must be 1. Generate the bits in between.
length -= 2;
int len = length * 2 + 3;
foreach (int permutation in BinaryPatterns(length, length * 2)) {
(int p, int l) = ((permutation << 1) + 1, len);
if (IsValidPattern(ref p, ref l)) yield return (permutation << 1) + 1;
}
}
///<summary>Generates all numbers with the given number of 1's and total length.</summary>
static IEnumerable<int> BinaryPatterns(int ones, int length) {
int initial = (1 << ones) - 1;
int blockMask = (1 << length) - 1;
for (int v = initial; v >= initial; ) {
yield return v;
int w = (v | (v - 1)) + 1;
w |= (((w & -w) / (v & -v)) >> 1) - 1;
v = w & blockMask;
}
}
static bool IsValidPattern(ref int pattern, ref int len) {
bool isNumber = (pattern & 1) == 0;
pattern >>= 1;
len--;
if (isNumber) return true;
IsValidPattern(ref pattern, ref len);
IsValidPattern(ref pattern, ref len);
return len == 0;
}
static Expr CreateExpression(int pattern) {
return Create();
Expr Create() {
bool isNumber = (pattern & 1) == 0;
pattern >>= 1;
if (isNumber) return new Const(0);
Expr right = Create();
Expr left = Create();
return new Binary('*', left, right);
}
}
static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences) {
IEnumerable<IEnumerable<T>> emptyProduct = new[] { Empty<T>() };
return sequences.Aggregate(
emptyProduct,
(accumulator, sequence) =>
from acc in accumulator
from item in sequence
select acc.Concat(new [] { item }));
}
private static List<int> helper = new List<int>();
public static IEnumerable<T[]> Permutations<T>(params T[] input) {
if (input == null || input.Length == 0) yield break;
helper.Clear();
for (int i = 0; i < input.Length; i++) helper.Add(i);
while (true) {
yield return input;
int cursor = helper.Count - 2;
while (cursor >= 0 && helper[cursor] > helper[cursor + 1]) cursor--;
if (cursor < 0) break;
int i = helper.Count - 1;
while (i > cursor && helper[i] < helper[cursor]) i--;
(helper[cursor], helper[i]) = (helper[i], helper[cursor]);
(input[cursor], input[i]) = (input[i], input[cursor]);
int firstIndex = cursor + 1;
for (int lastIndex = helper.Count - 1; lastIndex > firstIndex; ++firstIndex, --lastIndex) {
(helper[firstIndex], helper[lastIndex]) = (helper[lastIndex], helper[firstIndex]);
(input[firstIndex], input[lastIndex]) = (input[lastIndex], input[firstIndex]);
}
}
}
static Expr WithOperators(this Expr expr, char[] operators) {
int i = 0;
SetOperators(expr, operators, ref i);
return expr;
static void SetOperators(Expr expr, char[] operators, ref int i) {
if (expr is Binary b) {
b.Symbol = operators[i++];
SetOperators(b.Right, operators, ref i);
SetOperators(b.Left, operators, ref i);
}
}
}
static Expr WithValues(this Expr expr, int[] values) {
int i = 0;
SetValues(expr, values, ref i);
return expr;
static void SetValues(Expr expr, int[] values, ref int i) {
if (expr is Binary b) {
SetValues(b.Left, values, ref i);
SetValues(b.Right, values, ref i);
} else {
expr.Value = values[i++];
}
}
}
static bool HasPreferredTree(this Expr expr) => expr switch {
Const _ => true,
// a / b * c => a * c / b
((_, '/' ,_), '*', _) => false,
// c + a * b => a * b + c
(var l, '+', (_, '*' ,_) r) when l.Depth < r.Depth => false,
// c + a / b => a / b + c
(var l, '+', (_, '/' ,_) r) when l.Depth < r.Depth => false,
// a * (b + c) => (b + c) * a
(var l, '*', (_, '+' ,_) r) when l.Depth < r.Depth => false,
// a * (b - c) => (b - c) * a
(var l, '*', (_, '-' ,_) r) when l.Depth < r.Depth => false,
// (a +- b) + (c */ d) => ((c */ d) + a) +- b
((_, var p, _), '+', (_, var q, _)) when "+-".Contains(p) && "*/".Contains(q) => false,
// a + (b + c) => (a + b) + c
(var l, '+', (_, '+' ,_) r) => false,
// a + (b - c) => (a + b) - c
(var l, '+', (_, '-' ,_) r) => false,
// a - (b + c) => (a - b) + c
(_, '-', (_, '+', _)) => false,
// a * (b * c) => (a * b) * c
(var l, '*', (_, '*' ,_) r) => false,
// a * (b / c) => (a * b) / c
(var l, '*', (_, '/' ,_) r) => false,
// a / (b / c) => (a * c) / b
(var l, '/', (_, '/' ,_) r) => false,
// a - (b - c) * d => (c - b) * d + a
(_, '-', ((_, '-' ,_), '*', _)) => false,
// a - (b - c) / d => (c - b) / d + a
(_, '-', ((_, '-' ,_), '/', _)) => false,
// a - (b - c) => a + c - b
(_, '-', (_, '-', _)) => false,
// (a - b) + c => (a + c) - b
((_, '-', var b), '+', var c) => false,
(var l, _, var r) => l.HasPreferredTree() && r.HasPreferredTree() };
static bool HasPreferredValues(this Expr expr) => expr switch {
Const _ => true,
// -a + b => b - a
(var l, '+', var r) when l.Value < 0 && r.Value >= 0 => false,
// b * a => a * b
(var l, '*', var r) when l.Depth == r.Depth && l.Value > r.Value => false,
// b + a => a + b
(var l, '+', var r) when l.Depth == r.Depth && l.Value > r.Value => false,
// (b o c) * (a o d) => (a o d) * (b o c)
((var a, _, _) l, '*', (var c, _, _) r) when l.Value == r.Value && l.Depth == r.Depth && a.Value < c.Value => false,
// (b o c) + (a o d) => (a o d) + (b o c)
((var a, var p, _) l, '+', (var c, var q, _) r) when l.Value == r.Value && l.Depth == r.Depth && a.Value < c.Value => false,
// (a * c) * b => (a * b) * c
((_, '*', var c), '*', var b) when b.Value < c.Value => false,
// (a + c) + b => (a + b) + c
((_, '+', var c), '+', var b) when b.Value < c.Value => false,
// (a - b) - c => (a - c) - b
((_, '-', var b), '-', var c) when b.Value < c.Value => false,
// a / 1 => a * 1
(_, '/', var b) when b.Value == 1 => false,
// a * b / b => a + b - b
((_, '*', var b), '/', var c) when b.Value == c.Value => false,
// a * 1 * 1 => a + 1 - 1
((_, '*', var b), '*', var c) when b.Value == 1 && c.Value == 1 => false,
(var l, _, var r) => l.HasPreferredValues() && r.HasPreferredValues() };
private struct Fraction : IEquatable<Fraction>, IComparable<Fraction>
{
public readonly int Numerator, Denominator;
public Fraction(int numerator, int denominator)
=> (Numerator, Denominator) = (numerator, denominator) switch
{
(_, 0) => (Math.Sign(numerator), 0),
(0, _) => (0, 1),
(_, var d) when d < 0 => (-numerator, -denominator),
_ => (numerator, denominator)
};
public static implicit operator Fraction(int i) => new Fraction(i, 1);
public static Fraction operator +(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator + a.Denominator * b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator -(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator + a.Denominator * -b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator *(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Numerator, a.Denominator * b.Denominator);
public static Fraction operator /(Fraction a, Fraction b) =>
new Fraction(a.Numerator * b.Denominator, a.Denominator * b.Numerator);
public static bool operator ==(Fraction a, Fraction b) => a.CompareTo(b) == 0;
public static bool operator !=(Fraction a, Fraction b) => a.CompareTo(b) != 0;
public static bool operator <(Fraction a, Fraction b) => a.CompareTo(b) < 0;
public static bool operator >(Fraction a, Fraction b) => a.CompareTo(b) > 0;
public static bool operator <=(Fraction a, Fraction b) => a.CompareTo(b) <= 0;
public static bool operator >=(Fraction a, Fraction b) => a.CompareTo(b) >= 0;
public bool Equals(Fraction other) => Numerator == other.Numerator && Denominator == other.Denominator;
public override string ToString() => Denominator == 1 ? Numerator.ToString() : $"[{Numerator}/{Denominator}]";
public int CompareTo(Fraction other) => (Numerator, Denominator, other.Numerator, other.Denominator) switch {
var ( n1, d1, n2, d2) when n1 == n2 && d1 == d2 => 0,
( 0, 0, _, _) => (-1),
( _, _, 0, 0) => 1,
var ( n1, d1, n2, d2) when d1 == d2 => n1.CompareTo(n2),
(var n1, 0, _, _) => Math.Sign(n1),
( _, _, var n2, 0) => Math.Sign(n2),
var ( n1, d1, n2, d2) => (n1 * d2).CompareTo(n2 * d1)
};
}
private abstract class Expr
{
protected Expr(char symbol) => Symbol = symbol;
public char Symbol { get; set; }
public abstract Fraction Value { get; set; }
public abstract int Depth { get; }
public abstract void Deconstruct(out Expr left, out char symbol, out Expr right);
}
private sealed class Const : Expr
{
public Const(Fraction value) : base('c') => Value = value;
public override Fraction Value { get; set; }
public override int Depth => 0;
public override void Deconstruct(out Expr left, out char symbol, out Expr right) => (left, symbol, right) = (this, Symbol, this);
public override string ToString() => Value.ToString();
}
private sealed class Binary : Expr
{
public Binary(char symbol, Expr left, Expr right) : base(symbol) => (Left, Right) = (left, right);
public Expr Left { get; }
public Expr Right { get; }
public override int Depth => Math.Max(Left.Depth, Right.Depth) + 1;
public override void Deconstruct(out Expr left, out char symbol, out Expr right) => (left, symbol, right) = (Left, Symbol, Right);
public override Fraction Value {
get => Symbol switch {
'*' => Left.Value * Right.Value,
'/' => Left.Value / Right.Value,
'+' => Left.Value + Right.Value,
'-' => Left.Value - Right.Value,
_ => throw new InvalidOperationException() };
set {}
}
public override string ToString() => Symbol switch {
'*' => ToString("+-".Contains(Left.Symbol), "+-".Contains(Right.Symbol)),
'/' => ToString("+-".Contains(Left.Symbol), "*/+-".Contains(Right.Symbol)),
'+' => ToString(false, false),
'-' => ToString(false, "+-".Contains(Right.Symbol)),
_ => $"[{Value}]"
};
private string ToString(bool wrapLeft, bool wrapRight) =>
$"{(wrapLeft ? $"({Left})" : $"{Left}")} {Symbol} {(wrapRight ? $"({Right})" : $"{Right}")}";
}
}</lang>
- Output:
(1 + 2) * (1 + 7) = 24 (1 + 3) * (2 + 4) = 24 1 * 2 * 3 * 4 = 24 (1 + 2 + 3) * 4 = 24 (5 - 1) * (2 + 4) = 24 (2 + 5 - 1) * 4 = 24 (7 * 7 - 1) / 2 = 24 4 / (1 - 5 / 6) = 24 6 / (5 / 4 - 1) = 24 8 / (3 - 8 / 3) = 24 Cannot make 24 with 4, 4, 5, 9 5 * 5 - 5 / 5 = 24 (8 - 6) * (5 + 7) = 24 6 * 8 / (7 - 5) = 24 (5 + 7 - 8) * 6 = 24 6 + 6 + 6 + 6 = 24 6 * 6 - 6 - 6 = 24 6 * 8 / (9 - 7) = 24 (9 / 9 + 9) * (9 / 9 + 9) = 100
Ceylon
Don't forget to import ceylon.random in your module.ceylon file. <lang ceylon>import ceylon.random { DefaultRandom }
shared sealed class Rational(numerator, denominator = 1) satisfies Numeric<Rational> {
shared Integer numerator; shared Integer denominator;
Integer gcd(Integer a, Integer b) => if (b == 0) then a else gcd(b, a % b);
shared Rational inverted => Rational(denominator, numerator);
shared Rational simplified => let (largestFactor = gcd(numerator, denominator)) Rational(numerator / largestFactor, denominator / largestFactor);
divided(Rational other) => (this * other.inverted).simplified;
negated => Rational(-numerator, denominator).simplified;
plus(Rational other) => let (top = numerator*other.denominator + other.numerator*denominator, bottom = denominator * other.denominator) Rational(top, bottom).simplified;
times(Rational other) => Rational(numerator * other.numerator, denominator * other.denominator).simplified;
shared Integer integer => numerator / denominator; shared Float float => numerator.float / denominator.float;
string => denominator == 1 then numerator.string else "``numerator``/``denominator``";
shared actual Boolean equals(Object that) { if (is Rational that) { value simplifiedThis = this.simplified; value simplifiedThat = that.simplified; return simplifiedThis.numerator==simplifiedThat.numerator && simplifiedThis.denominator==simplifiedThat.denominator; } else { return false; } } }
shared Rational? rational(Integer numerator, Integer denominator = 1) => if (denominator == 0) then null else Rational(numerator, denominator).simplified;
shared Rational numeratorOverOne(Integer numerator) => Rational(numerator);
shared abstract class Operation(String lexeme) of addition | subtraction | multiplication | division { shared formal Rational perform(Rational left, Rational right); string => lexeme; }
shared object addition extends Operation("+") { perform(Rational left, Rational right) => left + right; } shared object subtraction extends Operation("-") { perform(Rational left, Rational right) => left - right; } shared object multiplication extends Operation("*") { perform(Rational left, Rational right) => left * right; } shared object division extends Operation("/") { perform(Rational left, Rational right) => left / right; }
shared Operation[] operations = `Operation`.caseValues;
shared interface Expression of NumberExpression | OperationExpression { shared formal Rational evaluate(); }
shared class NumberExpression(Rational number) satisfies Expression { evaluate() => number; string => number.string; } shared class OperationExpression(Expression left, Operation op, Expression right) satisfies Expression { evaluate() => op.perform(left.evaluate(), right.evaluate()); string => "(``left`` ``op`` ``right``)"; }
shared void run() {
value twentyfour = numeratorOverOne(24);
value random = DefaultRandom();
function buildExpressions({Rational*} numbers, Operation* ops) { assert (is NumberExpression[4] numTuple = numbers.collect(NumberExpression).tuple()); assert (is Operation[3] opTuple = ops.sequence().tuple()); value [a, b, c, d] = numTuple; value [op1, op2, op3] = opTuple; value opExp = OperationExpression; // this is just to give it a shorter name return [ opExp(opExp(opExp(a, op1, b), op2, c), op3, d), opExp(opExp(a, op1, opExp(b, op2, c)), op3, d), opExp(a, op1, opExp(opExp(b, op2, c), op3, d)), opExp(a, op1, opExp(b, op2, opExp(c, op3, d))) ]; }
print("Please enter your 4 numbers to see how they form 24 or enter the letter r for random numbers.");
if (exists line = process.readLine()) {
Rational[] chosenNumbers;
if (line.trimmed.uppercased == "R") { chosenNumbers = random.elements(1..9).take(4).collect((Integer element) => numeratorOverOne(element)); print("The random numbers are ``chosenNumbers``"); } else { chosenNumbers = line.split().map(Integer.parse).narrow<Integer>().collect(numeratorOverOne); }
value expressions = { for (numbers in chosenNumbers.permutations) for (op1 in operations) for (op2 in operations) for (op3 in operations) for (exp in buildExpressions(numbers, op1, op2, op3)) if (exp.evaluate() == twentyfour) exp };
print("The solutions are:"); expressions.each(print); } }</lang>
Clojure
<lang Clojure>(ns rosettacode.24game.solve
(:require [clojure.math.combinatorics :as c]
[clojure.walk :as w]))
(def ^:private op-maps
(map #(zipmap [:o1 :o2 :o3] %) (c/selections '(* + - /) 3)))
(def ^:private patterns '(
(:o1 (:o2 :n1 :n2) (:o3 :n3 :n4)) (:o1 :n1 (:o2 :n2 (:o3 :n3 :n4))) (:o1 (:o2 (:o3 :n1 :n2) :n3) :n4)))
(defn play24 [& digits]
{:pre (and (every? #(not= 0 %) digits)
(= (count digits) 4))}
(->> (for [:let [digit-maps
(->> digits sort c/permutations
(map #(zipmap [:n1 :n2 :n3 :n4] %)))]
om op-maps, dm digit-maps]
(w/prewalk-replace dm
(w/prewalk-replace om patterns)))
(filter #(= (eval %) 24))
(map println)
doall
count))</lang>
The function play24 works by substituting the given digits and the four operations into the binary tree patterns (o (o n n) (o n n)), (o (o (o n n) n) n), and (o n (o n (o n n))).
The substitution is the complex part of the program: two pairs of nested maps (the function) are used to substitute in operations and digits, which are replaced into the tree patterns.
COBOL
<lang cobol> >>SOURCE FORMAT FREE
- > This code is dedicated to the public domain
- > This is GNUCobol 2.0
identification division. program-id. twentyfoursolve. environment division. configuration section. repository. function all intrinsic. input-output section. file-control.
select count-file
assign to count-file-name
file status count-file-status
organization line sequential.
data division. file section. fd count-file. 01 count-record pic x(7).
working-storage section. 01 count-file-name pic x(64) value 'solutioncounts'. 01 count-file-status pic xx.
01 command-area.
03 nd pic 9.
03 number-definition.
05 n occurs 4 pic 9.
03 number-definition-9 redefines number-definition
pic 9(4).
03 command-input pic x(16).
03 command pic x(5).
03 number-count pic 9999.
03 l1 pic 99.
03 l2 pic 99.
03 expressions pic zzz,zzz,zz9.
01 number-validation.
03 px pic 99.
03 permutations value
'1234'
& '1243'
& '1324'
& '1342'
& '1423'
& '1432'
& '2134'
& '2143'
& '2314'
& '2341'
& '2413'
& '2431'
& '3124'
& '3142'
& '3214'
& '3241'
& '3423'
& '3432'
& '4123'
& '4132'
& '4213'
& '4231'
& '4312'
& '4321'.
05 permutation occurs 24 pic x(4).
03 cpx pic 9.
03 current-permutation pic x(4).
03 od1 pic 9.
03 od2 pic 9.
03 od3 pic 9.
03 operator-definitions pic x(4) value '+-*/'.
03 cox pic 9.
03 current-operators pic x(3).
03 rpn-forms value
'nnonono'
& 'nnonnoo'
& 'nnnonoo'
& 'nnnoono'
& 'nnnnooo'.
05 rpn-form occurs 5 pic x(7).
03 rpx pic 9.
03 current-rpn-form pic x(7).
01 calculation-area.
03 oqx pic 99.
03 output-queue pic x(7).
03 work-number pic s9999.
03 top-numerator pic s9999 sign leading separate.
03 top-denominator pic s9999 sign leading separate.
03 rsx pic 9.
03 result-stack occurs 8.
05 numerator pic s9999.
05 denominator pic s9999.
03 divide-by-zero-error pic x.
01 totals.
03 s pic 999.
03 s-lim pic 999 value 600.
03 s-max pic 999 value 0.
03 solution occurs 600 pic x(7).
03 sc pic 999.
03 sc1 pic 999.
03 sc2 pic 9.
03 sc-max pic 999 value 0.
03 sc-lim pic 999 value 600.
03 solution-counts value zeros.
05 solution-count occurs 600 pic 999.
03 ns pic 9999.
03 ns-max pic 9999 value 0.
03 ns-lim pic 9999 value 6561.
03 number-solutions occurs 6561.
05 ns-number pic x(4).
05 ns-count pic 999.
03 record-counts pic 9999.
03 total-solutions pic 9999.
01 infix-area.
03 i pic 9. 03 i-s pic 9. 03 i-s1 pic 9. 03 i-work pic x(16). 03 i-stack occurs 7 pic x(13).
procedure division. start-twentyfoursolve.
display 'start twentyfoursolve'
perform display-instructions
perform get-command
perform until command-input = spaces
display space
initialize command number-count
unstring command-input delimited by all space
into command number-count
move command-input to number-definition
move spaces to command-input
evaluate command
when 'h'
when 'help'
perform display-instructions
when 'list'
if ns-max = 0
perform load-solution-counts
end-if
perform list-counts
when 'show'
if ns-max = 0
perform load-solution-counts
end-if
perform show-numbers
when other
if number-definition-9 not numeric
display 'invalid number'
else
perform get-solutions
perform display-solutions
end-if
end-evaluate
if command-input = spaces
perform get-command
end-if
end-perform
display 'exit twentyfoursolve'
stop run
.
display-instructions.
display space display 'enter a number <n> as four integers from 1-9 to see its solutions' display 'enter list to see counts of solutions for all numbers' display 'enter show <n> to see numbers having <n> solutions' display '<enter> ends the program' .
get-command.
display space move spaces to command-input display '(h for help)?' with no advancing accept command-input .
ask-for-more.
display space
move 0 to l1
add 1 to l2
if l2 = 10
display 'more (<enter>)?' with no advancing
accept command-input
move 0 to l2
end-if
.
list-counts.
add 1 to sc-max giving sc
display 'there are ' sc ' solution counts'
display space
display 'solutions/numbers'
move 0 to l1
move 0 to l2
perform varying sc from 1 by 1 until sc > sc-max
or command-input <> spaces
if solution-count(sc) > 0
subtract 1 from sc giving sc1 *> offset to capture zero counts
display sc1 '/' solution-count(sc) space with no advancing
add 1 to l1
if l1 = 8
perform ask-for-more
end-if
end-if
end-perform
if l1 > 0
display space
end-if
.
show-numbers. *> with number-count solutions
add 1 to number-count giving sc1 *> offset for zero count
evaluate true
when number-count >= sc-max
display 'no number has ' number-count ' solutions'
exit paragraph
when solution-count(sc1) = 1 and number-count = 1
display '1 number has 1 solution'
when solution-count(sc1) = 1
display '1 number has ' number-count ' solutions'
when number-count = 1
display solution-count(sc1) ' numbers have 1 solution'
when other
display solution-count(sc1) ' numbers have ' number-count ' solutions'
end-evaluate
display space
move 0 to l1
move 0 to l2
perform varying ns from 1 by 1 until ns > ns-max
or command-input <> spaces
if ns-count(ns) = number-count
display ns-number(ns) space with no advancing
add 1 to l1
if l1 = 14
perform ask-for-more
end-if
end-if
end-perform
if l1 > 0
display space
end-if
.
display-solutions.
evaluate s-max
when 0 display number-definition ' has no solutions'
when 1 display number-definition ' has 1 solution'
when other display number-definition ' has ' s-max ' solutions'
end-evaluate
display space
move 0 to l1
move 0 to l2
perform varying s from 1 by 1 until s > s-max
or command-input <> spaces
*> convert rpn solution(s) to infix
move 0 to i-s
perform varying i from 1 by 1 until i > 7
if solution(s)(i:1) >= '1' and <= '9'
add 1 to i-s
move solution(s)(i:1) to i-stack(i-s)
else
subtract 1 from i-s giving i-s1
move spaces to i-work
string '(' i-stack(i-s1) solution(s)(i:1) i-stack(i-s) ')'
delimited by space into i-work
move i-work to i-stack(i-s1)
subtract 1 from i-s
end-if
end-perform
display solution(s) space i-stack(1) space space with no advancing
add 1 to l1
if l1 = 3
perform ask-for-more
end-if
end-perform
if l1 > 0
display space
end-if
.
load-solution-counts.
move 0 to ns-max *> numbers and their solution count
move 0 to sc-max *> solution counts
move spaces to count-file-status
open input count-file
if count-file-status <> '00'
perform create-count-file
move 0 to ns-max *> numbers and their solution count
move 0 to sc-max *> solution counts
open input count-file
end-if
read count-file
move 0 to record-counts
move zeros to solution-counts
perform until count-file-status <> '00'
add 1 to record-counts
perform increment-ns-max
move count-record to number-solutions(ns-max)
add 1 to ns-count(ns-max) giving sc *> offset 1 for zero counts
if sc > sc-lim
display 'sc ' sc ' exceeds sc-lim ' sc-lim
stop run
end-if
if sc > sc-max
move sc to sc-max
end-if
add 1 to solution-count(sc)
read count-file
end-perform
close count-file
.
create-count-file.
open output count-file
display 'Counting solutions for all numbers'
display 'We will examine 9*9*9*9 numbers'
display 'For each number we will examine 4! permutations of the digits'
display 'For each permutation we will examine 4*4*4 combinations of operators'
display 'For each permutation and combination we will examine 5 rpn forms'
display 'We will count the number of unique solutions for the given number'
display 'Each number and its counts will be written to file ' trim(count-file-name)
compute expressions = 9*9*9*9*factorial(4)*4*4*4*5
display 'So we will evaluate ' trim(expressions) ' statements'
display 'This will take a few minutes'
display 'In the future if ' trim(count-file-name) ' exists, this step will be bypassed'
move 0 to record-counts
move 0 to total-solutions
perform varying n(1) from 1 by 1 until n(1) = 0
perform varying n(2) from 1 by 1 until n(2) = 0
display n(1) n(2) '..' *> show progress
perform varying n(3) from 1 by 1 until n(3) = 0
perform varying n(4) from 1 by 1 until n(4) = 0
perform get-solutions
perform increment-ns-max
move number-definition to ns-number(ns-max)
move s-max to ns-count(ns-max)
move number-solutions(ns-max) to count-record
write count-record
add s-max to total-solutions
add 1 to record-counts
add 1 to ns-count(ns-max) giving sc *> offset by 1 for zero counts
if sc > sc-lim
display 'error: ' sc ' solution count exceeds ' sc-lim
stop run
end-if
add 1 to solution-count(sc)
end-perform
end-perform
end-perform
end-perform
close count-file
display record-counts ' numbers and counts written to ' trim(count-file-name)
display total-solutions ' total solutions'
display space
.
increment-ns-max.
if ns-max >= ns-lim
display 'error: numbers exceeds ' ns-lim
stop run
end-if
add 1 to ns-max
.
get-solutions.
move 0 to s-max
perform varying px from 1 by 1 until px > 24
move permutation(px) to current-permutation
perform varying od1 from 1 by 1 until od1 > 4
move operator-definitions(od1:1) to current-operators(1:1)
perform varying od2 from 1 by 1 until od2 > 4
move operator-definitions(od2:1) to current-operators(2:1)
perform varying od3 from 1 by 1 until od3 > 4
move operator-definitions(od3:1) to current-operators(3:1)
perform varying rpx from 1 by 1 until rpx > 5
move rpn-form(rpx) to current-rpn-form
move 0 to cpx cox
move spaces to output-queue
perform varying oqx from 1 by 1 until oqx > 7
if current-rpn-form(oqx:1) = 'n'
add 1 to cpx
move current-permutation(cpx:1) to nd
move n(nd) to output-queue(oqx:1)
else
add 1 to cox
move current-operators(cox:1) to output-queue(oqx:1)
end-if
end-perform
perform evaluate-rpn
if divide-by-zero-error = space
and 24 * top-denominator = top-numerator
perform varying s from 1 by 1 until s > s-max
or solution(s) = output-queue
continue
end-perform
if s > s-max
if s >= s-lim
display 'error: solutions ' s ' for ' number-definition ' exceeds ' s-lim
stop run
end-if
move s to s-max
move output-queue to solution(s-max)
end-if
end-if
end-perform
end-perform
end-perform
end-perform
end-perform
.
evaluate-rpn.
move space to divide-by-zero-error
move 0 to rsx *> stack depth
perform varying oqx from 1 by 1 until oqx > 7
if output-queue(oqx:1) >= '1' and <= '9'
*> push the digit onto the stack
add 1 to rsx
move top-numerator to numerator(rsx)
move top-denominator to denominator(rsx)
move output-queue(oqx:1) to top-numerator
move 1 to top-denominator
else
*> apply the operation
evaluate output-queue(oqx:1)
when '+'
compute top-numerator = top-numerator * denominator(rsx)
+ top-denominator * numerator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '-'
compute top-numerator = top-denominator * numerator(rsx)
- top-numerator * denominator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '*'
compute top-numerator = top-numerator * numerator(rsx)
compute top-denominator = top-denominator * denominator(rsx)
when '/'
compute work-number = numerator(rsx) * top-denominator
compute top-denominator = denominator(rsx) * top-numerator
if top-denominator = 0
move 'y' to divide-by-zero-error
exit paragraph
end-if
move work-number to top-numerator
end-evaluate
*> pop the stack
subtract 1 from rsx
end-if
end-perform
.
end program twentyfoursolve.</lang>
- Output:
prompt$ cobc -xj twentyfoursolve.cob start twentyfoursolve enter a number <n> as four integers from 1-9 to see its solutions enter list to see counts of solutions for all numbers enter show <n> to see numbers having <n> solutions <enter> ends the program (h for help)?5678 5678 has 026 solutions 57+8-6* (((5+7)-8)*6) 57+86-* ((5+7)*(8-6)) 578-+6* ((5+(7-8))*6) 58-7+6* (((5-8)+7)*6) 587--6* ((5-(8-7))*6) 657+8-* (6*((5+7)-8)) 6578-+* (6*(5+(7-8))) 658-7+* (6*((5-8)+7)) 6587--* (6*(5-(8-7))) 675+8-* (6*((7+5)-8)) 6758-+* (6*(7+(5-8))) 675-/8* ((6/(7-5))*8) 675-8// (6/((7-5)/8)) 678-5+* (6*((7-8)+5)) 6785--* (6*(7-(8-5))) 6875-/* (6*(8/(7-5))) 68*75-/ ((6*8)/(7-5)) 75+8-6* (((7+5)-8)*6) 75+86-* ((7+5)*(8-6)) 758-+6* ((7+(5-8))*6) 86-57+* ((8-6)*(5+7)) 86-75+* ((8-6)*(7+5)) 8675-/* (8*(6/(7-5))) 86*75-/ ((8*6)/(7-5)) 875-/6* ((8/(7-5))*6) 875-6// (8/((7-5)/6)) (h for help)?
CoffeeScript
<lang coffeescript>
- This program tries to find some way to turn four digits into an arithmetic
- expression that adds up to 24.
- Example solution for 5, 7, 8, 8:
- (((8 + 7) * 8) / 5)
solve_24_game = (digits...) ->
# Create an array of objects for our helper functions
arr = for digit in digits
{
val: digit
expr: digit
}
combo4 arr...
combo4 = (a, b, c, d) ->
arr = [a, b, c, d]
# Reduce this to a three-node problem by combining two
# nodes from the array.
permutations = [
[0, 1, 2, 3]
[0, 2, 1, 3]
[0, 3, 1, 2]
[1, 2, 0, 3]
[1, 3, 0, 2]
[2, 3, 0, 1]
]
for permutation in permutations
[i, j, k, m] = permutation
for combo in combos arr[i], arr[j]
answer = combo3 combo, arr[k], arr[m]
return answer if answer
null
combo3 = (a, b, c) ->
arr = [a, b, c]
permutations = [
[0, 1, 2]
[0, 2, 1]
[1, 2, 0]
]
for permutation in permutations
[i, j, k] = permutation
for combo in combos arr[i], arr[j]
answer = combo2 combo, arr[k]
return answer if answer
null
combo2 = (a, b) ->
for combo in combos a, b return combo.expr if combo.val == 24 null
combos = (a, b) ->
[
val: a.val + b.val
expr: "(#{a.expr} + #{b.expr})"
,
val: a.val * b.val
expr: "(#{a.expr} * #{b.expr})"
,
val: a.val - b.val
expr: "(#{a.expr} - #{b.expr})"
,
val: b.val - a.val
expr: "(#{b.expr} - #{a.expr})"
,
val: a.val / b.val
expr: "(#{a.expr} / #{b.expr})"
,
val: b.val / a.val
expr: "(#{b.expr} / #{a.expr})"
,
]
- test
do ->
rand_digit = -> 1 + Math.floor (9 * Math.random())
for i in [1..15]
a = rand_digit()
b = rand_digit()
c = rand_digit()
d = rand_digit()
solution = solve_24_game a, b, c, d
console.log "Solution for #{[a,b,c,d]}: #{solution ? 'no solution'}"
</lang>
- Output:
> coffee 24_game.coffee Solution for 8,3,1,8: ((1 + 8) * (8 / 3)) Solution for 6,9,5,7: (6 - ((5 - 7) * 9)) Solution for 4,2,1,1: no solution Solution for 3,5,1,3: (((3 + 5) * 1) * 3) Solution for 6,4,1,7: ((7 - (4 - 1)) * 6) Solution for 8,1,3,1: (((8 + 1) - 1) * 3) Solution for 6,1,3,3: (((6 + 1) * 3) + 3) Solution for 7,1,5,6: (((7 - 1) * 5) - 6) Solution for 4,2,3,1: ((3 + 1) * (4 + 2)) Solution for 8,8,5,8: ((5 * 8) - (8 + 8)) Solution for 3,8,4,1: ((1 - (3 - 8)) * 4) Solution for 6,4,3,8: ((8 - (6 / 3)) * 4) Solution for 2,1,8,7: (((2 * 8) + 1) + 7) Solution for 5,2,7,5: ((2 * 7) + (5 + 5)) Solution for 2,4,8,9: ((9 - (2 + 4)) * 8)
Common Lisp
<lang lisp>(defconstant +ops+ '(* / + -))
(defun digits ()
(sort (loop repeat 4 collect (1+ (random 9))) #'<))
(defun expr-value (expr)
(eval expr))
(defun divides-by-zero-p (expr)
(when (consp expr)
(destructuring-bind (op &rest args) expr
(or (divides-by-zero-p (car args))
(and (eq op '/)
(or (and (= 1 (length args))
(zerop (expr-value (car args))))
(some (lambda (arg)
(or (divides-by-zero-p arg)
(zerop (expr-value arg))))
(cdr args))))))))
(defun solvable-p (digits &optional expr)
(unless (divides-by-zero-p expr)
(if digits
(destructuring-bind (next &rest rest) digits
(if expr
(some (lambda (op)
(solvable-p rest (cons op (list next expr))))
+ops+)
(solvable-p rest (list (car +ops+) next))))
(when (and expr
(eql 24 (expr-value expr)))
(merge-exprs expr)))))
(defun merge-exprs (expr)
(if (atom expr)
expr
(destructuring-bind (op &rest args) expr
(if (and (member op '(* +))
(= 1 (length args)))
(car args)
(cons op
(case op
((* +)
(loop for arg in args
for merged = (merge-exprs arg)
when (and (consp merged)
(eq op (car merged)))
append (cdr merged)
else collect merged))
(t (mapcar #'merge-exprs args))))))))
(defun solve-24-game (digits)
"Generate a lisp form using the operators in +ops+ and the given
digits which evaluates to 24. The first form found is returned, or NIL if there is no solution."
(solvable-p digits))</lang>
- Output:
CL-USER 138 > (loop repeat 24 for soln = (solve-24-game (digits)) when soln do (pprint soln)) (+ 7 5 (* 4 3)) (* 6 4 (- 3 2)) (+ 9 8 4 3) (* 8 (- 6 (* 3 1))) (* 6 4 (/ 2 2)) (* 9 (/ 8 (- 8 5))) NIL
D
This uses the Rational struct and permutations functions of two other Rosetta Code Tasks.
<lang d>import std.stdio, std.algorithm, std.range, std.conv, std.string,
std.concurrency, permutations2, arithmetic_rational;
string solve(in int target, in int[] problem) {
static struct T { Rational r; string e; }
Generator!T computeAllOperations(in Rational[] L) {
return new typeof(return)({
if (!L.empty) {
immutable x = L[0];
if (L.length == 1) {
yield(T(x, x.text));
} else {
foreach (const o; computeAllOperations(L.dropOne)) {
immutable y = o.r;
auto sub = [T(x * y, "*"), T(x + y, "+"), T(x - y, "-")];
if (y) sub ~= [T(x / y, "/")];
foreach (const e; sub)
yield(T(e.r, format("(%s%s%s)", x, e.e, o.e)));
}
}
}
});
}
foreach (const p; problem.map!Rational.array.permutations!false)
foreach (const sol; computeAllOperations(p))
if (sol.r == target)
return sol.e;
return "No solution";
}
void main() {
foreach (const prob; [[6, 7, 9, 5], [3, 3, 8, 8], [1, 1, 1, 1]])
writeln(prob, ": ", solve(24, prob));
}</lang>
- Output:
[6, 7, 9, 5]: (6+(9*(7-5))) [3, 3, 8, 8]: (8/(3-(8/3))) [1, 1, 1, 1]: No solution
EchoLisp
The program takes n numbers - not limited to 4 - builds the all possible legal rpn expressions according to the game rules, and evaluates them. Time saving : 4 5 + is the same as 5 4 + . Do not generate twice. Do not generate expressions like 5 6 * + which are not legal.
<lang scheme>
- use task RPN_to_infix_conversion#EchoLisp to print results
(define (rpn->string rpn)
(if (vector? rpn)
(infix->string (rpn->infix rpn))
"😥 Not found"))
(string-delimiter "")
(define OPS #(* + - // )) ;; use float division
(define-syntax-rule (commutative? op) (or (= op *) (= op +)))
- ---------------------------------
- calc rpn -> num value or #f if bad rpn
- rpn is a vector of ops or numbers
- ----------------------------------
(define (calc rpn) (define S (stack 'S))
(for ((token rpn))
(if (procedure? token)
(let [(op2 (pop S)) (op1 (pop S))]
(if (and op1 op2)
(push S (apply token (list op1 op2)))
(push S #f))) ;; not-well formed
(push S token ))
#:break (not (stack-top S)))
(if (= 1 (stack-length S)) (pop S) #f))
- check for legal rpn -> #f if not legal
(define (rpn? rpn) (define S (stack 'S))
(for ((token rpn))
(if (procedure? token)
(push S (and (pop S) (pop S)))
(push S token ))
#:break (not (stack-top S)))
(stack-top S))
- --------------------------------------
- build-rpn
- push next rpn op or number
- dleft is number of not used digits
- ---------------------------------------
(define count 0)
(define (build-rpn into: rpn depth maxdepth digits ops dleft target &hit ) (define cmpop #f)
(cond
- tooo long
[(> (++ count) 200_000) (set-box! &hit 'not-found)]
- stop on first hit
[(unbox &hit) &hit]
- partial rpn must be legal
[(not (rpn? rpn)) #f]
- eval rpn if complete
[(> depth maxdepth)
(when (= target (calc rpn)) (set-box! &hit rpn))]
- else, add a digit to rpn
[else
[when (< depth maxdepth) ;; digits anywhere except last
(for [(d digits) (i 10)]
#:continue (zero? d)
(vector-set! digits i 0) ;; mark used
(vector-set! rpn depth d)
(build-rpn rpn (1+ depth) maxdepth digits ops (1- dleft) target &hit)
(vector-set! digits i d)) ;; mark unused
] ;; add digit
- or, add an op
- ops anywhere except positions 0,1
[when (and (> depth 1) (<= (+ depth dleft) maxdepth));; cutter : must use all digits
(set! cmpop
(and (number? [rpn (1- depth)])
(number? [rpn (- depth 2)])
(> [rpn (1- depth)] [rpn (- depth 2)])))
(for [(op ops)]
#:continue (and cmpop (commutative? op)) ;; cutter : 3 4 + === 4 3 +
(vector-set! rpn depth op)
(build-rpn rpn (1+ depth) maxdepth digits ops dleft target &hit)
(vector-set! rpn depth 0))] ;; add op
] ; add something to rpn vector
)) ; build-rpn
- ------------------------
- gen24
- num random numbers
- ------------------------
(define (gen24 num maxrange)
(->> (append (range 1 maxrange)(range 1 maxrange)) shuffle (take num)))
- -------------------------------------------
- try-rpn
- sets starter values for build-rpn
- -------------------------------------------
(define (try-rpn digits target)
(set! digits (list-sort > digits)) ;; seems to accelerate things
(define rpn (make-vector (1- (* 2 (length digits)))))
(define &hit (box #f))
(set! count 0)
(build-rpn rpn starter-depth: 0
max-depth: (1- (vector-length rpn))
(list->vector digits)
OPS
remaining-digits: (length digits)
target &hit )
(writeln target '= (rpn->string (unbox &hit)) 'tries= count))
- -------------------------------
- (task numdigits target maxrange)
- --------------------------------
(define (task (numdigits 4) (target 24) (maxrange 10))
(define digits (gen24 numdigits maxrange))
(writeln digits '→ target)
(try-rpn digits target))
</lang>
- Output:
(task 4) ;; standard 24-game (7 9 2 4) → 24 24 = 9 + 7 + 4 * 2 tries= 35 (task 4) (1 9 3 4) → 24 24 = 9 + (4 + 1) * 3 tries= 468 (task 5 ) ;; 5 digits (4 8 6 9 8) → 24 24 = 9 * 8 * (8 / (6 * 4)) tries= 104 (task 5 100) ;; target = 100 (5 6 5 1 3) → 100 100 = (6 + (5 * 3 - 1)) * 5 tries= 10688 (task 5 (random 100)) (1 1 8 6 8) → 31 31 = 8 * (6 - 1) - (8 + 1) tries= 45673 (task 6 (random 100)) ;; 6 digits (7 2 7 8 3 1) → 40 40 = 8 / (7 / (7 * (3 + 2 * 1))) tries= 154 (task 6 (random 1000) 100) ;; 6 numbers < 100 , target < 1000 (19 15 83 74 61 48) → 739 739 = (83 + (74 - (61 + 48))) * 15 + 19 tries= 29336 (task 6 (random 1000) 100) ;; 6 numbers < 100 (73 29 65 78 22 43) → 1 1 = 😥 Not found tries= 200033 (task 7 (random 1000) 100) ;; 7 numbers < 100 (7 55 94 4 71 58 93) → 705 705 = 94 + 93 + 71 + 58 + 55 * 7 + 4 tries= 5982 (task 6 (random -100) 10) ;; negative target (5 9 7 3 6 3) → -54 -54 = 9 * (7 + (6 - 5 * 3)) * 3 tries= 2576
Elixir
<lang elixir>defmodule Game24 do
@expressions [ ["((", "", ")", "", ")", ""],
["(", "(", "", "", "))", ""],
["(", "", ")", "(", "", ")"],
["", "((", "", "", ")", ")"],
["", "(", "", "(", "", "))"] ]
def solve(digits) do
dig_perm = permute(digits) |> Enum.uniq
operators = perm_rep(~w[+ - * /], 3)
for dig <- dig_perm, ope <- operators, expr <- @expressions,
check?(str = make_expr(dig, ope, expr)),
do: str
end
defp check?(str) do
try do
{val, _} = Code.eval_string(str)
val == 24
rescue
ArithmeticError -> false # division by zero
end
end
defp permute([]), do: [[]]
defp permute(list) do
for x <- list, y <- permute(list -- [x]), do: [x|y]
end
defp perm_rep([], _), do: [[]]
defp perm_rep(_, 0), do: [[]]
defp perm_rep(list, i) do
for x <- list, y <- perm_rep(list, i-1), do: [x|y]
end
defp make_expr([a,b,c,d], [x,y,z], [e0,e1,e2,e3,e4,e5]) do
e0 <> a <> x <> e1 <> b <> e2 <> y <> e3 <> c <> e4 <> z <> d <> e5
end
end
case Game24.solve(System.argv) do
[] -> IO.puts "no solutions"
solutions ->
IO.puts "found #{length(solutions)} solutions, including #{hd(solutions)}"
IO.inspect Enum.sort(solutions)
end</lang>
- Output:
C:\Elixir>elixir game24.exs 1 1 3 4 found 12 solutions, including ((1+1)*3)*4 ["((1+1)*3)*4", "((1+1)*4)*3", "(1+1)*(3*4)", "(1+1)*(4*3)", "(3*(1+1))*4", "(3*4)*(1+1)", "(4*(1+1))*3", "(4*3)*(1+1)", "3*((1+1)*4)", "3*(4*(1+1))", "4*((1+1)*3)", "4*(3*(1+1))"] C:\Elixir>elixir game24.exs 6 7 8 9 found 8 solutions, including (6*8)/(9-7) ["(6*8)/(9-7)", "(6/(9-7))*8", "(8*6)/(9-7)", "(8/(9-7))*6", "6*(8/(9-7))", "6/((9-7)/8)", "8*(6/(9-7))", "8/((9-7)/6)"] C:\Elixir>elixir game24.exs 1 2 2 3 no solutions
ERRE
ERRE hasn't an "EVAL" function so we must write an evaluation routine; this task is solved via "brute-force". <lang ERR> PROGRAM 24SOLVE
LABEL 98,99,2540,2550,2560
! possible brackets CONST NBRACKETS=11,ST_CONST$="+-*/^("
DIM D[4],PERM[24,4] DIM BRAKETS$[NBRACKETS] DIM OP$[3] DIM STACK$[50]
PROCEDURE COMPATTA_STACK
IF NS>1 THEN
R=1
WHILE R<NS DO
IF INSTR(ST_CONST$,STACK$[R])=0 AND INSTR(ST_CONST$,STACK$[R+1])=0 THEN
FOR R1=R TO NS-1 DO
STACK$[R1]=STACK$[R1+1]
END FOR
NS=NS-1
END IF
R=R+1
END WHILE
END IF
END PROCEDURE
PROCEDURE CALC_ARITM
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="^" THEN
IF L>=NS2 THEN GOTO 99 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="^" THEN
RI#=N1#^N2#
END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="*" OR STACK$[L]="/" THEN
IF L>=NS2 THEN GOTO 99 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="*" THEN
RI#=N1#*N2#
ELSE
IF N2#<>0 THEN RI#=N1#/N2# ELSE NERR=6 RI#=0 END IF
END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="+" OR STACK$[L]="-" THEN
EXIT IF L>=NS2
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="+" THEN RI#=N1#+N2# ELSE RI#=N1#-N2# END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
99:
IF NOP<2 THEN ! precedenza tra gli operatori
DB#=VAL(STACK$[NS1])
ELSE
IF NOP<3 THEN
DB#=VAL(STACK$[NS1+2])
ELSE
DB#=VAL(STACK$[NS1+4])
END IF
END IF
END PROCEDURE
PROCEDURE SVOLGI_PAR
NPA=NPA-1
FOR J=NS TO 1 STEP -1 DO
EXIT IF STACK$[J]="("
END FOR
IF J=0 THEN
NS1=1 NS2=NS CALC_ARITM NERR=7
ELSE
FOR R=J TO NS-1 DO
STACK$[R]=STACK$[R+1]
END FOR
NS1=J NS2=NS-1 CALC_ARITM
IF NS1=2 THEN
NS1=1 STACK$[1]=STACK$[2]
END IF
NS=NS1
COMPATTA_STACK
END IF
END PROCEDURE
PROCEDURE MYEVAL(EXPRESSION$,DB#,NERR->DB#,NERR)
NOP=0 NPA=0 NS=1 K$="" NERR=0
STACK$[1]="@" ! init stack
FOR W=1 TO LEN(EXPRESSION$) DO
LOOP
CODE=ASC(MID$(EXPRESSION$,W,1))
IF (CODE>=48 AND CODE<=57) OR CODE=46 THEN
K$=K$+CHR$(CODE)
W=W+1 IF W>LEN(EXPRESSION$) THEN GOTO 98 END IF
ELSE
EXIT IF K$=""
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN
STACK$[NS]=K$
ELSE
STACK$[NS]=STR$(VAL(K$)*FLAG)
END IF
K$="" FLAG=0
EXIT
END IF
END LOOP
IF CODE=43 THEN K$="+" END IF
IF CODE=45 THEN K$="-" END IF
IF CODE=42 THEN K$="*" END IF
IF CODE=47 THEN K$="/" END IF
IF CODE=94 THEN K$="^" END IF
CASE CODE OF
43,45,42,47,94-> ! +-*/^
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
IF INSTR(ST_CONST$,STACK$[NS])<>0 THEN
NERR=5
ELSE
NS=NS+1 STACK$[NS]=K$ NOP=NOP+1
IF NOP>=2 THEN
FOR J=NS TO 1 STEP -1 DO
IF STACK$[J]<>"(" THEN GOTO 2540 END IF
IF J<NS-2 THEN GOTO 2550 ELSE GOTO 2560 END IF
2540: END FOR 2550: NS1=J+1 NS2=NS CALC_ARITM
NS=NS2 STACK$[NS]=K$
REGISTRO_X#=VAL(STACK$[NS-1])
END IF
END IF
2560: END ->
40-> ! (
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
STACK$[NS]="(" NPA=NPA+1
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
END ->
41-> ! )
SVOLGI_PAR
IF NERR=7 THEN
NERR=0 NOP=0 NPA=0 NS=1
ELSE
IF NERR=0 OR NERR=1 THEN
DB#=VAL(STACK$[NS])
REGISTRO_X#=DB#
ELSE
NOP=0 NPA=0 NS=1
END IF
END IF
END ->
OTHERWISE
NERR=8
END CASE
K$=""
END FOR
98:
IF K$<>"" THEN
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN STACK$[NS]=K$ ELSE STACK$[NS]=STR$(VAL(K$)*FLAG) END IF
END IF
IF INSTR(ST_CONST$,STACK$[NS])<>0 THEN
NERR=6
ELSE
WHILE NPA<>0 DO
SVOLGI_PAR
END WHILE
IF NERR<>7 THEN NS1=1 NS2=NS CALCARITM END IF
END IF
NS=1 NOP=0 NPA=0
END PROCEDURE
BEGIN
PRINT(CHR$(12);) ! CLS
! possible brackets
DATA("4#4#4#4")
DATA("(4#4)#4#4")
DATA("4#(4#4)#4")
DATA("4#4#(4#4)")
DATA("(4#4)#(4#4)")
DATA("(4#4#4)#4")
DATA("4#(4#4#4)")
DATA("((4#4)#4)#4")
DATA("(4#(4#4))#4")
DATA("4#((4#4)#4)")
DATA("4#(4#(4#4))")
FOR I=1 TO NBRACKETS DO
READ(BRAKETS$[I])
END FOR
INPUT("ENTER 4 DIGITS: ",A$)
ND=0
FOR I=1 TO LEN(A$) DO
C$=MID$(A$,I,1)
IF INSTR("123456789",C$)>0 THEN
ND=ND+1
D[ND]=VAL(C$)
END IF
END FOR
! precompute permutations. dumb way.
NPERM=1*2*3*4
N=0
FOR I=1 TO 4 DO
FOR J=1 TO 4 DO
FOR K=1 TO 4 DO
FOR L=1 TO 4 DO
! valid permutation (no dupes)
IF I<>J AND I<>K AND I<>L AND J<>K AND J<>L AND K<>L THEN
N=N+1
! actually,we can as well permute given digits
PERM[N,1]=D[I]
PERM[N,2]=D[J]
PERM[N,3]=D[K]
PERM[N,4]=D[L]
END IF
END FOR
END FOR
END FOR
END FOR
! operations: full search
COUNT=0
OPS$="+-*/"
FOR OP1=1 TO 4 DO
OP$[1]=MID$(OPS$,OP1,1)
FOR OP2=1 TO 4 DO
OP$[2]=MID$(OPS$,OP2,1)
FOR OP3=1 TO 4 DO
OP$[3]=MID$(OPS$,OP3,1)
! substitute all brackets
FOR T=1 TO NBRACKETS DO
TMPL$=BRAKETS$[T]
! now,substitute all digits: permutations.
FOR P=1 TO NPERM DO
RES$=""
NOP=0
ND=0
FOR I=1 TO LEN(TMPL$) DO
C$=MID$(TMPL$,I,1)
CASE C$ OF
"#"-> ! operations
NOP=NOP+1
RES$=RES$+OP$[NOP]
END ->
"4"-> ! digits
ND=NOP+1
RES$=RES$+MID$(STR$(PERM[P,ND]),2)
END ->
OTHERWISE ! brackets goes here
RES$=RES$+C$
END CASE
END FOR
! eval here
MY_EVAL(RES$,DB#,NERR->DB#,NERR)
IF DB#=24 AND NERR=0 THEN
PRINT("24=";RES$)
COUNT=COUNT+1
END IF
END FOR
END FOR
END FOR
END FOR
END FOR
IF COUNT=0 THEN
PRINT("If you see this, probably task cannot be solved with these digits")
ELSE
PRINT("Total=";COUNT)
END IF
END PROGRAM </lang>
- Output:
ENTER 4 DIGITS: ? 6759 24=6+(7-5)*9 24=6+((7-5)*9) 24=6+9*(7-5) 24=6+(9*(7-5)) 24=6-(5-7)*9 24=6-((5-7)*9) 24=(7-5)*9+6 24=((7-5)*9)+6 24=6-9*(5-7) 24=6-(9*(5-7)) 24=9*(7-5)+6 24=(9*(7-5))+6 Total= 12
Euler Math Toolbox
Via brute force.
<lang Euler Math Toolbox> >function try24 (v) ... $n=cols(v); $if n==1 and v[1]~=24 then $ "Solved the problem", $ return 1; $endif $loop 1 to n $ w=tail(v,2); $ loop 1 to n-1 $ h=w; a=v[1]; b=w[1]; $ w[1]=a+b; if try24(w); ""+a+"+"+b+"="+(a+b), return 1; endif; $ w[1]=a-b; if try24(w); ""+a+"-"+b+"="+(a-b), return 1; endif; $ w[1]=a*b; if try24(w); ""+a+"*"+b+"="+(a*b), return 1; endif; $ if not b~=0 then $ w[1]=a/b; if try24(w); ""+a+"/"+b+"="+(a/b), return 1; endif; $ endif; $ w=rotright(w); $ end; $ v=rotright(v); $end; $return 0; $endfunction </lang>
<lang Euler Math Toolbox> >try24([1,2,3,4]);
Solved the problem 6*4=24 3+3=6 1+2=3
>try24([8,7,7,1]);
Solved the problem 22+2=24 14+8=22 7+7=14
>try24([8,4,7,1]);
Solved the problem 6*4=24 7-1=6 8-4=4
>try24([3,4,5,6]);
Solved the problem 4*6=24 -1+5=4 3-4=-1
</lang>
F#
The program wants to give all solutions for a given set of 4 digits. It eliminates all duplicate solutions which result from transposing equal digits. The basic solution is an adaption of the OCaml program. <lang fsharp>open System
let rec gcd x y = if x = y || x = 0 then y else if x < y then gcd y x else gcd y (x-y) let abs (x : int) = Math.Abs x let sign (x: int) = Math.Sign x let cint s = Int32.Parse(s)
type Rat(x : int, y : int) =
let g = if y = 0 then 0 else gcd (abs x) (abs y)
member this.n = if g = 0 then sign y * sign x else sign y * x / g // store a minus sign in the numerator
member this.d =
if y = 0 then 0 else sign y * y / g
static member (~-) (x : Rat) = Rat(-x.n, x.d)
static member (+) (x : Rat, y : Rat) = Rat(x.n * y.d + y.n * x.d, x.d * y.d)
static member (-) (x : Rat, y : Rat) = x + Rat(-y.n, y.d)
static member (*) (x : Rat, y : Rat) = Rat(x.n * y.n, x.d * y.d)
static member (/) (x : Rat, y : Rat) = x * Rat(y.d, y.n)
interface System.IComparable with
member this.CompareTo o =
match o with
| :? Rat as that -> compare (this.n * that.d) (that.n * this.d)
| _ -> invalidArg "o" "cannot compare values of differnet types."
override this.Equals(o) =
match o with
| :? Rat as that -> this.n = that.n && this.d = that.d
| _ -> false
override this.ToString() =
if this.d = 1 then this.n.ToString()
else sprintf @"<%d,%d>" this.n this.d
new(x : string, y : string) = if y = "" then Rat(cint x, 1) else Rat(cint x, cint y)
type expression =
| Const of Rat | Sum of expression * expression | Diff of expression * expression | Prod of expression * expression | Quot of expression * expression
let rec eval = function
| Const c -> c | Sum (f, g) -> eval f + eval g | Diff(f, g) -> eval f - eval g | Prod(f, g) -> eval f * eval g | Quot(f, g) -> eval f / eval g
let print_expr expr =
let concat (s : seq<string>) = System.String.Concat s
let paren p prec op_prec = if prec > op_prec then p else ""
let rec print prec = function
| Const c -> c.ToString()
| Sum(f, g) ->
concat [ (paren "(" prec 0); (print 0 f); " + "; (print 0 g); (paren ")" prec 0) ]
| Diff(f, g) ->
concat [ (paren "(" prec 0); (print 0 f); " - "; (print 1 g); (paren ")" prec 0) ]
| Prod(f, g) ->
concat [ (paren "(" prec 2); (print 2 f); " * "; (print 2 g); (paren ")" prec 2) ]
| Quot(f, g) ->
concat [ (paren "(" prec 2); (print 2 f); " / "; (print 3 g); (paren ")" prec 2) ]
print 0 expr
let rec normal expr =
let norm epxr =
match expr with
| Sum(x, y) -> if eval x <= eval y then expr else Sum(normal y, normal x)
| Prod(x, y) -> if eval x <= eval y then expr else Prod(normal y, normal x)
| _ -> expr
match expr with
| Const c -> expr
| Sum(x, y) -> norm (Sum(normal x, normal y))
| Prod(x, y) -> norm (Prod(normal x, normal y))
| Diff(x, y) -> Diff(normal x, normal y)
| Quot(x, y) -> Quot(normal x, normal y)
let rec insert v = function
| [] -> v | x::xs as li -> (v::li) :: (List.map (fun y -> x::y) (insert v xs))
let permutations li =
List.foldBack (fun x z -> List.concat (List.map (insert x) z)) li [[]]
let rec comp expr rest = seq {
match rest with
| x::xs ->
yield! comp (Sum (expr, x)) xs;
yield! comp (Diff(x, expr)) xs;
yield! comp (Diff(expr, x)) xs;
yield! comp (Prod(expr, x)) xs;
yield! comp (Quot(x, expr)) xs;
yield! comp (Quot(expr, x)) xs;
| [] -> if eval expr = Rat(24,1) then yield print_expr (normal expr)
}
[<EntryPoint>] let main argv =
let digits = List.init 4 (fun i -> Const (Rat(argv.[i],"")))
let solutions =
permutations digits
|> Seq.groupBy (sprintf "%A")
|> Seq.map snd |> Seq.map Seq.head
|> Seq.map (fun x -> comp (List.head x) (List.tail x))
|> Seq.choose (fun x -> if Seq.isEmpty x then None else Some x)
|> Seq.concat
if Seq.isEmpty solutions then
printfn "No solutions."
else
solutions
|> Seq.groupBy id
|> Seq.iter (fun x -> printfn "%s" (fst x))
0</lang>
- Output:
>solve24 3 3 3 4 4 * (3 * 3 - 3) 3 + 3 * (3 + 4) >solve24 3 3 3 5 No solutions. solve24 3 3 3 6 6 + 3 * (3 + 3) (3 / 3 + 3) * 6 3 * (3 + 6) - 3 3 + 3 + 3 * 6 >solve24 3 3 8 8 8 / (3 - 8 / 3) >solve24 3 8 8 9 3 * (9 - 8 / 8) (9 - 8) * 3 * 8 3 / (9 - 8) * 8 8 / ((9 - 8) / 3) 3 * (9 - 8) * 8 3 * 8 / (9 - 8) 3 / ((9 - 8) / 8)
Factor
Factor is well-suited for this task due to its homoiconicity and because it is a reverse-Polish notation evaluator. All we're doing is grouping each permutation of digits with three selections of the possible operators into quotations (blocks of code that can be stored like sequences). Then we call each quotation and print out the ones that equal 24. The recover word is an exception handler that is used to intercept divide-by-zero errors and continue gracefully by removing those quotations from consideration.
<lang factor>USING: continuations grouping io kernel math math.combinatorics
prettyprint quotations random sequences sequences.deep ;
IN: rosetta-code.24-game
- 4digits ( -- seq ) 4 9 random-integers [ 1 + ] map ;
- expressions ( digits -- exprs )
all-permutations [ [ + - * / ] 3 selections [ append ] with map ] map flatten 7 group ;
- 24= ( exprs -- )
>quotation dup call( -- x ) 24 = [ . ] [ drop ] if ;
- 24-game ( -- )
4digits dup "The numbers: " write . "The solutions: " print expressions [ [ 24= ] [ 2drop ] recover ] each ;
24-game</lang>
- Output:
The numbers: { 4 9 3 1 }
The solutions:
[ 4 9 3 1 * - * ]
[ 4 9 3 1 / - * ]
[ 4 9 1 3 * - * ]
[ 4 1 9 3 - * * ]
[ 4 1 9 3 - / / ]
[ 9 3 4 1 + * + ]
[ 9 3 1 4 + * + ]
[ 1 4 9 3 - * * ]
[ 1 4 9 3 * - - ]
[ 1 4 3 9 * - - ]
The numbers: { 1 7 4 9 }
The solutions:
The numbers: { 1 5 6 8 }
The solutions:
[ 6 1 5 8 - - * ]
[ 6 1 8 5 - + * ]
[ 6 8 1 5 - + * ]
[ 6 8 5 1 - - * ]
Fortran
<lang Fortran>program solve_24
use helpers implicit none real :: vector(4), reals(4), p, q, r, s integer :: numbers(4), n, i, j, k, a, b, c, d character, parameter :: ops(4) = (/ '+', '-', '*', '/' /) logical :: last real,parameter :: eps = epsilon(1.0)
do n=1,12
call random_number(vector)
reals = 9 * vector + 1
numbers = int(reals)
call Insertion_Sort(numbers)
permutations: do
a = numbers(1); b = numbers(2); c = numbers(3); d = numbers(4)
reals = real(numbers)
p = reals(1); q = reals(2); r = reals(3); s = reals(4)
! combinations of operators:
do i=1,4
do j=1,4
do k=1,4
if ( abs(op(op(op(p,i,q),j,r),k,s)-24.0) < eps ) then
write (*,*) numbers, ' : ', '((',a,ops(i),b,')',ops(j),c,')',ops(k),d
exit permutations
else if ( abs(op(op(p,i,op(q,j,r)),k,s)-24.0) < eps ) then
write (*,*) numbers, ' : ', '(',a,ops(i),'(',b,ops(j),c,'))',ops(k),d
exit permutations
else if ( abs(op(p,i,op(op(q,j,r),k,s))-24.0) < eps ) then
write (*,*) numbers, ' : ', a,ops(i),'((',b,ops(j),c,')',ops(k),d,')'
exit permutations
else if ( abs(op(p,i,op(q,j,op(r,k,s)))-24.0) < eps ) then
write (*,*) numbers, ' : ', a,ops(i),'(',b,ops(j),'(',c,ops(k),d,'))'
exit permutations
else if ( abs(op(op(p,i,q),j,op(r,k,s))-24.0) < eps ) then
write (*,*) numbers, ' : ', '(',a,ops(i),b,')',ops(j),'(',c,ops(k),d,')'
exit permutations
end if
end do
end do
end do
call nextpermutation(numbers,last)
if ( last ) then
write (*,*) numbers, ' : no solution.'
exit permutations
end if
end do permutations
end do
contains
pure real function op(x,c,y)
integer, intent(in) :: c
real, intent(in) :: x,y
select case ( ops(c) )
case ('+')
op = x+y
case ('-')
op = x-y
case ('*')
op = x*y
case ('/')
op = x/y
end select
end function op
end program solve_24</lang>
<lang Fortran>module helpers
contains
pure subroutine Insertion_Sort(a)
integer, intent(inout) :: a(:)
integer :: temp, i, j
do i=2,size(a)
j = i-1
temp = a(i)
do while ( j>=1 .and. a(j)>temp )
a(j+1) = a(j)
j = j - 1
end do
a(j+1) = temp
end do
end subroutine Insertion_Sort
subroutine nextpermutation(perm,last)
integer, intent(inout) :: perm(:)
logical, intent(out) :: last
integer :: k,l
k = largest1()
last = k == 0
if ( .not. last ) then
l = largest2(k)
call swap(l,k)
call reverse(k)
end if
contains
pure integer function largest1()
integer :: k, max
max = 0
do k=1,size(perm)-1
if ( perm(k) < perm(k+1) ) then
max = k
end if
end do
largest1 = max
end function largest1
pure integer function largest2(k)
integer, intent(in) :: k
integer :: l, max
max = k+1
do l=k+2,size(perm)
if ( perm(k) < perm(l) ) then
max = l
end if
end do
largest2 = max
end function largest2
subroutine swap(l,k)
integer, intent(in) :: k,l
integer :: temp
temp = perm(k)
perm(k) = perm(l)
perm(l) = temp
end subroutine swap
subroutine reverse(k)
integer, intent(in) :: k
integer :: i
do i=1,(size(perm)-k)/2
call swap(k+i,size(perm)+1-i)
end do
end subroutine reverse
end subroutine nextpermutation
end module helpers</lang>
- Output:
(using g95)
3 6 7 9 : 3 *(( 6 - 7 )+ 9 ) 3 9 5 8 : (( 3 * 9 )+ 5 )- 8 4 5 6 9 : (( 4 + 5 )+ 6 )+ 9 2 9 9 8 : ( 2 +( 9 / 9 ))* 8 1 4 7 5 : ( 1 +( 4 * 7 ))- 5 8 7 7 6 : no solution. 3 3 8 9 : ( 3 *( 3 + 8 ))- 9 1 5 6 7 : ( 1 +( 5 * 6 ))- 7 2 3 5 3 : 2 *(( 3 * 5 )- 3 ) 4 5 6 9 : (( 4 + 5 )+ 6 )+ 9 1 1 3 6 : ( 1 +( 1 * 3 ))* 6 2 4 6 8 : (( 2 / 4 )* 6 )* 8
GAP
<lang gap># Solution in RPN check := function(x, y, z) local r, c, s, i, j, k, a, b, p; i := 0; j := 0; k := 0; s := [ ]; r := ""; for c in z do if c = 'x' then i := i + 1; k := k + 1; s[k] := x[i]; Append(r, String(x[i])); else j := j + 1; b := s[k]; k := k - 1; a := s[k]; p := y[j]; r[Size(r) + 1] := p; if p = '+' then a := a + b; elif p = '-' then a := a - b; elif p = '*' then a := a * b; elif p = '/' then if b = 0 then continue; else a := a / b; fi; else return fail; fi; s[k] := a; fi; od; if s[1] = 24 then return r; else return fail; fi; end;
Player24 := function(digits) local u, v, w, x, y, z, r; u := PermutationsList(digits); v := Tuples("+-*/", 3); w := ["xx*x*x*", "xx*xx**", "xxx**x*", "xxx*x**", "xxxx***"]; for x in u do for y in v do for z in w do r := check(x, y, z); if r <> fail then return r; fi; od; od; od; return fail; end;
Player24([1,2,7,7]);
- "77*1-2/"
Player24([9,8,7,6]);
- "68*97-/"
Player24([1,1,7,7]);
- fail
- Solutions with only one distinct digit are found only for 3, 4, 5, 6:
Player24([3,3,3,3]);
- "33*3*3-"
Player24([4,4,4,4]);
- "44*4+4+"
Player24([5,5,5,5]);
- "55*55/-"
Player24([6,6,6,6]);
- "66*66+-"
- A tricky one:
Player24([3,3,8,8]); "8383/-/"</lang>
Go
<lang go>package main
import ( "fmt" "math/rand" "time" )
const ( op_num = iota op_add op_sub op_mul op_div )
type frac struct { num, denom int }
// Expression: can either be a single number, or a result of binary // operation from left and right node type Expr struct { op int left, right *Expr value frac }
var n_cards = 4 var goal = 24 var digit_range = 9
func (x *Expr) String() string { if x.op == op_num { return fmt.Sprintf("%d", x.value.num) }
var bl1, br1, bl2, br2, opstr string switch { case x.left.op == op_num: case x.left.op >= x.op: case x.left.op == op_add && x.op == op_sub: bl1, br1 = "", "" default: bl1, br1 = "(", ")" }
if x.right.op == op_num || x.op < x.right.op { bl2, br2 = "", "" } else { bl2, br2 = "(", ")" }
switch { case x.op == op_add: opstr = " + " case x.op == op_sub: opstr = " - " case x.op == op_mul: opstr = " * " case x.op == op_div: opstr = " / " }
return bl1 + x.left.String() + br1 + opstr + bl2 + x.right.String() + br2 }
func expr_eval(x *Expr) (f frac) { if x.op == op_num { return x.value }
l, r := expr_eval(x.left), expr_eval(x.right)
switch x.op { case op_add: f.num = l.num*r.denom + l.denom*r.num f.denom = l.denom * r.denom return
case op_sub: f.num = l.num*r.denom - l.denom*r.num f.denom = l.denom * r.denom return
case op_mul: f.num = l.num * r.num f.denom = l.denom * r.denom return
case op_div: f.num = l.num * r.denom f.denom = l.denom * r.num return } return }
func solve(ex_in []*Expr) bool { // only one expression left, meaning all numbers are arranged into // a binary tree, so evaluate and see if we get 24 if len(ex_in) == 1 { f := expr_eval(ex_in[0]) if f.denom != 0 && f.num == f.denom*goal { fmt.Println(ex_in[0].String()) return true } return false }
var node Expr ex := make([]*Expr, len(ex_in)-1)
// try to combine a pair of expressions into one, thus reduce // the list length by 1, and recurse down for i := range ex { copy(ex[i:len(ex)], ex_in[i+1:len(ex_in)])
ex[i] = &node for j := i + 1; j < len(ex_in); j++ { node.left = ex_in[i] node.right = ex_in[j]
// try all 4 operators for o := op_add; o <= op_div; o++ { node.op = o if solve(ex) { return true } }
// also - and / are not commutative, so swap arguments node.left = ex_in[j] node.right = ex_in[i]
node.op = op_sub if solve(ex) { return true }
node.op = op_div if solve(ex) { return true }
if j < len(ex) { ex[j] = ex_in[j] } } ex[i] = ex_in[i] } return false }
func main() { cards := make([]*Expr, n_cards) rand.Seed(time.Now().Unix())
for k := 0; k < 10; k++ { for i := 0; i < n_cards; i++ { cards[i] = &Expr{op_num, nil, nil, frac{rand.Intn(digit_range-1) + 1, 1}} fmt.Printf(" %d", cards[i].value.num) } fmt.Print(": ") if !solve(cards) { fmt.Println("No solution") } } }</lang>
- Output:
8 6 7 6: No solution 7 2 6 6: (7 - 2) * 6 - 6 4 8 7 3: 4 * (7 - 3) + 8 3 8 8 7: 3 * 8 * (8 - 7) 5 7 3 7: No solution 5 7 8 3: 5 * 7 - 8 - 3 3 6 5 2: ((3 + 5) * 6) / 2 8 4 5 4: (8 - 4) * 5 + 4 2 2 8 8: (2 + 2) * 8 - 8 6 8 8 2: 6 + 8 + 8 + 2
Gosu
<lang Gosu> uses java.lang.Integer uses java.lang.Double uses java.lang.System uses java.util.ArrayList uses java.util.LinkedList uses java.util.List uses java.util.Scanner uses java.util.Stack
function permutations<T>( lst : List<T> ) : List<List<T>> {
if( lst.size() == 0 ) return {}
if( lst.size() == 1 ) return { lst }
var pivot = lst.get(lst.size()-1)
var sublist = new ArrayList<T>( lst ) sublist.remove( sublist.size() - 1 )
var subPerms = permutations( sublist )
var ret = new ArrayList<List<T>>()
for( x in subPerms ) {
for( e in x index i ) {
var next = new LinkedList<T>( x )
next.add( i, pivot )
ret.add( next )
}
x.add( pivot )
ret.add( x )
}
return ret
}
function readVals() : List<Integer> {
var line = new java.io.BufferedReader( new java.io.InputStreamReader( System.in ) ).readLine() var scan = new Scanner( line )
var ret = new ArrayList<Integer>()
for( i in 0..3 ) {
var next = scan.nextInt()
if( 0 >= next || next >= 10 ) {
print( "Invalid entry: ${next}" )
return null
}
ret.add( next )
}
return ret
}
function getOp( i : int ) : char[] {
var ret = new char[3]
var ops = { '+', '-', '*', '/' }
ret[0] = ops[i / 16]
ret[1] = ops[(i / 4) % 4 ]
ret[2] = ops[i % 4 ]
return ret
}
function isSoln( nums : List<Integer>, ops : char[] ) : boolean {
var stk = new Stack<Double>()
for( n in nums ) {
stk.push( n )
}
for( c in ops ) {
var r = stk.pop().doubleValue()
var l = stk.pop().doubleValue()
if( c == '+' ) {
stk.push( l + r )
} else if( c == '-' ) {
stk.push( l - r )
} else if( c == '*' ) {
stk.push( l * r )
} else if( c == '/' ) {
// Avoid division by 0
if( r == 0.0 ) {
return false
}
stk.push( l / r )
}
}
return java.lang.Math.abs( stk.pop().doubleValue() - 24.0 ) < 0.001
}
function printSoln( nums : List<Integer>, ops : char[] ) {
// RPN: a b c d + - *
// Infix (a * (b - (c + d)))
print( "Found soln: (${nums.get(0)} ${ops[0]} (${nums.get(1)} ${ops[1]} (${nums.get(2)} ${ops[2]} ${nums.get(3)})))" )
}
System.out.print( "#> " ) var vals = readVals()
var opPerms = 0..63 var solnFound = false
for( i in permutations( vals ) ) {
for( j in opPerms ) {
var opList = getOp( j )
if( isSoln( i, opList ) ) {
printSoln( i, opList )
solnFound = true
}
}
}
if( ! solnFound ) {
print( "No solution!" )
} </lang>
Haskell
<lang haskell>import Data.List import Data.Ratio import Control.Monad import System.Environment (getArgs)
data Expr = Constant Rational |
Expr :+ Expr | Expr :- Expr | Expr :* Expr | Expr :/ Expr deriving (Eq)
ops = [(:+), (:-), (:*), (:/)]
instance Show Expr where
show (Constant x) = show $ numerator x
-- In this program, we need only print integers.
show (a :+ b) = strexp "+" a b
show (a :- b) = strexp "-" a b
show (a :* b) = strexp "*" a b
show (a :/ b) = strexp "/" a b
strexp :: String -> Expr -> Expr -> String strexp op a b = "(" ++ show a ++ " " ++ op ++ " " ++ show b ++ ")"
templates :: [[Expr] -> Expr] templates = do
op1 <- ops
op2 <- ops
op3 <- ops
[\[a, b, c, d] -> op1 a $ op2 b $ op3 c d,
\[a, b, c, d] -> op1 (op2 a b) $ op3 c d,
\[a, b, c, d] -> op1 a $ op2 (op3 b c) d,
\[a, b, c, d] -> op1 (op2 a $ op3 b c) d,
\[a, b, c, d] -> op1 (op2 (op3 a b) c) d]
eval :: Expr -> Maybe Rational eval (Constant c) = Just c eval (a :+ b) = liftM2 (+) (eval a) (eval b) eval (a :- b) = liftM2 (-) (eval a) (eval b) eval (a :* b) = liftM2 (*) (eval a) (eval b) eval (a :/ b) = do
denom <- eval b guard $ denom /= 0 liftM (/ denom) $ eval a
solve :: Rational -> [Rational] -> [Expr] solve target r4 = filter (maybe False (== target) . eval) $
liftM2 ($) templates $ nub $ permutations $ map Constant r4
main = getArgs >>= mapM_ print . solve 24 . map (toEnum . read)</lang>
Example use:
$ runghc 24Player.hs 2 3 8 9 (8 * (9 - (3 * 2))) (8 * (9 - (2 * 3))) ((9 - (2 * 3)) * 8) ((9 - (3 * 2)) * 8) ((9 - 3) * (8 / 2)) ((8 / 2) * (9 - 3)) (8 * ((9 - 3) / 2)) (((9 - 3) / 2) * 8) ((9 - 3) / (2 / 8)) ((8 * (9 - 3)) / 2) (((9 - 3) * 8) / 2) (8 / (2 / (9 - 3)))
Alternative version
<lang haskell>import Control.Applicative import Data.List import Text.PrettyPrint
data Expr = C Int | Op String Expr Expr
toDoc (C x ) = int x toDoc (Op op x y) = parens $ toDoc x <+> text op <+> toDoc y
ops :: [(String, Int -> Int -> Int)] ops = [("+",(+)), ("-",(-)), ("*",(*)), ("/",div)]
solve :: Int -> [Int] -> [Expr]
solve res = filter ((Just res ==) . eval) . genAst
where
genAst [x] = [C x]
genAst xs = do
(ys,zs) <- split xs
let f (Op op _ _) = op `notElem` ["+","*"] || ys <= zs
filter f $ Op <$> map fst ops <*> genAst ys <*> genAst zs
eval (C x ) = Just x eval (Op "/" _ y) | Just 0 <- eval y = Nothing eval (Op op x y) = lookup op ops <*> eval x <*> eval y
select :: Int -> [Int] -> Int
select 0 _ = [[]]
select n xs = [x:zs | k <- [0..length xs - n]
, let (x:ys) = drop k xs
, zs <- select (n - 1) ys
]
split :: [Int] -> [([Int],[Int])] split xs = [(ys, xs \\ ys) | n <- [1..length xs - 1]
, ys <- nub . sort $ select n xs
]
main = mapM_ (putStrLn . render . toDoc) $ solve 24 [2,3,8,9]</lang>
- Output:
((8 / 2) * (9 - 3)) ((2 / 9) + (3 * 8)) ((3 * 8) - (2 / 9)) ((8 - (2 / 9)) * 3) (((2 / 9) + 8) * 3) (((8 + 9) / 2) * 3) ((2 + (8 * 9)) / 3) ((3 - (2 / 9)) * 8) ((9 - (2 * 3)) * 8) (((2 / 9) + 3) * 8) (((2 + 9) / 3) * 8) (((9 - 3) / 2) * 8) (((9 - 3) * 8) / 2)
Icon and Unicon
This shares code with and solves the 24 game. A series of pattern expressions are built up and then populated with the permutations of the selected digits. Equations are skipped if they have been seen before. The procedure 'eval' was modified to catch zero divides. The solution will find either all occurrences or just the first occurrence of a solution.
<lang Icon>invocable all link strings # for csort, deletec, permutes
procedure main() static eL initial {
eoP := [] # set-up expression and operator permutation patterns
every ( e := !["a@b#c$d", "a@(b#c)$d", "a@b#(c$d)", "a@(b#c$d)", "a@(b#(c$d))"] ) &
( o := !(opers := "+-*/") || !opers || !opers ) do
put( eoP, map(e,"@#$",o) ) # expr+oper perms
eL := [] # all cases
every ( e := !eoP ) & ( p := permutes("wxyz") ) do
put(eL, map(e,"abcd",p))
}
write("This will attempt to find solutions to 24 for sets of numbers by\n",
"combining 4 single digits between 1 and 9 to make 24 using only + - * / and ( ).\n",
"All operations have equal precedence and are evaluated left to right.\n",
"Enter 'use n1 n2 n3 n4' or just hit enter (to use a random set),",
"'first'/'all' shows the first or all solutions, 'quit' to end.\n\n")
repeat {
e := trim(read()) | fail
e ? case tab(find(" ")|0) of {
"q"|"quit" : break
"u"|"use" : e := tab(0)
"f"|"first": first := 1 & next
"a"|"all" : first := &null & next
"" : e := " " ||(1+?8) || " " || (1+?8) ||" " || (1+?8) || " " || (1+?8)
}
writes("Attempting to solve 24 for",e)
e := deletec(e,' \t') # no whitespace
if e ? ( tab(many('123456789')), pos(5), pos(0) ) then
write(":")
else write(" - invalid, only the digits '1..9' are allowed.") & next
eS := set()
every ex := map(!eL,"wxyz",e) do {
if member(eS,ex) then next # skip duplicates of final expression
insert(eS,ex)
if ex ? (ans := eval(E()), pos(0)) then # parse and evaluate
if ans = 24 then {
write("Success ",image(ex)," evaluates to 24.")
if \first then break
}
}
}
write("Quiting.") end
procedure eval(X) #: return the evaluated AST
if type(X) == "list" then {
x := eval(get(X))
while o := get(X) do
if y := get(X) then
x := o( real(x), (o ~== "/" | fail, eval(y) ))
else write("Malformed expression.") & fail
}
return \x | X
end
procedure E() #: expression
put(lex := [],T())
while put(lex,tab(any('+-*/'))) do
put(lex,T())
suspend if *lex = 1 then lex[1] else lex # strip useless []
end
procedure T() #: Term
suspend 2(="(", E(), =")") | # parenthesized subexpression, or ...
tab(any(&digits)) # just a value
end</lang>
strings.icn provides deletec and permutes
J
<lang J>perm=: (A.&i.~ !) 4 ops=: ' ',.'+-*%' {~ >,{i.each 4 4 4 cmask=: 1 + 0j1 * i.@{:@$@[ e. ] left=: [ #!.'('~"1 cmask right=: [ #!.')'~"1 cmask paren=: 2 :'[: left&m right&n' parens=: ], 0 paren 3, 0 paren 5, 2 paren 5, [: 0 paren 7 (0 paren 3) all=: [: parens [:,/ ops ,@,."1/ perm { [:;":each answer=: ({.@#~ 24 = ".)@all</lang>
This implementation tests all 7680 candidate sentences.
Example use:
answer 2 3 5 7 2+7+3*5 answer 8 4 7 1 8*7-4*1 answer 1 1 2 7 (1+2)*1+7
The answer will be either a suitable J sentence or blank if none can be found. "J sentence" means that, for example, the sentence 8*7-4*1 is equivalent to the sentence 8*(7-(4*1)). [Many infix languages use operator precedence to make polynomials easier to express without parenthesis, but J has other mechanisms for expressing polynomials and minimal operator precedence makes the language more regular.]
Here is an alternative version that supports multi-digit numbers. It prefers expressions without parens, but searches for ones with if needed.
<lang J>ops=: > , { 3#<'+-*%' perms=: [: ":"0 [: ~. i.@!@# A. ] build=: 1 : '(#~ 24 = ".) @: u'
combp=: dyad define 'a b c d'=. y['f g h'=. x ('(',a,f,b,g,c,')',h,d),('(',a,f,b,')',g,c,h,d),(a,f,'(',b,g,c,')',h,d),:('((',a,f,b,')',g,c,')',h,d) )
math24=: monad define assert. 4 = # y NB. prefer expressions without parens & fallback if needed es=. ([: ,/ ops ([: , (' ',[) ,. ])"1 2/ perms) build y if. 0 = #es do. es =. ([: ,/ [: ,/ ops combp"1 2/ perms) build y end. es -."1 ' ' )</lang>
- Output:
math24 2 3 5 12 12%3-5%2 math24 2 3 8 9 8*9-2*3 8*9-3*2 8%2%9-3 math24 3 6 6 11 (6+6*11)%3 (6+11*6)%3 ((6*11)+6)%3 ((11*6)+6)%3
Java
Playable version, will print solution on request.
Note that this version does not extend to different digit ranges. <lang java>import java.util.*;
public class Game24Player {
final String[] patterns = {"nnonnoo", "nnonono", "nnnoono", "nnnonoo",
"nnnnooo"};
final String ops = "+-*/^";
String solution; List<Integer> digits;
public static void main(String[] args) {
new Game24Player().play();
}
void play() {
digits = getSolvableDigits();
Scanner in = new Scanner(System.in);
while (true) {
System.out.print("Make 24 using these digits: ");
System.out.println(digits);
System.out.println("(Enter 'q' to quit, 's' for a solution)");
System.out.print("> ");
String line = in.nextLine();
if (line.equalsIgnoreCase("q")) {
System.out.println("\nThanks for playing");
return;
}
if (line.equalsIgnoreCase("s")) {
System.out.println(solution);
digits = getSolvableDigits();
continue;
}
char[] entry = line.replaceAll("[^*+-/)(\\d]", "").toCharArray();
try {
validate(entry);
if (evaluate(infixToPostfix(entry))) {
System.out.println("\nCorrect! Want to try another? ");
digits = getSolvableDigits();
} else {
System.out.println("\nNot correct.");
}
} catch (Exception e) {
System.out.printf("%n%s Try again.%n", e.getMessage());
}
}
}
void validate(char[] input) throws Exception {
int total1 = 0, parens = 0, opsCount = 0;
for (char c : input) {
if (Character.isDigit(c))
total1 += 1 << (c - '0') * 4;
else if (c == '(')
parens++;
else if (c == ')')
parens--;
else if (ops.indexOf(c) != -1)
opsCount++;
if (parens < 0)
throw new Exception("Parentheses mismatch.");
}
if (parens != 0)
throw new Exception("Parentheses mismatch.");
if (opsCount != 3)
throw new Exception("Wrong number of operators.");
int total2 = 0;
for (int d : digits)
total2 += 1 << d * 4;
if (total1 != total2)
throw new Exception("Not the same digits.");
}
boolean evaluate(char[] line) throws Exception {
Stack<Float> s = new Stack<>();
try {
for (char c : line) {
if ('0' <= c && c <= '9')
s.push((float) c - '0');
else
s.push(applyOperator(s.pop(), s.pop(), c));
}
} catch (EmptyStackException e) {
throw new Exception("Invalid entry.");
}
return (Math.abs(24 - s.peek()) < 0.001F);
}
float applyOperator(float a, float b, char c) {
switch (c) {
case '+':
return a + b;
case '-':
return b - a;
case '*':
return a * b;
case '/':
return b / a;
default:
return Float.NaN;
}
}
List<Integer> randomDigits() {
Random r = new Random();
List<Integer> result = new ArrayList<>(4);
for (int i = 0; i < 4; i++)
result.add(r.nextInt(9) + 1);
return result;
}
List<Integer> getSolvableDigits() {
List<Integer> result;
do {
result = randomDigits();
} while (!isSolvable(result));
return result;
}
boolean isSolvable(List<Integer> digits) {
Set<List<Integer>> dPerms = new HashSet<>(4 * 3 * 2);
permute(digits, dPerms, 0);
int total = 4 * 4 * 4;
List<List<Integer>> oPerms = new ArrayList<>(total);
permuteOperators(oPerms, 4, total);
StringBuilder sb = new StringBuilder(4 + 3);
for (String pattern : patterns) {
char[] patternChars = pattern.toCharArray();
for (List<Integer> dig : dPerms) {
for (List<Integer> opr : oPerms) {
int i = 0, j = 0;
for (char c : patternChars) {
if (c == 'n')
sb.append(dig.get(i++));
else
sb.append(ops.charAt(opr.get(j++)));
}
String candidate = sb.toString();
try {
if (evaluate(candidate.toCharArray())) {
solution = postfixToInfix(candidate);
return true;
}
} catch (Exception ignored) {
}
sb.setLength(0);
}
}
}
return false;
}
String postfixToInfix(String postfix) {
class Expression {
String op, ex;
int prec = 3;
Expression(String e) {
ex = e;
}
Expression(String e1, String e2, String o) {
ex = String.format("%s %s %s", e1, o, e2);
op = o;
prec = ops.indexOf(o) / 2;
}
}
Stack<Expression> expr = new Stack<>();
for (char c : postfix.toCharArray()) {
int idx = ops.indexOf(c);
if (idx != -1) {
Expression r = expr.pop();
Expression l = expr.pop();
int opPrec = idx / 2;
if (l.prec < opPrec)
l.ex = '(' + l.ex + ')';
if (r.prec <= opPrec)
r.ex = '(' + r.ex + ')';
expr.push(new Expression(l.ex, r.ex, "" + c));
} else {
expr.push(new Expression("" + c));
}
}
return expr.peek().ex;
}
char[] infixToPostfix(char[] infix) throws Exception {
StringBuilder sb = new StringBuilder();
Stack<Integer> s = new Stack<>();
try {
for (char c : infix) {
int idx = ops.indexOf(c);
if (idx != -1) {
if (s.isEmpty())
s.push(idx);
else {
while (!s.isEmpty()) {
int prec2 = s.peek() / 2;
int prec1 = idx / 2;
if (prec2 >= prec1)
sb.append(ops.charAt(s.pop()));
else
break;
}
s.push(idx);
}
} else if (c == '(') {
s.push(-2);
} else if (c == ')') {
while (s.peek() != -2)
sb.append(ops.charAt(s.pop()));
s.pop();
} else {
sb.append(c);
}
}
while (!s.isEmpty())
sb.append(ops.charAt(s.pop()));
} catch (EmptyStackException e) {
throw new Exception("Invalid entry.");
}
return sb.toString().toCharArray();
}
void permute(List<Integer> lst, Set<List<Integer>> res, int k) {
for (int i = k; i < lst.size(); i++) {
Collections.swap(lst, i, k);
permute(lst, res, k + 1);
Collections.swap(lst, k, i);
}
if (k == lst.size())
res.add(new ArrayList<>(lst));
}
void permuteOperators(List<List<Integer>> res, int n, int total) {
for (int i = 0, npow = n * n; i < total; i++)
res.add(Arrays.asList((i / npow), (i % npow) / n, i % n));
}
}</lang>
- Output:
Make 24 using these digits: [5, 7, 1, 8] (Enter 'q' to quit, 's' for a solution) > (8-5) * (7+1) Correct! Want to try another? Make 24 using these digits: [3, 9, 2, 9] (Enter 'q' to quit, 's' for a solution) > (3*2) + 9 + 9 Correct! Want to try another? Make 24 using these digits: [4, 4, 8, 5] (Enter 'q' to quit, 's' for a solution) > s 4 * 5 - (4 - 8) Make 24 using these digits: [2, 5, 9, 1] (Enter 'q' to quit, 's' for a solution) > 2+5+9+1 Not correct. Make 24 using these digits: [2, 5, 9, 1] (Enter 'q' to quit, 's' for a solution) > 2 * 9 + 5 + 1 Correct! Want to try another? Make 24 using these digits: [8, 4, 3, 1] (Enter 'q' to quit, 's' for a solution) > s (8 + 4) * (3 - 1) Make 24 using these digits: [9, 4, 5, 6] (Enter 'q' to quit, 's' for a solution) > (9 +4) * 2 - 2 Not the same digits. Try again. Make 24 using these digits: [9, 4, 5, 6] (Enter 'q' to quit, 's' for a solution) > q Thanks for playing
JavaScript
This is a translation of the C code. <lang javascript>var ar=[],order=[0,1,2],op=[],val=[]; var NOVAL=9999,oper="+-*/",out;
function rnd(n){return Math.floor(Math.random()*n)}
function say(s){
try{document.write(s+"
")}
catch(e){WScript.Echo(s)}
}
function getvalue(x,dir){
var r=NOVAL;
if(dir>0)++x;
while(1){
if(val[x]!=NOVAL){
r=val[x];
val[x]=NOVAL;
break;
}
x+=dir;
}
return r*1;
}
function calc(){
var c=0,l,r,x;
val=ar.join('/').split('/');
while(c<3){
x=order[c];
l=getvalue(x,-1);
r=getvalue(x,1);
switch(op[x]){
case 0:val[x]=l+r;break;
case 1:val[x]=l-r;break;
case 2:val[x]=l*r;break;
case 3:
if(!r||l%r)return 0;
val[x]=l/r;
}
++c;
}
return getvalue(-1,1);
}
function shuffle(s,n){
var x=n,p=eval(s),r,t;
while(x--){
r=rnd(n);
t=p[x];
p[x]=p[r];
p[r]=t;
}
}
function parenth(n){
while(n>0)--n,out+='(';
while(n<0)++n,out+=')';
}
function getpriority(x){
for(var z=3;z--;)if(order[z]==x)return 3-z; return 0;
}
function showsolution(){
var x=0,p=0,lp=0,v=0;
while(x<4){
if(x<3){
lp=p;
p=getpriority(x);
v=p-lp;
if(v>0)parenth(v);
}
out+=ar[x];
if(x<3){
if(v<0)parenth(v);
out+=oper.charAt(op[x]);
}
++x;
}
parenth(-p);
say(out);
}
function solve24(s){
var z=4,r;
while(z--)ar[z]=s.charCodeAt(z)-48;
out="";
for(z=100000;z--;){
r=rnd(256);
op[0]=r&3;
op[1]=(r>>2)&3;
op[2]=(r>>4)&3;
shuffle("ar",4);
shuffle("order",3);
if(calc()!=24)continue;
showsolution();
break;
}
}
solve24("1234"); solve24("6789"); solve24("1127");</lang>
Examples:
(((3*1)*4)*2) ((6*8)/((9-7))) (((1+7))*(2+1))
jq
The following solution is generic: the objective (e.g. 24) is specified as the argument to solve/1, and the user may specify any number of numbers.
Infrastructure: <lang jq># Generate a stream of the permutations of the input array. def permutations:
if length == 0 then [] else range(0;length) as $i | [.[$i]] + (del(.[$i])|permutations) end ;
- Generate a stream of arrays of length n,
- with members drawn from the input array.
def take(n):
length as $l | if n == 1 then range(0;$l) as $i | [ .[$i] ] else take(n-1) + take(1) end;
- Emit an array with elements that alternate between those in the input array and those in short,
- starting with the former, and using nothing if "short" is too too short.
def intersperse(short):
. as $in
| reduce range(0;length) as $i
([]; . + [ $in[$i], (short[$i] // empty) ]);
- Emit a stream of all the nested triplet groupings of the input array elements,
- e.g. [1,2,3,4,5] =>
- [1,2,[3,4,5]]
- [[1,2,3],4,5]
def triples:
. as $in
| if length == 3 then .
elif length == 1 then $in[0]
elif length < 3 then empty
else
(range(0; (length-1) / 2) * 2 + 1) as $i
| ($in[0:$i] | triples) as $head
| ($in[$i+1:] | triples) as $tail
| [$head, $in[$i], $tail]
end;</lang>
Evaluation and pretty-printing of allowed expressions <lang jq># Evaluate the input, which must be a number or a triple: [x, op, y] def eval:
if type == "array" then
.[1] as $op
| if .[0] == null or .[2] == null then null
else
(.[0] | eval) as $left | (.[2] | eval) as $right
| if $left == null or $right == null then null
elif $op == "+" then $left + $right
elif $op == "-" then $left - $right
elif $op == "*" then $left * $right
elif $op == "/" then
if $right == 0 then null
else $left / $right
end
else "invalid arithmetic operator: \($op)" | error
end
end else . end;
def pp:
"\(.)" | explode | map([.] | implode | if . == "," then " " elif . == "\"" then "" else . end) | join("");</lang>
24 Game: <lang jq>def OPERATORS: ["+", "-", "*", "/"];
- Input: an array of 4 digits
- o: an array of 3 operators
- Output: a stream
def EXPRESSIONS(o):
intersperse( o ) | triples;
def solve(objective):
length as $length | [ (OPERATORS | take($length-1)) as $poperators | permutations | EXPRESSIONS($poperators) | select( eval == objective) ] as $answers | if $answers|length > 3 then "That was too easy. I found \($answers|length) answers, e.g. \($answers[0] | pp)" elif $answers|length > 1 then $answers[] | pp else "You lose! There are no solutions." end
solve(24), "Please try again."</lang>
- Output:
<lang sh>$ jq -r -f Solve.jq [1,2,3,4] That was too easy. I found 242 answers, e.g. [4 * [1 + [2 + 3]]] Please try again. [1,2,3,40,1] That was too easy. I found 636 answers, e.g. [[[1 / 2] * 40] + [3 + 1]] Please try again. [3,8,9] That was too easy. I found 8 answers, e.g. [[8 / 3] * 9] Please try again. [4,5,6] You lose! There are no solutions. Please try again. [1,2,3,4,5,6] That was too easy. I found 197926 answers, e.g. [[2 * [1 + 4]] + [3 + [5 + 6]]] Please try again.</lang>
Julia
For julia version 0.5 and higher, the Combinatorics package must be installed and imported (`using Combinatorics`). Combinatorial functions like `nthperm` have been moved from Base to that package and are not available by default anymore. <lang julia>function solve24(nums)
length(nums) != 4 && error("Input must be a 4-element Array")
syms = [+,-,*,/]
for x in syms, y in syms, z in syms
for i = 1:24
a,b,c,d = nthperm(nums,i)
if round(x(y(a,b),z(c,d)),5) == 24
return "($a$y$b)$x($c$z$d)"
elseif round(x(a,y(b,z(c,d))),5) == 24
return "$a$x($b$y($c$z$d))"
elseif round(x(y(z(c,d),b),a),5) == 24
return "(($c$z$d)$y$b)$x$a"
elseif round(x(y(b,z(c,d)),a),5) == 24
return "($b$y($c$z$d))$x$a"
end
end
end
return "0"
end</lang>
- Output:
julia> for i in 1:10
nums = rand(1:9, 4)
println("solve24($nums) -> $(solve24(nums))")
end
solve24([9,4,4,5]) -> 0
solve24([1,7,2,7]) -> ((7*7)-1)/2
solve24([5,7,5,4]) -> 4*(7-(5/5))
solve24([1,4,6,6]) -> 6+(6*(4-1))
solve24([2,3,7,3]) -> ((2+7)*3)-3
solve24([8,7,9,7]) -> 0
solve24([1,6,2,6]) -> 6+(6*(1+2))
solve24([7,9,4,1]) -> (7-4)*(9-1)
solve24([6,4,2,2]) -> (2-2)+(6*4)
solve24([5,7,9,7]) -> (5+7)*(9-7)
Kotlin
<lang scala>// version 1.1.3
import java.util.Random
const val N_CARDS = 4 const val SOLVE_GOAL = 24 const val MAX_DIGIT = 9
class Frac(val num: Int, val den: Int)
enum class OpType { NUM, ADD, SUB, MUL, DIV }
class Expr(
var op: OpType = OpType.NUM, var left: Expr? = null, var right: Expr? = null, var value: Int = 0
)
fun showExpr(e: Expr?, prec: OpType, isRight: Boolean) {
if (e == null) return
val op = when (e.op) {
OpType.NUM -> { print(e.value); return }
OpType.ADD -> " + "
OpType.SUB -> " - "
OpType.MUL -> " x "
OpType.DIV -> " / "
}
if ((e.op == prec && isRight) || e.op < prec) print("(")
showExpr(e.left, e.op, false)
print(op)
showExpr(e.right, e.op, true)
if ((e.op == prec && isRight) || e.op < prec) print(")")
}
fun evalExpr(e: Expr?): Frac {
if (e == null) return Frac(0, 1)
if (e.op == OpType.NUM) return Frac(e.value, 1)
val l = evalExpr(e.left)
val r = evalExpr(e.right)
return when (e.op) {
OpType.ADD -> Frac(l.num * r.den + l.den * r.num, l.den * r.den)
OpType.SUB -> Frac(l.num * r.den - l.den * r.num, l.den * r.den)
OpType.MUL -> Frac(l.num * r.num, l.den * r.den)
OpType.DIV -> Frac(l.num * r.den, l.den * r.num)
else -> throw IllegalArgumentException("Unknown op: ${e.op}")
}
}
fun solve(ea: Array<Expr?>, len: Int): Boolean {
if (len == 1) {
val final = evalExpr(ea[0])
if (final.num == final.den * SOLVE_GOAL && final.den != 0) {
showExpr(ea[0], OpType.NUM, false)
return true
}
}
val ex = arrayOfNulls<Expr>(N_CARDS)
for (i in 0 until len - 1) {
for (j in i + 1 until len) ex[j - 1] = ea[j]
val node = Expr()
ex[i] = node
for (j in i + 1 until len) {
node.left = ea[i]
node.right = ea[j]
for (k in OpType.values().drop(1)) {
node.op = k
if (solve(ex, len - 1)) return true
}
node.left = ea[j]
node.right = ea[i]
node.op = OpType.SUB
if (solve(ex, len - 1)) return true
node.op = OpType.DIV
if (solve(ex, len - 1)) return true
ex[j] = ea[j]
}
ex[i] = ea[i]
}
return false
}
fun solve24(n: IntArray) =
solve (Array(N_CARDS) { Expr(value = n[it]) }, N_CARDS)
fun main(args: Array<String>) {
val r = Random()
val n = IntArray(N_CARDS)
for (j in 0..9) {
for (i in 0 until N_CARDS) {
n[i] = 1 + r.nextInt(MAX_DIGIT)
print(" ${n[i]}")
}
print(": ")
println(if (solve24(n)) "" else "No solution")
}
}</lang>
Sample output:
8 4 1 7: (8 - 4) x (7 - 1) 6 1 4 1: ((6 + 1) - 1) x 4 8 8 5 4: (8 / 8 + 5) x 4 9 6 9 8: 8 / ((9 - 6) / 9) 6 6 9 6: (6 x 6) / 9 x 6 9 9 7 7: No solution 1 1 2 5: No solution 6 9 4 1: 6 x (9 - 4 - 1) 7 7 6 4: 7 + 7 + 6 + 4 4 8 8 4: 4 + 8 + 8 + 4
Liberty BASIC
<lang lb>dim d(4) input "Enter 4 digits: "; a$ nD=0 for i =1 to len(a$)
c$=mid$(a$,i,1)
if instr("123456789",c$) then
nD=nD+1
d(nD)=val(c$)
end if
next 'for i = 1 to 4 ' print d(i); 'next
'precompute permutations. Dumb way. nPerm = 1*2*3*4 dim perm(nPerm, 4) n = 0 for i = 1 to 4
for j = 1 to 4
for k = 1 to 4
for l = 1 to 4
'valid permutation (no dupes?)
if i<>j and i<>k and i<>l _
and j<>k and j<>l _
and k<>l then
n=n+1
'
' perm(n,1)=i ' perm(n,2)=j ' perm(n,3)=k ' perm(n,4)=l
'actually, we can as well permute given digits
perm(n,1)=d(i)
perm(n,2)=d(j)
perm(n,3)=d(k)
perm(n,4)=d(l)
end if
next
next
next
next 'check if permutations look OK. They are 'for i =1 to n ' print i, ' for j =1 to 4: print perm(i,j);:next ' print 'next
'possible brackets NBrackets = 11 dim Brakets$(NBrackets) DATA "4#4#4#4" DATA "(4#4)#4#4" DATA "4#(4#4)#4" DATA "4#4#(4#4)" DATA "(4#4)#(4#4)" DATA "(4#4#4)#4" DATA "4#(4#4#4)" DATA "((4#4)#4)#4" DATA "(4#(4#4))#4" DATA "4#((4#4)#4)" DATA "4#(4#(4#4))" for i = 1 to NBrackets
read Tmpl$: Brakets$(i) = Tmpl$
next
'operations: full search count = 0 Ops$="+ - * /" dim Op$(3) For op1=1 to 4
Op$(1)=word$(Ops$,op1)
For op2=1 to 4
Op$(2)=word$(Ops$,op2)
For op3=1 to 4
Op$(3)=word$(Ops$,op3)
'print "*"
'substitute all brackets
for t = 1 to NBrackets
Tmpl$=Brakets$(t)
'print , Tmpl$
'now, substitute all digits: permutations.
for p = 1 to nPerm
res$= ""
nOp=0
nD=0
for i = 1 to len(Tmpl$)
c$ = mid$(Tmpl$, i, 1)
select case c$
case "#" 'operations
nOp = nOp+1
res$ = res$+Op$(nOp)
case "4" 'digits
nD = nOp+1
res$ = res$; perm(p,nD)
case else 'brackets goes here
res$ = res$+ c$
end select
next
'print,, res$
'eval here
if evalWithErrCheck(res$) = 24 then
print "24 = ";res$
end 'comment it out if you want to see all versions
end if
count = count + 1
next
next
Next
Next
next
print "If you see this, probably task cannot be solved with these digits" 'print count end
function evalWithErrCheck(expr$)
on error goto [handler] evalWithErrCheck=eval(expr$) exit function
[handler] end function</lang>
Lua
Generic solver: pass card of any size with 1st argument and target number with second.
<lang lua> local SIZE = #arg[1] local GOAL = tonumber(arg[2]) or 24
local input = {} for v in arg[1]:gmatch("%d") do table.insert(input, v) end assert(#input == SIZE, 'Invalid input')
local operations = {'+', '-', '*', '/'}
local function BinaryTrees(vert) if vert == 0 then return {false} else local buf = {} for leften = 0, vert - 1 do local righten = vert - leften - 1 for _, left in pairs(BinaryTrees(leften)) do for _, right in pairs(BinaryTrees(righten)) do table.insert(buf, {left, right}) end end end return buf end end local trees = BinaryTrees(SIZE-1) local c, opc, oper, str local max = math.pow(#operations, SIZE-1) local function op(a,b) opc = opc + 1 local i = math.floor(oper/math.pow(#operations, opc-1))%#operations+1 return '('.. a .. operations[i] .. b ..')' end
local function EvalTree(tree) if tree == false then c = c + 1 return input[c-1] else return op(EvalTree(tree[1]), EvalTree(tree[2])) end end
local function printResult() for _, v in ipairs(trees) do for i = 0, max do c, opc, oper = 1, 0, i str = EvalTree(v) loadstring('res='..str)() if(res == GOAL) then print(str, '=', res) end end end end
local uniq = {} local function permgen (a, n) if n == 0 then local str = table.concat(a) if not uniq[str] then printResult() uniq[str] = true end else for i = 1, n do a[n], a[i] = a[i], a[n] permgen(a, n - 1) a[n], a[i] = a[i], a[n] end end end
permgen(input, SIZE) </lang>
- Output:
$ lua 24game.solve.lua 2389 (8*(9-(3*2))) = 24 (8*((9-3)/2)) = 24 ((8*(9-3))/2) = 24 ((9-3)*(8/2)) = 24 (((9-3)*8)/2) = 24 (8*(9-(2*3))) = 24 (8/(2/(9-3))) = 24 ((8/2)*(9-3)) = 24 ((9-3)/(2/8)) = 24 ((9-(3*2))*8) = 24 (((9-3)/2)*8) = 24 ((9-(2*3))*8) = 24 $ lua 24game.solve.lua 1172 ((1+7)*(2+1)) = 24 ((7+1)*(2+1)) = 24 ((1+2)*(7+1)) = 24 ((2+1)*(7+1)) = 24 ((1+2)*(1+7)) = 24 ((2+1)*(1+7)) = 24 ((1+7)*(1+2)) = 24 ((7+1)*(1+2)) = 24 $ lua 24game.solve.lua 123456789 1000 (2*(3+(4-(5+(6-(7*(8*(9*1)))))))) = 1000 (2*(3+(4-(5+(6-(7*(8*(9/1)))))))) = 1000 (2*(3*(4*(5+(6*(7-(8/(9*1)))))))) = 1000 (2*(3*(4*(5+(6*(7-(8/(9/1)))))))) = 1000 (2*(3+(4-(5+(6-(7*((8*9)*1))))))) = 1000 (2*(3+(4-(5+(6-(7*((8*9)/1))))))) = 1000 (2*(3*(4*(5+(6*(7-((8/9)*1))))))) = 1000 (2*(3*(4*(5+(6*(7-((8/9)/1))))))) = 1000 .....
Mathematica / Wolfram Language
The code: <lang Mathematica> treeR[n_] := Table[o[trees[a], trees[n - a]], {a, 1, n - 1}] treeR[1] := n tree[n_] :=
Flatten[treeR[n] //. {o[a_List, b_] :> (o[#, b] & /@ a),
o[a_, b_List] :> (o[a, #] & /@ b)}]
game24play[val_List] :=
Union[StringReplace[StringTake[ToString[#, InputForm], {10, -2}],
"-1*" ~~ n_ :> "-" <> n] & /@ (HoldForm /@
Select[Union@
Flatten[Outer[# /. {o[q_Integer] :> #2q,
n[q_] :> #3q} &,
Block[{O = 1, N = 1}, # /. {o :> o[O++], n :> n[N++]}] & /@
tree[4], Tuples[{Plus, Subtract, Times, Divide}, 3],
Permutations[Array[v, 4]], 1]],
Quiet[(# /. v[q_] :> valq) == 24] &] /.
Table[v[q] -> valq, {q, 4}])]</lang>
The treeR method recursively computes all possible operator trees for a certain number of inputs. It does this by tabling all combinations of distributions of inputs across the possible values. (For example, treeR[4] is allotted 4 inputs, so it returns {o[treeR[3],treeR[1]],o[treeR[2],treeR[2]],o[treeR[1],treeR[3]]}, where o is the operator (generic at this point).
The base case treeR[1] returns n (the input).
The final output of tree[4] (the 24 game has 4 random inputs) (tree cleans up the output of treeR) is:
{o[n, o[n, o[n, n]]],
o[n, o[o[n, n], n]],
o[o[n, n], o[n, n]],
o[o[n, o[n, n]], n],
o[o[o[n, n], n], n]}
game24play takes the four random numbers as input and does the following (the % refers to code output from previous bullets):
Block[{O = 1, N = 1}, # /. {o :> o[O++], n :> n[N++]}] & /@ tree[4]- Assign ascending numbers to the input and operator placeholders.
- Ex:
o[1][o[2][n[1], n[2]], o[3][n[3], n[4]]]
Tuples[{Plus, Subtract, Times, Divide}, 3]- Find all combinations (
Tuplesallows repeats) of the four allowed operations. - Ex:
{{Plus, Plus, Plus}, {Plus, Plus, Subtract}, <<60>>, {Divide, Divide, Times}, {Divide, Divide, Divide}}
- Find all combinations (
Permutations[Array[v, 4]]- Find all permutations (
Permutationsdoes not allow repeats) of the four given values. - Ex:
{{v[1],v[2],v[3],v[4]}, {v[1],v[2],v[4],v[3]}, <<20>>, {v[4],v[3],v[1],v[2]}, {v[4],v[3],v[2],v[1]}}
- Find all permutations (
Outer[# /. {o[q_Integer] :> #2[[q]], n[q_] :> #3[[q]]} &, %%%, %%, %, 1]- Perform an outer join on the three above lists (every combination of each element) and with each combination put into the first (the operator tree) the second (the operation at each level) and the third (the value indexes, not actual values).
- Ex:
v[1] + v[2] - v[3] + v[4]
Union@Flatten[%]- Get rid of any sublists caused by
Outerand remove any duplicates (Union).
- Get rid of any sublists caused by
Select[%, Quiet[(# /. v[q_] :> val[[q]]) == 24] &]- Select the elements of the above list where substituting the real values returns 24 (and do it
Quietly because of div-0 concerns).
- Select the elements of the above list where substituting the real values returns 24 (and do it
HoldForm /@ % /. Table[v[q] -> val[[q]], {q, 4}]- Apply
HoldFormso that substituting numbers will not cause evaluation (otherwise it would only ever return lists like{24, 24, 24}!) and substitute the numbers in.
- Apply
Union[StringReplace[StringTake[ToString[#, InputForm], {10, -2}], "-1*" ~~ n_ :> "-" <> n] & /@ %]- For each result, turn the expression into a string (for easy manipulation), strip the "
HoldForm" wrapper, replace numbers like "-1*7" with "-7" (a idiosyncrasy of the conversion process), and remove any lingering duplicates. Some duplicates will still remain, notably constructs like "3 - 3" vs. "-3 + 3" and trivially similar expressions like "(8*3)*(6-5)" vs "(8*3)/(6-5)". Example run input and outputs:
- For each result, turn the expression into a string (for easy manipulation), strip the "
<lang Mathematica>game24play[RandomInteger[{1, 9}, 4]]</lang>
- Output:
{7, 2, 9, 5}
{-2 - 9 + 7*5}
{7, 5, 6, 2}
{6*(7 - 5 + 2), (7 - 5)*6*2, 7 + 5 + 6*2}
{7, 6, 7, 7}
{}
{3, 7, 6, 1}
{(-3 + 6)*(7 + 1), ((-3 + 7)*6)/1, (-3 + 7)*6*1,
6 - 3*(-7 + 1), 6*(-3 + 7*1), 6*(-3 + 7/1),
6 + 3*(7 - 1), 6*(7 - 3*1), 6*(7 - 3/1), 7 + 3*6 - 1}
Note that although this program is designed to be extensible to higher numbers of inputs, the largest working set in the program (the output of the Outer function can get very large:
tree[n]returns a list with the length being the (n-1)-th Catalan number.Tuples[{Plus, Subtract, Times, Divide}, 3]has fixed length 64 (or p3 for p operations).Permutations[Array[v, n]]returns permutations.
Therefore, the size of the working set is , where is the quadruple factorial. It goes without saying that this number increases very fast. For this game, the total is 7680 elements. For higher numbers of inputs, it is {7 680, 107 520, 1 935 360, 42 577 920, 1 107 025 920, ...}.
An alternative solution operates on Mathematica expressions directly without using any inert intermediate form for the expression tree, but by using Hold to prevent Mathematica from evaluating the expression tree.
<lang Mathematica>evaluate[HoldForm[op_[l_, r_]]] := op[evaluate[l], evaluate[r]]; evaluate[x_] := x; combine[l_, r_ /; evaluate[r] != 0] := {HoldForm[Plus[l, r]],
HoldForm[Subtract[l, r]], HoldForm[Times[l, r]], HoldForm[Divide[l, r]] };
combine[l_, r_] := {HoldForm[Plus[l, r]], HoldForm[Subtract[l, r]],
HoldForm[Times[l, r]]};
split[items_] :=
Table[{items1 ;; i, items[[i + 1 ;; Length[items]]]}, {i, 1,
Length[items] - 1}];
expressions[{x_}] := {x}; expressions[items_] :=
Flatten[Table[
Flatten[Table[
combine[l, r], {l, expressions[sp1]}, {r,
expressions[sp2]}], 2], {sp, split[items]}]];
(* Must use all atoms in given order. *) solveMaintainOrder[goal_, items_] :=
Select[expressions[items], (evaluate[#] == goal) &];
(* Must use all atoms, but can permute them. *) solveCanPermute[goal_, items_] :=
Flatten[Table[
solveMaintainOrder[goal, pitems], {pitems,
Permutations[items]}]];
(* Can use any subset of atoms. *) solveSubsets[goal_, items_] :=
Flatten[Table[
solveCanPermute[goal, is], {is,
Subsets[items, {1, Length[items]}]}], 2];
(* Demonstration to find all the ways to create 1/5 from {2, 3, 4, 5}. *) solveMaintainOrder[1/5, Range[2, 5]] solveCanPermute[1/5, Range[2, 5]] solveSubsets[1/5, Range[2, 5]]</lang>
Nim
<lang nim>import algorithm, sequtils, strformat
type
Operation = enum opAdd = "+" opSub = "-" opMul = "*" opDiv = "/"
const Ops = @[opAdd, opSub, opMul, opDiv]
func opr(o: Operation, a, b: float): float =
case o of opAdd: a + b of opSub: a - b of opMul: a * b of opDiv: a / b
func solve(nums: array[4, int]): string =
func `~=`(a, b: float): bool = abs(a - b) <= 1e-5
result = "not found"
let sortedNums = nums.sorted.mapIt float it
for i in product Ops.repeat 3:
let (x, y, z) = (i[0], i[1], i[2])
var nums = sortedNums
while true:
let (a, b, c, d) = (nums[0], nums[1], nums[2], nums[3])
if x.opr(y.opr(a, b), z.opr(c, d)) ~= 24.0:
return fmt"({a:0} {y} {b:0}) {x} ({c:0} {z} {d:0})"
if x.opr(a, y.opr(b, z.opr(c, d))) ~= 24.0:
return fmt"{a:0} {x} ({b:0} {y} ({c:0} {z} {d:0}))"
if x.opr(y.opr(z.opr(c, d), b), a) ~= 24.0:
return fmt"(({c:0} {z} {d:0}) {y} {b:0}) {x} {a:0}"
if x.opr(y.opr(b, z.opr(c, d)), a) ~= 24.0:
return fmt"({b:0} {y} ({c:0} {z} {d:0})) {x} {a:0}"
if not nextPermutation(nums): break
proc main() =
for nums in [
[9, 4, 4, 5],
[1, 7, 2, 7],
[5, 7, 5, 4],
[1, 4, 6, 6],
[2, 3, 7, 3],
[8, 7, 9, 7],
[1, 6, 2, 6],
[7, 9, 4, 1],
[6, 4, 2, 2],
[5, 7, 9, 7],
[3, 3, 8, 8], # Difficult case requiring precise division
]:
echo fmt"solve({nums}) -> {solve(nums)}"
when isMainModule: main()</lang>
- Output:
solve([9, 4, 4, 5]) -> not found solve([1, 7, 2, 7]) -> ((7 * 7) - 1) / 2 solve([5, 7, 5, 4]) -> 4 * (7 - (5 / 5)) solve([1, 4, 6, 6]) -> 6 - (6 * (1 - 4)) solve([2, 3, 7, 3]) -> (7 - 3) * (2 * 3) solve([8, 7, 9, 7]) -> not found solve([1, 6, 2, 6]) -> (6 - 2) / (1 / 6) solve([7, 9, 4, 1]) -> (1 - 9) * (4 - 7) solve([6, 4, 2, 2]) -> 2 * (4 / (2 / 6)) solve([5, 7, 9, 7]) -> (5 + 7) * (9 - 7) solve([3, 3, 8, 8]) -> 8 / (3 - (8 / 3))
OCaml
<lang ocaml>type expression =
| Const of float | Sum of expression * expression (* e1 + e2 *) | Diff of expression * expression (* e1 - e2 *) | Prod of expression * expression (* e1 * e2 *) | Quot of expression * expression (* e1 / e2 *)
let rec eval = function
| Const c -> c | Sum (f, g) -> eval f +. eval g | Diff(f, g) -> eval f -. eval g | Prod(f, g) -> eval f *. eval g | Quot(f, g) -> eval f /. eval g
let print_expr expr =
let open_paren prec op_prec =
if prec > op_prec then print_string "(" in
let close_paren prec op_prec =
if prec > op_prec then print_string ")" in
let rec print prec = function (* prec is the current precedence *)
| Const c -> Printf.printf "%g" c
| Sum(f, g) ->
open_paren prec 0;
print 0 f; print_string " + "; print 0 g;
close_paren prec 0
| Diff(f, g) ->
open_paren prec 0;
print 0 f; print_string " - "; print 1 g;
close_paren prec 0
| Prod(f, g) ->
open_paren prec 2;
print 2 f; print_string " * "; print 2 g;
close_paren prec 2
| Quot(f, g) ->
open_paren prec 2;
print 2 f; print_string " / "; print 3 g;
close_paren prec 2
in
print 0 expr
let rec insert v = function
| [] -> v | x::xs as li -> (v::li) :: (List.map (fun y -> x::y) (insert v xs))
let permutations li =
List.fold_right (fun x z -> List.concat (List.map (insert x) z)) li [[]]
let rec comp expr = function
| x::xs ->
comp (Sum (expr, x)) xs;
comp (Diff(expr, x)) xs;
comp (Prod(expr, x)) xs;
comp (Quot(expr, x)) xs;
| [] ->
if (eval expr) = 24.0
then (print_expr expr; print_newline())
let () =
Random.self_init(); let digits = Array.init 4 (fun _ -> 1 + Random.int 9) in print_string "Input digits: "; Array.iter (Printf.printf " %d") digits; print_newline(); let digits = Array.to_list(Array.map float_of_int digits) in let digits = List.map (fun v -> Const v) digits in let all = permutations digits in List.iter (function | x::xs -> comp x xs | [] -> assert false ) all</lang>
Input digits: 5 7 4 1 7 * 4 - 5 + 1 7 * 4 + 1 - 5 4 * 7 - 5 + 1 4 * 7 + 1 - 5 (5 - 1) * 7 - 4
(notice that the printer only puts parenthesis when needed)
Perl
Will generate all possible solutions of any given four numbers according to the rules of the 24 game.
Note: the permute function was taken from here
<lang Perl># Fischer-Krause ordered permutation generator
sub permute (&@) { my $code = shift; my @idx = 0..$#_; while ( $code->(@_[@idx]) ) { my $p = $#idx; --$p while $idx[$p-1] > $idx[$p]; my $q = $p or return; push @idx, reverse splice @idx, $p; ++$q while $idx[$p-1] > $idx[$q]; @idx[$p-1,$q]=@idx[$q,$p-1]; } }
@formats = ( '((%d %s %d) %s %d) %s %d', '(%d %s (%d %s %d)) %s %d', '(%d %s %d) %s (%d %s %d)', '%d %s ((%d %s %d) %s %d)', '%d %s (%d %s (%d %s %d))', );
- generate all possible combinations of operators
@op = qw( + - * / ); @operators = map{ $a=$_; map{ $b=$_; map{ "$a $b $_" }@op }@op }@op;
while(1) { print "Enter four integers or 'q' to exit: "; chomp($ent = <>); last if $ent eq 'q';
if($ent !~ /^[1-9] [1-9] [1-9] [1-9]$/){ print "invalid input\n"; next }
@n = split / /,$ent; permute { push @numbers,join ' ',@_ }@n;
for $format (@formats) { for(@numbers) { @n = split; for(@operators) { @o = split; $str = sprintf $format,$n[0],$o[0],$n[1],$o[1],$n[2],$o[2],$n[3]; $r = eval($str); print "$str\n" if $r == 24; } } } }</lang>
- Output:
E:\Temp>24solve.pl Enter four integers or 'q' to exit: 1 3 3 8 ((1 + 8) * 3) - 3 ((1 + 8) * 3) - 3 ((8 + 1) * 3) - 3 ((8 - 1) * 3) + 3 ((8 + 1) * 3) - 3 ((8 - 1) * 3) + 3 (3 * (1 + 8)) - 3 (3 * (8 + 1)) - 3 (3 * (8 - 1)) + 3 (3 * (1 + 8)) - 3 (3 * (8 + 1)) - 3 (3 * (8 - 1)) + 3 3 - ((1 - 8) * 3) 3 + ((8 - 1) * 3) 3 - ((1 - 8) * 3) 3 + ((8 - 1) * 3) 3 - (3 * (1 - 8)) 3 + (3 * (8 - 1)) 3 - (3 * (1 - 8)) 3 + (3 * (8 - 1)) Enter four integers or 'q' to exit: q E:\Temp>
Phix
<lang Phix>-- -- 24_game_solve.exw -- ================= -- -- Write a function that given four digits subject to the rules of the 24 game, computes an expression to solve the game if possible. -- Show examples of solutions generated by the function -- -- The following 5 parse expressions are possible. -- Obviously numbers 1234 represent 24 permutations from -- {1,2,3,4} to {4,3,2,1} of indexes to the real numbers. -- Likewise "+-*" is like "123" representing 64 combinations -- from {1,1,1} to {4,4,4} of indexes to "+-*/". -- Both will be replaced if/when the strings get printed. -- constant OPS = "+-*/" constant expressions = {"1+(2-(3*4))",
"1+((2-3)*4)",
"(1+2)-(3*4)",
"(1+(2-3))*4",
"((1+2)-3)*4"} -- (equivalent to "1+2-3*4")
--TODO: I'm sure there is a simple (recursive) way to programatically -- generate the above (for n=2..9) but I'm not seeing it yet...
-- The above represented as three sequential operations (the result gets -- left in <(map)1>, ie vars[perms[operations[i][3][1]]] aka vars[lhs]): constant operations = {{{3,'*',4},{2,'-',3},{1,'+',2}}, --3*=4; 2-=3; 1+=2
{{2,'-',3},{2,'*',4},{1,'+',2}}, --2-=3; 2*=4; 1+=2
{{1,'+',2},{3,'*',4},{1,'-',3}}, --1+=2; 3*=4; 1-=3
{{2,'-',3},{1,'+',2},{1,'*',4}}, --2-=3; 1+=2; 1*=4
{{1,'+',2},{1,'-',3},{1,'*',4}}} --1+=2; 1-=3; 1*=4
--TODO: ... and likewise for parsing "expressions" to yield "operations".
function evalopset(sequence opset, sequence perms, sequence ops, sequence vars) -- invoked 5*24*64 = 7680 times, to try all possible expressions/vars/operators -- (btw, vars is copy-on-write, like all parameters not explicitly returned, so -- we can safely re-use it without clobbering the callee version.) integer lhs,op,rhs atom inf
for i=1 to length(opset) do
{lhs,op,rhs} = opset[i]
lhs = perms[lhs]
op = ops[find(op,OPS)]
rhs = perms[rhs]
if op='+' then
vars[lhs] += vars[rhs]
elsif op='-' then
vars[lhs] -= vars[rhs]
elsif op='*' then
vars[lhs] *= vars[rhs]
elsif op='/' then
if vars[rhs]=0 then inf = 1e300*1e300 return inf end if
vars[lhs] /= vars[rhs]
end if
end for
return vars[lhs]
end function
integer nSolutions sequence xSolutions
procedure success(string expr, sequence perms, sequence ops, sequence vars, atom r) integer ch
for i=1 to length(expr) do
ch = expr[i]
if ch>='1' and ch<='9' then
expr[i] = vars[perms[ch-'0']]+'0'
else
ch = find(ch,OPS)
if ch then
expr[i] = ops[ch]
end if
end if
end for
if not find(expr,xSolutions) then
-- avoid duplicates for eg {1,1,2,7} because this has found
-- the "same" solution but with the 1st and 2nd 1s swapped,
-- and likewise whenever an operator is used more than once.
printf(1,"success: %s = %s\n",{expr,sprint(r)})
nSolutions += 1
xSolutions = append(xSolutions,expr)
end if
end procedure
procedure tryperms(sequence perms, sequence ops, sequence vars) atom r
for i=1 to length(operations) do
-- 5 parse expressions
r = evalopset(operations[i], perms, ops, vars)
if r=24 then
success(expressions[i], perms, ops, vars, r)
end if
end for
end procedure
include builtins/factorial.e include builtins/permute.e
procedure tryops(sequence ops, sequence vars)
for p=1 to factorial(4) do
-- 24 var permutations
tryperms(permute(p,{1,2,3,4}),ops, vars)
end for
end procedure
global procedure solve24(sequence vars)
nSolutions = 0
xSolutions = {}
for op1=1 to 4 do
for op2=1 to 4 do
for op3=1 to 4 do
-- 64 operator combinations
tryops({OPS[op1],OPS[op2],OPS[op3]},vars)
end for
end for
end for
printf(1,"\n%d solutions\n",{nSolutions})
end procedure
solve24({1,1,2,7})
if getc(0) then end if</lang>
- Output:
success: (1+2)*(7+1) = 24 success: (1+7)*(1+2) = 24 success: (1+2)*(1+7) = 24 success: (2+1)*(7+1) = 24 success: (7+1)*(1+2) = 24 success: (2+1)*(1+7) = 24 success: (1+7)*(2+1) = 24 success: (7+1)*(2+1) = 24 8 solutions
Picat
<lang Picat>import util.
main =>
Target=24, Nums = [5,6,7,8], All=findall(Expr, solve_num(Nums,Target,Expr)), foreach(Expr in All) println(Expr.flatten()) end, println(len=All.length), nl.
% A string based approach, inspired by - among others - the Raku solution. solve_num(Nums, Target,Expr) =>
Patterns = [
"A X B Y C Z D",
"(A X B) Y C Z D",
"(A X B Y C) Z D",
"((A X B) Y C) Z D",
"(A X B) Y (C Z D)",
"A X (B Y C Z D)",
"A X (B Y (C Z D))"
],
permutation(Nums,[A,B,C,D]),
Syms = [+,-,*,/],
member(X ,Syms),
member(Y ,Syms),
member(Z ,Syms),
member(Pattern,Patterns),
Expr = replace_all(Pattern,
"ABCDXYZ",
[A,B,C,D,X,Y,Z]),
catch(Target =:= Expr.eval(), E, ignore(E)).
eval(Expr) = parse_term(Expr.flatten()).apply().
ignore(_E) => fail. % ignore zero_divisor errors
% Replace all occurrences in S with From -> To. replace_all(S,From,To) = Res =>
R = S,
foreach({F,T} in zip(From,To))
R := replace(R, F,T.to_string())
end,
Res = R.
</lang>
Test:
Picat> main (5 + 7 - 8) * 6 ((5 + 7) - 8) * 6 (5 + 7) * (8 - 6) (5 - 8 + 7) * 6 ((5 - 8) + 7) * 6 6 * (5 + 7 - 8) 6 * (5 + (7 - 8)) 6 * (5 - 8 + 7) 6 * (5 - (8 - 7)) 6 * (7 + 5 - 8) 6 * (7 + (5 - 8)) 6 * (7 - 8 + 5) 6 * (7 - (8 - 5)) (6 * 8) / (7 - 5) 6 * (8 / (7 - 5)) (7 + 5 - 8) * 6 ((7 + 5) - 8) * 6 (7 + 5) * (8 - 6) (7 - 8 + 5) * 6 ((7 - 8) + 5) * 6 (8 - 6) * (5 + 7) (8 - 6) * (7 + 5) (8 * 6) / (7 - 5) 8 * (6 / (7 - 5)) len = 24
Another approach:
<lang Picat>import util.
main =>
Target=24, Nums = [5,6,7,8], _ = findall(Expr, solve_num2(Nums,Target)), nl.
solve_num2(Nums, Target) =>
Syms = [+,-,*,/],
Perms = permutations([I.to_string() : I in Nums]),
Seen = new_map(), % weed out duplicates
foreach(X in Syms,Y in Syms, Z in Syms)
foreach(P in Perms)
[A,B,C,D] = P,
if catch(check(A,X,B,Y,C,Z,D,Target,Expr),E,ignore(E)),
not Seen.has_key(Expr) then
println(Expr.flatten()=Expr.eval().round()),
Seen.put(Expr,1)
end
end
end.
to_string2(Expr) = [E.to_string() : E in Expr].flatten().
ignore(_E) => fail. % ignore zero_divisor errors
check(A,X,B,Y,C,Z,D,Target,Expr) ?=>
Expr = ["(",A,Y,B,")",X,"(",C,Z,D,")"].to_string2(),
Target =:= Expr.eval().
check(A,X,B,Y,C,Z,D,Target,Expr) ?=>
Expr = [A,X,"(",B,Y,"(",C,Z,D,")",")"].to_string2(),
Target =:= Expr.eval().
check(A,X,B,Y,C,Z,D,Target,Expr) ?=>
Expr = ["(","(",C,Z,D,")",Y,B,")",X,A].to_string2(),
Target =:= Expr.eval().
check(A,X,B,Y,C,Z,D,Target,Expr) ?=>
Expr = ["(",B,Y,"(",C,Z,D,")",")",X,A].to_string2(),
Target =:= Expr.eval().
check(A,X,B,Y,C,Z,D,Target,Expr) =>
Expr = [A,X,"(","(",B,Y,C,")", Z,D,")"].to_string2(),
Target =:= Expr.eval().
</lang>
Test:
> main 6*(5+(7-8)) = 24 6*(7+(5-8)) = 24 (5+7)*(8-6) = 24 (7+5)*(8-6) = 24 6*((7-8)+5) = 24 6*((5-8)+7) = 24 ((5+7)-8)*6 = 24 ((7+5)-8)*6 = 24 (8-6)*(5+7) = 24 (8-6)*(7+5) = 24 6*(7-(8-5)) = 24 6*(5-(8-7)) = 24 6*(8/(7-5)) = 24 8*(6/(7-5)) = 24 6/((7-5)/8) = 24 8/((7-5)/6) = 24 (6*8)/(7-5) = 24 (8*6)/(7-5) = 24
PicoLisp
We use Pilog (PicoLisp Prolog) to solve this task <lang PicoLisp>(be play24 (@Lst @Expr) # Define Pilog rule
(permute @Lst (@A @B @C @D))
(member @Op1 (+ - * /))
(member @Op2 (+ - * /))
(member @Op3 (+ - * /))
(or
((equal @Expr (@Op1 (@Op2 @A @B) (@Op3 @C @D))))
((equal @Expr (@Op1 @A (@Op2 @B (@Op3 @C @D))))) )
(^ @ (= 24 (catch '("Div/0") (eval (-> @Expr))))) )
(de play24 (A B C D) # Define PicoLisp function
(pilog
(quote
@L (list A B C D)
(play24 @L @X) )
(println @X) ) )
(play24 5 6 7 8) # Call 'play24' function</lang>
- Output:
(* (+ 5 7) (- 8 6)) (* 6 (+ 5 (- 7 8))) (* 6 (- 5 (- 8 7))) (* 6 (- 5 (/ 8 7))) (* 6 (+ 7 (- 5 8))) (* 6 (- 7 (- 8 5))) (* 6 (/ 8 (- 7 5))) (/ (* 6 8) (- 7 5)) (* (+ 7 5) (- 8 6)) (* (- 8 6) (+ 5 7)) (* (- 8 6) (+ 7 5)) (* 8 (/ 6 (- 7 5))) (/ (* 8 6) (- 7 5))
ProDOS
Note This example uses the math module: <lang ProDOS>editvar /modify -random- = <10
- a
editvar /newvar /withothervar /value=-random- /title=1 editvar /newvar /withothervar /value=-random- /title=2 editvar /newvar /withothervar /value=-random- /title=3 editvar /newvar /withothervar /value=-random- /title=4 printline These are your four digits: -1- -2- -3- -4- printline Use an algorithm to make the number 24. editvar /newvar /value=a /userinput=1 /title=Algorithm: do -a- if -a- /hasvalue 24 printline Your algorithm worked! & goto :b ( ) else printline Your algorithm did not work. editvar /newvar /value=b /userinput=1 /title=Do you want to see how you could have done it? if -b- /hasvalue y goto :c else goto :b
- b
editvar /newvar /value=c /userinput=1 /title=Do you want to play again? if -c- /hasvalue y goto :a else exitcurrentprogram
- c
editvar /newvar /value=do -1- + -2- + -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- - -2- + -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- / -2- + -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- * -2- + -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- - -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- / -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- * -3- + -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- + -3- - -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- + -3- / -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- + -2- + -3- * -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- - -2- - -3- - -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- / -2- / -3- / -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve editvar /newvar /value=do -1- * -2- * -3- * -4- /title=c & do -c- >d & if -d- /hasvalue 24 goto :solve
- solve
printline you could have done it by doing -c- stoptask goto :b</lang>
- Output:
These are your four digits: 1 4 5 2 Use an algorithm to make the number 24. Algorithm: 4 + 2 - 5 + 1 Your algorithm did not work. Do you want to play again? y These are your four digits: 1 8 9 6 Use an algorithm to make the number 24. Algorithm: 1 + 8 + 9 + 6 Your algorithm worked! Do you want to play again? n
Prolog
Works with SWI-Prolog.
The game is generic, you can choose to play with a goal different of 24,
any number of numbers in other ranges than 1 .. 9 !
rdiv/2 is use instead of //2 to enable the program to solve difficult cases as [3 3 8 8].
<lang Prolog>play24(Len, Range, Goal) :- game(Len, Range, Goal, L, S), maplist(my_write, L), format(': ~w~n', [S]).
game(Len, Range, Value, L, S) :- length(L, Len), maplist(choose(Range), L), compute(L, Value, [], S).
choose(Range, V) :-
V is random(Range) + 1.
write_tree([M], [M]).
write_tree([+, M, N], S) :- write_tree(M, MS), write_tree(N, NS), append(MS, [+ | NS], S).
write_tree([-, M, N], S) :- write_tree(M, MS), write_tree(N, NS), ( is_add(N) -> append(MS, [-, '(' | NS], Temp), append(Temp, ')', S) ; append(MS, [- | NS], S)).
write_tree([Op, M, N], S) :-
member(Op, [*, /]),
write_tree(M, MS),
write_tree(N, NS),
( is_add(M) -> append(['(' | MS], [')'], TempM)
; TempM = MS),
( is_add(N) -> append(['(' | NS], [')'], TempN)
; TempN = NS),
append(TempM, [Op | TempN], S).
is_add([Op, _, _]) :- member(Op, [+, -]).
compute([Value], Value, _R-S1, S) :- write_tree(S1, S2), with_output_to(atom(S), maplist(write, S2)).
compute(L, Value, CS, S) :- select(M, L, L1), select(N, L1, L2), next_value(M, N, R, CS, Expr), compute([R|L2], Value, Expr, S).
next_value(M, N, R, CS,[[R - [+, M1, N1]] | CS2]) :- R is M+N, ( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM ; M1 = [M], CS1 = CS ), ( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN ; N1 = [N], CS2 = CS1 ).
next_value(M, N, R, CS,[[R - [-, M1, N1]] | CS2]) :- R is M-N, ( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM ; M1 = [M], CS1 = CS ), ( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN ; N1 = [N], CS2 = CS1 ).
next_value(M, N, R, CS,[[R - [*, M1, N1]] | CS2]) :- R is M*N, ( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM ; M1 = [M], CS1 = CS ), ( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN ; N1 = [N], CS2 = CS1 ).
next_value(M, N, R, CS,[[R - [/, M1, N1]] | CS2]) :- N \= 0, R is rdiv(M,N), ( member([M-ExprM], CS) -> select([M-ExprM], CS, CS1), M1 = ExprM ; M1 = [M], CS1 = CS ), ( member([N-ExprN], CS1) -> select([N-ExprN], CS1, CS2), N1 = ExprN ; N1 = [N], CS2 = CS1 ).
my_write(V) :- format('~w ', [V]).</lang>
- Output:
?- play24(4,9, 24). 6 2 3 4 : (6-2+4)*3 true ; 6 2 3 4 : 3*(6-2+4) true ; 6 2 3 4 : (6-2+4)*3 true ; 6 2 3 4 : 3*(6-2+4) true ; 6 2 3 4 : (6*2-4)*3 true ; 6 2 3 4 : 3*(6*2-4) true ; 6 2 3 4 : 3*4+6*2 true ; 6 2 3 4 : 3*4+6*2 true ; 6 2 3 4 : 4*3+6*2 true ; 6 2 3 4 : 4*3+6*2 true ; 6 2 3 4 : (6/2+3)*4 true ; 6 2 3 4 : 4*(6/2+3) true ; 6 2 3 4 : (6/2+3)*4 true ; 6 2 3 4 : 4*(6/2+3) true ; 6 2 3 4 : (6-3)*2*4 true ; 6 2 3 4 : 4*(6-3)*2 true ; 6 2 3 4 : (6-3)*4*2 ... ?- play24(7,99, 1). 66 40 2 76 95 59 12 : (66+40)/2-76+95-59-12 true ; 66 40 2 76 95 59 12 : (66+40)/2-76+95-12-59 true ; 66 40 2 76 95 59 12 : (66+40)/2-76-59+95-12 true ; 66 40 2 76 95 59 12 : (66+40)/2-76-59-12+95 true ; 66 40 2 76 95 59 12 : 95+(66+40)/2-76-59-12 true ; 66 40 2 76 95 59 12 : 95+(66+40)/2-76-59-12 true ; 66 40 2 76 95 59 12 : 95-12+(66+40)/2-76-59 true ; 66 40 2 76 95 59 12 : (66+40)/2-76-59+95-12 ....
Minimal version
Little efforts to remove duplicates (e.g. output for [4,6,9,9]). <lang prolog>:- initialization(main).
solve(N,Xs,Ast) :-
Err = evaluation_error(zero_divisor) , gen_ast(Xs,Ast), catch(Ast =:= N, error(Err,_), fail) .
gen_ast([N],N) :- between(1,9,N). gen_ast(Xs,Ast) :-
Ys = [_|_], Zs = [_|_], split(Xs,Ys,Zs) , ( member(Op, [(+),(*)]), Ys @=< Zs ; member(Op, [(-),(//)]) ) , gen_ast(Ys,A), gen_ast(Zs,B), Ast =.. [Op,A,B] .
split(Xs,Ys,Zs) :- sublist(Ys,Xs), select_all(Ys,Xs,Zs).
% where select_all([],Xs,Xs). select_all([Y|Ys],Xs,Zs) :- select(Y,Xs,X1), !, select_all(Ys,X1,Zs).
test(T) :- solve(24, [2,3,8,9], T).
main :- forall(test(T), (write(T), nl)), halt.</lang>
- Output:
(9-3)*8//2 3*8-2//9 (8+9)//2*3 (8-2//9)*3 (2//9+8)*3 (2+8*9)//3 2//9+3*8 8//2*(9-3) (9-3)//2*8 (9-2*3)*8 (3-2//9)*8 (2//9+3)*8 (2+9)//3*8
Python
Python Original
The function is called solve, and is integrated into the game player. The docstring of the solve function shows examples of its use when isolated at the Python command line. <lang Python>
The 24 Game Player Given any four digits in the range 1 to 9, which may have repetitions, Using just the +, -, *, and / operators; and the possible use of brackets, (), show how to make an answer of 24. An answer of "q" will quit the game. An answer of "!" will generate a new set of four digits. An answer of "!!" will ask you for a new set of four digits. An answer of "?" will compute an expression for the current digits. Otherwise you are repeatedly asked for an expression until it evaluates to 24 Note: you cannot form multiple digit numbers from the supplied digits, so an answer of 12+12 when given 1, 2, 2, and 1 would not be allowed.
from __future__ import division, print_function from itertools import permutations, combinations, product, \
chain
from pprint import pprint as pp from fractions import Fraction as F import random, ast, re import sys
if sys.version_info[0] < 3:
input = raw_input from itertools import izip_longest as zip_longest
else:
from itertools import zip_longest
def choose4():
'four random digits >0 as characters' return [str(random.randint(1,9)) for i in range(4)]
def ask4():
'get four random digits >0 from the player'
digits =
while len(digits) != 4 or not all(d in '123456789' for d in digits):
digits = input('Enter the digits to solve for: ')
digits = .join(digits.strip().split())
return list(digits)
def welcome(digits):
print (__doc__)
print ("Your four digits: " + ' '.join(digits))
def check(answer, digits):
allowed = set('() +-*/\t'+.join(digits))
ok = all(ch in allowed for ch in answer) and \
all(digits.count(dig) == answer.count(dig) for dig in set(digits)) \
and not re.search('\d\d', answer)
if ok:
try:
ast.parse(answer)
except:
ok = False
return ok
def solve(digits):
"""\
>>> for digits in '3246 4788 1111 123456 1127 3838'.split():
solve(list(digits))
Solution found: 2 + 3 * 6 + 4
'2 + 3 * 6 + 4'
Solution found: ( 4 + 7 - 8 ) * 8
'( 4 + 7 - 8 ) * 8'
No solution found for: 1 1 1 1
'!'
Solution found: 1 + 2 + 3 * ( 4 + 5 ) - 6
'1 + 2 + 3 * ( 4 + 5 ) - 6'
Solution found: ( 1 + 2 ) * ( 1 + 7 )
'( 1 + 2 ) * ( 1 + 7 )'
Solution found: 8 / ( 3 - 8 / 3 )
'8 / ( 3 - 8 / 3 )'
>>> """
digilen = len(digits)
# length of an exp without brackets
exprlen = 2 * digilen - 1
# permute all the digits
digiperm = sorted(set(permutations(digits)))
# All the possible operator combinations
opcomb = list(product('+-*/', repeat=digilen-1))
# All the bracket insertion points:
brackets = ( [()] + [(x,y)
for x in range(0, exprlen, 2)
for y in range(x+4, exprlen+2, 2)
if (x,y) != (0,exprlen+1)]
+ [(0, 3+1, 4+2, 7+3)] ) # double brackets case
for d in digiperm:
for ops in opcomb:
if '/' in ops:
d2 = [('F(%s)' % i) for i in d] # Use Fractions for accuracy
else:
d2 = d
ex = list(chain.from_iterable(zip_longest(d2, ops, fillvalue=)))
for b in brackets:
exp = ex[::]
for insertpoint, bracket in zip(b, '()'*(len(b)//2)):
exp.insert(insertpoint, bracket)
txt = .join(exp)
try:
num = eval(txt)
except ZeroDivisionError:
continue
if num == 24:
if '/' in ops:
exp = [ (term if not term.startswith('F(') else term[2])
for term in exp ]
ans = ' '.join(exp).rstrip()
print ("Solution found:",ans)
return ans
print ("No solution found for:", ' '.join(digits))
return '!'
def main():
digits = choose4()
welcome(digits)
trial = 0
answer =
chk = ans = False
while not (chk and ans == 24):
trial +=1
answer = input("Expression %i: " % trial)
chk = check(answer, digits)
if answer == '?':
solve(digits)
answer = '!'
if answer.lower() == 'q':
break
if answer == '!':
digits = choose4()
trial = 0
print ("\nNew digits:", ' '.join(digits))
continue
if answer == '!!':
digits = ask4()
trial = 0
print ("\nNew digits:", ' '.join(digits))
continue
if not chk:
print ("The input '%s' was wonky!" % answer)
else:
if '/' in answer:
# Use Fractions for accuracy in divisions
answer = .join( (('F(%s)' % char) if char in '123456789' else char)
for char in answer )
ans = eval(answer)
print (" = ", ans)
if ans == 24:
print ("Thats right!")
print ("Thank you and goodbye")
main()</lang>
- Output:
The 24 Game Player Given any four digits in the range 1 to 9, which may have repetitions, Using just the +, -, *, and / operators; and the possible use of brackets, (), show how to make an answer of 24. An answer of "q" will quit the game. An answer of "!" will generate a new set of four digits. An answer of "?" will compute an expression for the current digits. Otherwise you are repeatedly asked for an expression until it evaluates to 24 Note: you cannot form multiple digit numbers from the supplied digits, so an answer of 12+12 when given 1, 2, 2, and 1 would not be allowed. Your four digits: 6 7 9 5 Expression 1: ? Solution found: 6 - ( 5 - 7 ) * 9 Thank you and goodbye
Difficult case requiring precise division
The digits 3,3,8 and 8 have a solution that is not equal to 24 when using Pythons double-precision floating point because of a division in all answers. The solver above switches to precise fractional arithmetic when division is involved and so can both recognise and solve for cases like this, (rather than allowing some range of closeness to 24).
Evaluation needing precise division
- Output:
... Expression 1: !! Enter the digits to solve for: 3388 New digits: 3 3 8 8 Expression 1: 8/(3-(8/3)) = 24 Thats right! Thank you and goodbye
Solving needing precise division
- Output:
... Expression 1: !! Enter the digits to solve for: 3388 New digits: 3 3 8 8 Expression 1: ? Solution found: 8 / ( 3 - 8 / 3 )
Python Succinct
Based on the Julia example above. <lang python># -*- coding: utf-8 -*- import operator from itertools import product, permutations
def mydiv(n, d):
return n / d if d != 0 else 9999999
syms = [operator.add, operator.sub, operator.mul, mydiv] op = {sym: ch for sym, ch in zip(syms, '+-*/')}
def solve24(nums):
for x, y, z in product(syms, repeat=3):
for a, b, c, d in permutations(nums):
if round(x(y(a,b),z(c,d)),5) == 24:
return f"({a} {op[y]} {b}) {op[x]} ({c} {op[z]} {d})"
elif round(x(a,y(b,z(c,d))),5) == 24:
return f"{a} {op[x]} ({b} {op[y]} ({c} {op[z]} {d}))"
elif round(x(y(z(c,d),b),a),5) == 24:
return f"(({c} {op[z]} {d}) {op[y]} {b}) {op[x]} {a}"
elif round(x(y(b,z(c,d)),a),5) == 24:
return f"({b} {op[y]} ({c} {op[z]} {d})) {op[x]} {a}"
return '--Not Found--'
if __name__ == '__main__':
#nums = eval(input('Four integers in the range 1:9 inclusive, separated by commas: '))
for nums in [
[9,4,4,5],
[1,7,2,7],
[5,7,5,4],
[1,4,6,6],
[2,3,7,3],
[8,7,9,7],
[1,6,2,6],
[7,9,4,1],
[6,4,2,2],
[5,7,9,7],
[3,3,8,8], # Difficult case requiring precise division
]:
print(f"solve24({nums}) -> {solve24(nums)}")</lang>
- Output:
solve24([9, 4, 4, 5]) -> --Not Found-- solve24([1, 7, 2, 7]) -> ((7 * 7) - 1) / 2 solve24([5, 7, 5, 4]) -> 4 * (7 - (5 / 5)) solve24([1, 4, 6, 6]) -> 6 + (6 * (4 - 1)) solve24([2, 3, 7, 3]) -> ((2 + 7) * 3) - 3 solve24([8, 7, 9, 7]) -> --Not Found-- solve24([1, 6, 2, 6]) -> 6 + (6 * (1 + 2)) solve24([7, 9, 4, 1]) -> (7 - 4) * (9 - 1) solve24([6, 4, 2, 2]) -> (2 - 2) + (6 * 4) solve24([5, 7, 9, 7]) -> (5 + 7) * (9 - 7) solve24([3, 3, 8, 8]) -> 8 / (3 - (8 / 3))
Python Recursive
This works for any amount of numbers by recursively picking two and merging them using all available operands until there is only one value left. <lang python># -*- coding: utf-8 -*-
- Python 3
from operator import mul, sub, add
def div(a, b):
if b == 0:
return 999999.0
return a / b
ops = {mul: '*', div: '/', sub: '-', add: '+'}
def solve24(num, how, target):
if len(num) == 1:
if round(num[0], 5) == round(target, 5):
yield str(how[0]).replace(',', ).replace("'", )
else:
for i, n1 in enumerate(num):
for j, n2 in enumerate(num):
if i != j:
for op in ops:
new_num = [n for k, n in enumerate(num) if k != i and k != j] + [op(n1, n2)]
new_how = [h for k, h in enumerate(how) if k != i and k != j] + [(how[i], ops[op], how[j])]
yield from solve24(new_num, new_how, target)
tests = [
[1, 7, 2, 7],
[5, 7, 5, 4],
[1, 4, 6, 6],
[2, 3, 7, 3],
[1, 6, 2, 6],
[7, 9, 4, 1],
[6, 4, 2, 2],
[5, 7, 9, 7],
[3, 3, 8, 8], # Difficult case requiring precise division
[8, 7, 9, 7], # No solution
[9, 4, 4, 5], # No solution
]
for nums in tests:
print(nums, end=' : ')
try:
print(next(solve24(nums, nums, 24)))
except StopIteration:
print("No solution found")
</lang>
- Output:
[1, 7, 2, 7] : (((7 * 7) - 1) / 2) [5, 7, 5, 4] : (4 * (7 - (5 / 5))) [1, 4, 6, 6] : (6 - (6 * (1 - 4))) [2, 3, 7, 3] : ((2 * 3) * (7 - 3)) [1, 6, 2, 6] : ((1 * 6) * (6 - 2)) [7, 9, 4, 1] : ((7 - 4) * (9 - 1)) [6, 4, 2, 2] : ((6 * 4) * (2 / 2)) [5, 7, 9, 7] : ((5 + 7) * (9 - 7)) [3, 3, 8, 8] : (8 / (3 - (8 / 3))) [8, 7, 9, 7] : No solution found [9, 4, 4, 5] : No solution found
Python: using tkinter
<lang python> Python 3.6.5 code using Tkinter graphical user interface.
Combination of '24 game' and '24 game/Solve' allowing user or random selection of 4-digit number and user or computer solution. Note that all computer solutions are displayed
from tkinter import * from tkinter import messagebox from tkinter.scrolledtext import ScrolledText
- 'from tkinter import scrolledtext' in later versions?
import random import itertools
- ************************************************
class Game:
def __init__(self, gw):
self.window = gw
self.digits = '0000'
a1 = "(Enter '4 Digits' & click 'My Digits'"
a2 = "or click 'Random Digits')"
self.msga = a1 + '\n' + a2
b1 = "(Enter 'Solution' & click 'Check Solution'"
b2 = "or click 'Show Solutions')"
self.msgb = b1 + '\n' + b2
# top frame:
self.top_fr = Frame(gw,
width=600,
height=100,
bg='dodger blue')
self.top_fr.pack(fill=X)
self.hdg = Label(self.top_fr,
text=' 21 Game ',
font='arial 22 bold',
fg='navy',
bg='lemon chiffon')
self.hdg.place(relx=0.5, rely=0.5,
anchor=CENTER)
self.close_btn = Button(self.top_fr,
text='Quit',
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.close_window)
self.close_btn.place(relx=0.07, rely=0.5,
anchor=W)
self.clear_btn = Button(self.top_fr,
text='Clear',
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.clear_screen)
self.clear_btn.place(relx=0.92, rely=0.5,
anchor=E)
# bottom frame:
self.btm_fr = Frame(gw,
width=600,
height=500,
bg='lemon chiffon')
self.btm_fr.pack(fill=X)
self.msg = Label(self.btm_fr,
text=self.msga,
font='arial 16 bold',
fg='navy',
bg='lemon chiffon')
self.msg.place(relx=0.5, rely=0.1,
anchor=CENTER)
self.user_dgt_btn = Button(self.btm_fr,
text='My Digits',
width=12,
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.get_digits)
self.user_dgt_btn.place(relx=0.07, rely=0.2,
anchor=W)
self.rdm_dgt_btn = Button(self.btm_fr,
text='Random Digits',
width=12,
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.gen_digits)
self.rdm_dgt_btn.place(relx=0.92, rely=0.2,
anchor=E)
self.dgt_fr = LabelFrame(self.btm_fr,
text=' 4 Digits ',
bg='dodger blue',
fg='navy',
bd=4,
relief=RIDGE,
font='arial 12 bold')
self.dgt_fr.place(relx=0.5, rely=0.27,
anchor=CENTER)
self.digit_ent = Entry(self.dgt_fr,
justify='center',
font='arial 16 bold',
fg='navy',
disabledforeground='navy',
bg='lemon chiffon',
disabledbackground='lemon chiffon',
bd=4,
width=6)
self.digit_ent.grid(row=0, column=0,
padx=(8,8),
pady=(8,8))
self.chk_soln_btn = Button(self.btm_fr,
text='Check Solution',
state='disabled',
width=14,
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.check_soln)
self.chk_soln_btn.place(relx=0.07, rely=.42,
anchor=W)
self.show_soln_btn = Button(self.btm_fr,
text='Show Solutions',
state='disabled',
width=14,
bd=5,
bg='navy',
fg='lemon chiffon',
font='arial 12 bold',
command=self.show_soln)
self.show_soln_btn.place(relx=0.92, rely=.42,
anchor=E)
self.soln_fr = LabelFrame(self.btm_fr,
text=' Solution ',
bg='dodger blue',
fg='navy',
bd=4,
relief=RIDGE,
font='arial 12 bold')
self.soln_fr.place(relx=0.07, rely=0.58,
anchor=W)
self.soln_ent = Entry(self.soln_fr,
justify='center',
font='arial 16 bold',
fg='navy',
disabledforeground='navy',
bg='lemon chiffon',
disabledbackground='lemon chiffon',
state='disabled',
bd=4,
width=15)
self.soln_ent.grid(row=0, column=0,
padx=(8,8), pady=(8,8))
self.solns_fr = LabelFrame(self.btm_fr,
text=' Solutions ',
bg='dodger blue',
fg='navy',
bd=4,
relief=RIDGE,
font='arial 12 bold')
self.solns_fr.place(relx=0.92, rely=0.5,
anchor='ne')
self.solns_all = ScrolledText(self.solns_fr,
font='courier 14 bold',
state='disabled',
fg='navy',
bg='lemon chiffon',
height=8,
width=14)
self.solns_all.grid(row=0, column=0,
padx=(8,8), pady=(8,8))
# validate '4 Digits' entry.
# save if valid and switch screen to solution mode.
def get_digits(self):
txt = self.digit_ent.get()
if not(len(txt) == 4 and txt.isdigit()):
self.err_msg('Please enter 4 digits (eg 1357)')
return
self.digits = txt # save
self.reset_one() # to solution mode
return
# generate 4 random digits, display them,
# save them, and switch screen to solution mode.
def gen_digits(self):
self.digit_ent.delete(0, 'end')
self.digits = .join([random.choice('123456789')
for i in range(4)])
self.digit_ent.insert(0, self.digits) # display
self.reset_one() # to solution mode
return
# switch screen from get digits to solution mode:
def reset_one(self):
self.digit_ent.config(state='disabled')
self.user_dgt_btn.config(state='disabled')
self.rdm_dgt_btn.config(state='disabled')
self.msg.config(text=self.msgb)
self.chk_soln_btn.config(state='normal')
self.show_soln_btn.config(state='normal')
self.soln_ent.config(state='normal')
return
# edit user's solution:
def check_soln(self):
txt = self.soln_ent.get() # user's expression
d = # save digits in expression
dgt_op = 'd' # expecting d:digit or o:operation
for t in txt:
if t not in '123456789+-*/() ':
self.err_msg('Invalid character found: ' + t)
return
if t.isdigit():
if dgt_op == 'd':
d += t
dgt_op = 'o'
else:
self.err_msg('Need operator between digits')
return
if t in '+-*/':
if dgt_op == 'o':
dgt_op = 'd'
else:
self.err_msg('Need digit befor operator')
return
if sorted(d) != sorted(self.digits):
self.err_msg("Use each digit in '4 Digits' once")
return
try:
# round covers up Python's
# representation of floats
if round(eval(txt),5) == 24:
messagebox.showinfo(
'Success',
'YOUR SOLUTION IS VADLID!')
self.show_soln() # show all solutions
return
except:
self.err_msg('Invalid arithmetic expression')
return
messagebox.showinfo(
'Failure',
'Your expression does not yield 24')
return
# show all solutions:
def show_soln(self):
# get all sets of 3 operands: ('+', '+', '*'), ...)
ops = ['+-*/', '+-*/', '+-*/']
combs = [p for p in itertools.product(*ops)]
# get unique permutations for requested 4 digits:
d = self.digits
perms = set([.join(p) for p in itertools.permutations(d)])
# list of all (hopefully) expressions for
# 4 operands and 3 operations:
formats = ['Aop1Bop2Cop3D',
'(Aop1Bop2C)op3D',
'((Aop1B)op2C)op3D',
'(Aop1(Bop2C))op3D',
'Aop1Bop2(Cop3D)',
'Aop1(Bop2C)op3D',
'(Aop1B)op2Cop3D',
'(Aop1B)op2(Cop3D)',
'Aop1(Bop2Cop3D)',
'Aop1((Bop2C)op3D)',
'Aop1(Bop2(Cop3D))']
lox = [] # list of valid expressions
for fm in formats: # pick a format
for c in combs: # plug in 3 ops
f = fm.replace('op1', c[0])
f = f.replace('op2', c[1])
f = f.replace('op3', c[2])
for A, B, C, D in perms: # plug in 4 digits
x = f.replace('A', A)
x = x.replace('B', B)
x = x.replace('C', C)
x = x.replace('D', D)
try: # evaluate expression
# round covers up Python's
# representation of floats
if round(eval(x),5) == 24:
lox.append(' ' + x)
except ZeroDivisionError: # can ignore these
continue
if lox:
txt = '\n'.join(x for x in lox)
else:
txt =' No Solution'
self.solns_all.config(state='normal')
self.solns_all.insert('end', txt) # show solutions
self.solns_all.config(state='disabled')
self.chk_soln_btn.config(state='disabled')
self.show_soln_btn.config(state='disabled')
self.soln_ent.config(state='disabled')
return
def err_msg(self, msg):
messagebox.showerror('Error Message', msg)
return
# restore screen to it's 'initial' state:
def clear_screen(self):
self.digits =
self.digit_ent.config(state='normal')
self.user_dgt_btn.config(state='normal')
self.rdm_dgt_btn.config(state='normal')
self.digit_ent.delete(0, 'end')
self.chk_soln_btn.config(state='disabled')
self.show_soln_btn.config(state='disabled')
self.soln_ent.config(state='normal')
self.soln_ent.delete(0, 'end')
self.soln_ent.config(state='disabled')
self.msg.config(text=self.msga)
self.clear_solns_all()
return
# clear the 'Solutions' frame.
# note: state must be 'normal' to change data
def clear_solns_all(self):
self.solns_all.config(state='normal')
self.solns_all.delete(1.0, 'end')
self.solns_all.config(state='disabled')
return
def close_window(self):
self.window.destroy()
- ************************************************
root = Tk() root.title('24 Game') root.geometry('600x600+100+50') root.resizable(False, False) g = Game(root) root.mainloop() </lang>
R
This uses exhaustive search and makes use of R's ability to work with expressions as data. It is in principle general for any set of operands and binary operators. <lang r> library(gtools)
solve24 <- function(vals=c(8, 4, 2, 1),
goal=24,
ops=c("+", "-", "*", "/")) {
val.perms <- as.data.frame(t(
permutations(length(vals), length(vals))))
nop <- length(vals)-1
op.perms <- as.data.frame(t(
do.call(expand.grid,
replicate(nop, list(ops)))))
ord.perms <- as.data.frame(t(
do.call(expand.grid,
replicate(n <- nop, 1:((n <<- n-1)+1)))))
for (val.perm in val.perms)
for (op.perm in op.perms)
for (ord.perm in ord.perms)
{
expr <- as.list(vals[val.perm])
for (i in 1:nop) {
expr[[ ord.perm[i] ]] <- call(as.character(op.perm[i]),
expr[[ ord.perm[i] ]],
expr[[ ord.perm[i]+1 ]])
expr <- expr[ -(ord.perm[i]+1) ]
}
if (identical(eval(expr1), goal)) return(expr1)
}
return(NA)
} </lang>
- Output:
<lang r> > solve24() 8 * (4 - 2 + 1) > solve24(c(6,7,9,5)) 6 + (7 - 5) * 9 > solve24(c(8,8,8,8)) [1] NA > solve24(goal=49) #different goal value 8 * (4 + 2) + 1 > solve24(goal=52) #no solution [1] NA > solve24(ops=c('-', '/')) #restricted set of operators (8 - 2)/(1/4) </lang>
Racket
The sequence of all possible variants of expressions with given numbers n1, n2, n3, n4 and operations o1, o2, o3. <lang racket> (define (in-variants n1 o1 n2 o2 n3 o3 n4)
(let ([o1n (object-name o1)]
[o2n (object-name o2)]
[o3n (object-name o3)])
(with-handlers ((exn:fail:contract:divide-by-zero? (λ (_) empty-sequence)))
(in-parallel
(list (o1 (o2 (o3 n1 n2) n3) n4)
(o1 (o2 n1 (o3 n2 n3)) n4)
(o1 (o2 n1 n2) (o3 n3 n4))
(o1 n1 (o2 (o3 n2 n3) n4))
(o1 n1 (o2 n2 (o3 n3 n4))))
(list `(((,n1 ,o3n ,n2) ,o2n ,n3) ,o1n ,n4)
`((,n1 ,o2n (,n2 ,o3n ,n3)) ,o1n ,n4)
`((,n1 ,o2n ,n2) ,o1n (,n3 ,o3n ,n4))
`(,n1 ,o1n ((,n2 ,o3n ,n3) ,o2n ,n4))
`(,n1 ,o1n (,n2 ,o2n (,n3 ,o3n ,n4))))))))
</lang>
Search for all solutions using brute force: <lang racket> (define (find-solutions numbers (goal 24))
(define in-operations (list + - * /))
(remove-duplicates
(for*/list ([n1 numbers]
[n2 (remove-from numbers n1)]
[n3 (remove-from numbers n1 n2)]
[n4 (remove-from numbers n1 n2 n3)]
[o1 in-operations]
[o2 in-operations]
[o3 in-operations]
[(res expr) (in-variants n1 o1 n2 o2 n3 o3 n4)]
#:when (= res goal))
expr)))
(define (remove-from numbers . n) (foldr remq numbers n)) </lang>
Examples:
> (find-solutions '(3 8 3 8)) '((8 / (3 - (8 / 3)))) > (find-solutions '(3 8 2 9)) '(((8 / 2) * (9 - 3)) (8 / (2 / (9 - 3))) (8 * (9 - (3 * 2))) (8 * ((9 - 3) / 2)) ((8 * (9 - 3)) / 2) (8 * (9 - (2 * 3))) ((9 - 3) * (8 / 2)) (((9 - 3) * 8) / 2) ((9 - (3 * 2)) * 8) (((9 - 3) / 2) * 8) ((9 - 3) / (2 / 8)) ((9 - (2 * 3)) * 8))
In order to find just one solution effectively one needs to change for*/list to for*/first in the function find-solutions.
Raku
(formerly Perl 6)
With EVAL
A loose translation of the Perl entry. Does not return every possible permutation of the possible solutions. Filters out duplicates (from repeated digits) and only reports the solution for a particular order of digits and operators with the fewest parenthesis (avoids reporting duplicate solutions only differing by unnecessary parenthesis). Does not guarantee the order in which results are returned.
Since Raku uses Rational numbers for division (whenever possible) there is no loss of precision as is common with floating point division. So a comparison like (1 + 7) / (1 / 3) == 24 "Just Works"™
<lang perl6>use MONKEY-SEE-NO-EVAL;
my @digits; my $amount = 4;
- Get $amount digits from the user,
- ask for more if they don't supply enough
while @digits.elems < $amount {
@digits.append: (prompt "Enter {$amount - @digits} digits from 1 to 9, "
~ '(repeats allowed): ').comb(/<[1..9]>/);
}
- Throw away any extras
@digits = @digits[^$amount];
- Generate combinations of operators
my @ops = [X,] <+ - * /> xx 3;
- Enough sprintf formats to cover most precedence orderings
my @formats = (
'%d %s %d %s %d %s %d', '(%d %s %d) %s %d %s %d', '(%d %s %d %s %d) %s %d', '((%d %s %d) %s %d) %s %d', '(%d %s %d) %s (%d %s %d)', '%d %s (%d %s %d %s %d)', '%d %s (%d %s (%d %s %d))',
);
- Brute force test the different permutations
(unique @digits.permutations).race.map: -> @p {
for @ops -> @o {
for @formats -> $format {
my $string = sprintf $format, flat roundrobin(|@p; |@o);
my $result = EVAL($string);
say "$string = 24" and last if $result and $result == 24;
}
}
}
- Only return unique sub-arrays
sub unique (@array) {
my %h = map { $_.Str => $_ }, @array;
%h.values;
}</lang>
- Output:
Enter 4 digits from 1 to 9, (repeats allowed): 3711 (1 + 7) * 3 * 1 = 24 (1 + 7) * 3 / 1 = 24 (1 * 3) * (1 + 7) = 24 3 * (1 + 1 * 7) = 24 (3 * 1) * (1 + 7) = 24 3 * (1 / 1 + 7) = 24 (3 / 1) * (1 + 7) = 24 3 / (1 / (1 + 7)) = 24 (1 + 7) * 1 * 3 = 24 (1 + 7) / 1 * 3 = 24 (1 + 7) / (1 / 3) = 24 (1 * 7 + 1) * 3 = 24 (7 + 1) * 3 * 1 = 24 (7 + 1) * 3 / 1 = 24 (7 - 1) * (3 + 1) = 24 (1 + 1 * 7) * 3 = 24 (1 * 1 + 7) * 3 = 24 (1 / 1 + 7) * 3 = 24 (3 + 1) * (7 - 1) = 24 3 * (1 + 7 * 1) = 24 3 * (1 + 7 / 1) = 24 (3 * 1) * (7 + 1) = 24 (3 / 1) * (7 + 1) = 24 3 / (1 / (7 + 1)) = 24 (1 + 3) * (7 - 1) = 24 (1 * 3) * (7 + 1) = 24 (7 + 1) * 1 * 3 = 24 (7 + 1) / 1 * 3 = 24 (7 + 1) / (1 / 3) = 24 (7 - 1) * (1 + 3) = 24 (7 * 1 + 1) * 3 = 24 (7 / 1 + 1) * 3 = 24 3 * (7 + 1 * 1) = 24 3 * (7 + 1 / 1) = 24 3 * (7 * 1 + 1) = 24 3 * (7 / 1 + 1) = 24 Enter 4 digits from 1 to 9, (repeats allowed): 5 5 5 5 5 * 5 - 5 / 5 = 24 Enter 4 digits from 1 to 9, (repeats allowed): 8833 8 / (3 - 8 / 3) = 24
No EVAL
Alternately, a version that doesn't use EVAL. More general case. Able to handle 3 or 4 integers, able to select the goal value.
<lang perl6>my %*SUB-MAIN-OPTS = :named-anywhere;
sub MAIN (*@parameters, Int :$goal = 24) {
my @numbers;
if +@parameters == 1 {
@numbers = @parameters[0].comb(/\d/);
USAGE() and exit unless 2 < @numbers < 5;
} elsif +@parameters > 4 {
USAGE() and exit;
} elsif +@parameters == 3|4 {
@numbers = @parameters;
USAGE() and exit if @numbers.any ~~ /<-[-\d]>/;
} else {
USAGE();
exit if +@parameters == 2;
@numbers = 3,3,8,8;
say 'Running demonstration with: ', |@numbers, "\n";
}
solve @numbers, $goal
}
sub solve (@numbers, $goal = 24) {
my @operators = < + - * / >; my @ops = [X] @operators xx (@numbers - 1); my @perms = @numbers.permutations.unique( :with(&[eqv]) ); my @order = (^(@numbers - 1)).permutations; my @sol; @sol[250]; # preallocate some stack space
my $batch = ceiling +@perms/4;
my atomicint $i;
@perms.race(:batch($batch)).map: -> @p {
for @ops -> @o {
for @order -> @r {
my $result = evaluate(@p, @o, @r);
@sol[$i⚛++] = $result[1] if $result[0] and $result[0] == $goal;
}
}
}
@sol.=unique;
say @sol.join: "\n";
my $pl = +@sol == 1 ?? !! 's';
my $sg = $pl ?? !! 's';
say +@sol, " equation{$pl} evaluate{$sg} to $goal using: {@numbers}";
}
sub evaluate ( @digit, @ops, @orders ) {
my @result = @digit.map: { [ $_, $_ ] };
my @offset = 0 xx +@orders;
for ^@orders {
my $this = @orders[$_];
my $order = $this - @offset[$this];
my $op = @ops[$this];
my $result = op( $op, @result[$order;0], @result[$order+1;0] );
return [ NaN, Str ] unless defined $result;
my $string = "({@result[$order;1]} $op {@result[$order+1;1]})";
@result.splice: $order, 2, [ $[ $result, $string ] ];
@offset[$_]++ if $order < $_ for ^@offset;
}
@result[0];
}
multi op ( '+', $m, $n ) { $m + $n } multi op ( '-', $m, $n ) { $m - $n } multi op ( '/', $m, $n ) { $n == 0 ?? fail() !! $m / $n } multi op ( '*', $m, $n ) { $m * $n }
my $txt = "\e[0;96m"; my $cmd = "\e[0;92m> {$*EXECUTABLE-NAME} {$*PROGRAM-NAME}"; sub USAGE {
say qq:to
'========================================================================'
{$txt}Supply 3 or 4 integers on the command line, and optionally a value
to equate to.
Integers may be all one group: {$cmd} 2233{$txt}
Or, separated by spaces: {$cmd} 2 4 6 7{$txt}
If you wish to supply multi-digit or negative numbers, you must
separate them with spaces: {$cmd} -2 6 12{$txt}
If you wish to use a different equate value,
supply a new --goal parameter: {$cmd} --goal=17 2 -3 1 9{$txt}
If you don't supply any parameters, will use 24 as the goal, will run a demo and will show this message.\e[0m ========================================================================
}</lang>
- Output:
When supplied 1399 on the command line:
(((9 - 1) / 3) * 9) ((9 - 1) / (3 / 9)) ((9 / 3) * (9 - 1)) (9 / (3 / (9 - 1))) ((9 * (9 - 1)) / 3) (9 * ((9 - 1) / 3)) (((9 - 1) * 9) / 3) ((9 - 1) * (9 / 3)) 8 equations evaluate to 24 using: 1 3 9 9
REXX
<lang rexx>/*REXX program helps the user find solutions to the game of 24. */ /* start-of-help ┌───────────────────────────────────────────────────────────────────────┐ │ Argument is either of three forms: (blank) │~ │ ssss │~ │ ssss,tot │~ │ ssss-ffff │~ │ ssss-ffff,tot │~ │ -ssss │~ │ +ssss │~ │ │~ │ where SSSS and/or FFFF must be exactly four numerals (digits) │~ │ comprised soley of the numerals (digits) 1 ──> 9 (no zeroes). │~ │ │~ │ SSSS is the start, │~ │ FFFF is the start. │~ │ │~ │ │~ │ If ssss has a leading plus (+) sign, it is used as the number, and │~ │ the user is prompted to find a solution. │~ │ │~ │ If ssss has a leading minus (-) sign, a solution is looked for and │~ │ the user is told there is a solution (but no solutions are shown). │~ │ │~ │ If no argument is specified, this program finds a four digits (no │~ │ zeroes) which has at least one solution, and shows the digits to │~ │ the user, requesting that they enter a solution. │~ │ │~ │ If tot is entered, it is the desired answer. The default is 24. │~ │ │~ │ A solution to be entered can be in the form of: │ │ │ │ digit1 operator digit2 operator digit3 operator digit4 │ │ │ │ where DIGITn is one of the digits shown (in any order), and │ │ OPERATOR can be any one of: + - * / │ │ │ │ Parentheses () may be used in the normal manner for grouping, as │ │ well as brackets [] or braces {}. Blanks can be used anywhere. │ │ │ │ I.E.: for the digits 3448 the following could be entered. │ │ │ │ 3*8 + (4-4) │ └───────────────────────────────────────────────────────────────────────┘
end-of-help */
numeric digits 12 /*where rational arithmetic is needed. */ parse arg orig /*get the guess from the command line*/ orig= space(orig, 0) /*remove all blanks from ORIG. */ negatory= left(orig,1)=='-' /*=1, suppresses showing. */ pository= left(orig,1)=='+' /*=1, force $24 to use specific number.*/ if pository | negatory then orig=substr(orig,2) /*now, just use the absolute vaue. */ parse var orig orig ',' ?? /*get ?? (if specified, def=24). */ parse var orig start '-' finish /*get start and finish (maybe). */ opers= '*' || "/+-" /*legal arith. opers;order is important*/ ops= length(opers) /*the number of arithmetic operators. */ groupsym= '()[]{}' /*allowed grouping symbols. */ indent= left(, 30) /*indents display of solutions. */ show= 1 /*=1, shows solutions (semifore). */ digs= 123456789 /*numerals/digs that can be used. */ abuttals = 0 /*=1, allows digit abutal: 12+12 */ if ??== then ??= 24 /*the name of the game. */ ??= ?? / 1 /*normalize the answer. */ @abc= 'abcdefghijklmnopqrstuvwxyz' /*the Latin alphabet in order. */ @abcu= @abc; upper @abcu /*an uppercase version of @abc. */ x.= 0 /*method used to not re-interpret. */
do j=1 for ops; o.j=substr(opers, j, 1)
end /*j*/ /*used for fast execution. */
y= ?? if \datatype(??,'N') then do; call ger "isn't numeric"; exit 13; end if start\== & \pository then do; call ranger start,finish; exit 13; end show= 0 /*stop SOLVE blabbing solutions. */
do forever while \negatory /*keep truckin' until a solution. */
x.= 0 /*way to hold unique expressions. */
rrrr= random(1111, 9999) /*get a random set of digits. */
if pos(0, rrrr)\==0 then iterate /*but don't the use of zeroes. */
if solve(rrrr)\==0 then leave /*try to solve for these digits. */
end /*forever*/
if left(orig,1)=='+' then rrrr=start /*use what's specified. */ show= 1 /*enable SOLVE to show solutions. */ rrrr= sortc(rrrr) /*sort four elements. */ rd.= 0
do j=1 for 9 /*count for each digit in RRRR. */
_= substr(rrrr, j, 1); rd._= countchars(rrrr, _)
end
do guesses=1; say
say 'Using the digits' rrrr", enter an expression that equals" ?? ' (? or QUIT):'
pull y; y= space(y, 0)
if countchars(y, @abcu)>2 then exit /*the user must be desperate. */
helpstart= 0
if y=='?' then do j=1 for sourceline() /*use a lazy way to show help. */
_= sourceline(j)
if p(_)=='start-of-help' then do; helpstart=1; iterate; end
if p(_)=='end-of-help' then iterate guesses
if \helpstart then iterate
if right(_,1)=='~' then iterate
say ' ' _
end
_v= verify(y, digs || opers || groupsym) /*any illegal characters? */ if _v\==0 then do; call ger 'invalid character:' substr(y, _v, 1); iterate; end if y= then do; call validate y; iterate; end
do j=1 for length(y)-1 while \abuttals /*check for two digits adjacent. */
if \datatype(substr(y,j,1), 'W') then iterate
if datatype(substr(y,j+1,1),'W') then do
call ger 'invalid use of digit abuttal' substr(y,j,2)
iterate guesses
end
end /*j*/
yd= countchars(y, digs) /*count of legal digits 123456789 */ if yd<4 then do; call ger 'not enough digits entered.'; iterate guesses; end if yd>4 then do; call ger 'too many digits entered.' ; iterate guesses; end
do j=1 for length(groupsym) by 2
if countchars(y,substr(groupsym,j ,1))\==,
countchars(y,substr(groupsym,j+1,1)) then do
call ger 'mismatched' substr(groupsym,j,2)
iterate guesses
end
end /*j*/
do k=1 for 2 /*check for ** and // */
_= copies( substr( opers, k, 1), 2)
if pos(_, y)\==0 then do; call ger 'illegal operator:' _; iterate guesses; end
end /*k*/
do j=1 for 9; if rd.j==0 then iterate; _d= countchars(y, j)
if _d==rd.j then iterate
if _d<rd.j then call ger 'not enough' j "digits, must be" rd.j
else call ger 'too many' j "digits, must be" rd.j
iterate guesses
end /*j*/
y= translate(y, '()()', "[]{}")
interpret 'ans=(' y ") / 1"
if ans==?? then leave guesses
say right('incorrect, ' y'='ans, 50)
end /*guesses*/
say; say center('┌─────────────────────┐', 79)
say center('│ │', 79)
say center('│ congratulations ! │', 79)
say center('│ │', 79)
say center('└─────────────────────┘', 79)
say exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ countchars: procedure; arg x,c /*count of characters in X. */
return length(x) - length( space( translate(x, ,c ), 0) )
/*──────────────────────────────────────────────────────────────────────────────────────*/ ranger: parse arg ssss,ffff /*parse args passed to this sub. */
ffff= p(ffff ssss) /*create a FFFF if necessary. */
do g=ssss to ffff /*process possible range of values. */
if pos(0, g)\==0 then iterate /*ignore any G with zeroes. */
sols= solve(g); wols= sols
if sols==0 then wols= 'No' /*un-geek number of solutions (if any).*/
if negatory & sols\==0 then wols='A' /*found only the first solution? */
say
say wols 'solution's(sols) "found for" g
if ??\==24 then say 'for answers that equal' ??
end
return
/*──────────────────────────────────────────────────────────────────────────────────────*/ solve: parse arg qqqq; finds= 0 /*parse args passed to this sub. */ if \validate(qqqq) then return -1 parse value '( (( )) )' with L LL RR R /*assign some static variables. */ nq.= 0
do jq=1 for 4; _= substr(qqqq,jq,1) /*count the number of each digit. */
nq._= nq._ + 1
end /*jq*/
do gggg=1111 to 9999
if pos(0, gggg)\==0 then iterate /*ignore values with zeroes. */
if verify(gggg, qqqq)\==0 then iterate
if verify(qqqq, gggg)\==0 then iterate
ng.= 0
do jg=1 for 4; _= substr(gggg, jg, 1) /*count the number of each digit. */
g.jg= _; ng._= ng._ + 1
end /*jg*/
do kg=1 for 9 /*verify each number has same # digits.*/
if nq.kg\==ng.kg then iterate gggg
end /*kg*/
do i =1 for ops /*insert operator after 1st numeral. */
do j =1 for ops /* " " " 2nd " */
do k=1 for ops /* " " " 3rd " */
do m=0 for 10; !.= /*nullify all grouping symbols (parens)*/
select
when m==1 then do; !.1=L; !.3=R; end
when m==2 then do; !.1=L; !.5=R; end
when m==3 then do; !.1=L; !.3=R; !.4=L; !.6=R; end
when m==4 then do; !.1=L; !.2=L; !.6=RR; end
when m==5 then do; !.1=LL; !.5=R; !.6=R; end
when m==6 then do; !.2=L; !.5=R; end
when m==7 then do; !.2=L; !.6=R; end
when m==8 then do; !.2=L; !.4=L; !.6=RR; end
when m==9 then do; !.2=LL; !.5=R; !.6=R; end
otherwise nop
end /*select*/
e= space(!.1 g.1 o.i !.2 g.2 !.3 o.j !.4 g.3 !.5 o.k g.4 !.6, 0)
if x.e then iterate /*was the expression already used? */
x.e= 1 /*mark this expression as being used. */
/*(below) change the expression: /(yyy) ===> /div(yyy) */
origE= e /*keep original version for the display*/
pd= pos('/(', e) /*find pos of /( in E. */
if pd\==0 then do /*Found? Might have possible ÷ by zero*/
eo= e
lr= lastpos(')', e) /*find last right ) */
lm= pos('-', e, pd+1) /*find - after ( */
if lm>pd & lm<lr then e= changestr('/(',e,"/div(") /*change*/
if eo\==e then if x.e then iterate /*expression already used?*/
x.e= 1 /*mark this expression as being used. */
end
interpret 'x=(' e ") / 1" /*have REXX do the heavy lifting here. */
if x\==?? then do /*Not correct? Then try again. */
numeric digits 9; x= x / 1 /*re-do evaluation.*/
numeric digits 12 /*re-instate digits*/
if x\==?? then iterate /*Not correct? Then try again. */
end
finds= finds + 1 /*bump number of found solutions. */
if \show | negatory then return finds
_= translate(origE, '][', ")(") /*show [], not (). */
if show then say indent 'a solution for' g':' ??"=" _ /*show solution.*/
end /*m*/
end /*k*/
end /*j*/
end /*i*/
end /*gggg*/
return finds /*──────────────────────────────────────────────────────────────────────────────────────*/ sortc: procedure; arg nnnn; L= length(nnnn) /*sorts the chars NNNN */
do i=1 for L /*build array of digs from NNNN, */
a.i= substr(nnnn, i, 1) /*enabling SORT to sort an array. */
end /*i*/
do j=1 for L /*very simple sort, it's a small array*/
_= a.j
do k=j+1 to L
if a.k<_ then do; a.j= a.k; a.k= _; _= a.k; end
end /*k*/
end /*j*/
v= a.1
do m=2 to L; v= v || a.m /*build a string of digs from A.m */
end /*m*/
return v
/*──────────────────────────────────────────────────────────────────────────────────────*/ validate: parse arg y; errCode= 0; _v= verify(y, digs)
select
when y== then call ger 'no digits entered.'
when length(y)<4 then call ger 'not enough digits entered, must be 4'
when length(y)>4 then call ger 'too many digits entered, must be 4'
when pos(0,y)\==0 then call ger "can't use the digit 0 (zero)"
when _v\==0 then call ger 'illegal character:' substr(y,_v,1)
otherwise nop
end /*select*/
return \errCode
/*──────────────────────────────────────────────────────────────────────────────────────*/
div: procedure; parse arg q; if q=0 then q=1e9; return q /*tests if dividing by zero.*/
ger: say= '***error*** for argument:' y; say arg(1); errCode= 1; return 0
p: return word( arg(1), 1)
s: if arg(1)==1 then return arg(3); return word( arg(2) 's', 1)</lang>
Some older REXXes don't have a changestr BIF, so one is included here ──► CHANGESTR.REX.
- output when using the input of: 1156-1162
a solution for 1156: 24= [1*5-1]*6
a solution for 1156: 24= [[1*5-1]*6]
a solution for 1156: 24= 1*[5-1]*6
a solution for 1156: 24= 1*[[5-1]*6]
a solution for 1156: 24= [1*6]*[5-1]
a solution for 1156: 24= 1*[6*[5-1]]
a solution for 1156: 24= [5*1-1]*6
a solution for 1156: 24= [[5*1-1]*6]
a solution for 1156: 24= [5/1-1]*6
a solution for 1156: 24= [[5/1-1]*6]
a solution for 1156: 24= [5-1]*1*6
a solution for 1156: 24= [5-1*1]*6
a solution for 1156: 24= [5-1]*[1*6]
a solution for 1156: 24= [[5-1*1]*6]
a solution for 1156: 24= [5-1]/1*6
a solution for 1156: 24= [5-1/1]*6
a solution for 1156: 24= [[5-1/1]*6]
a solution for 1156: 24= [5-1]/[1/6]
a solution for 1156: 24= [5-1]*6*1
a solution for 1156: 24= [5-1]*[6*1]
a solution for 1156: 24= [5-1]*6/1
a solution for 1156: 24= [5-1]*[6/1]
a solution for 1156: 24= 5*[6-1]-1
a solution for 1156: 24= [6*1]*[5-1]
a solution for 1156: 24= [6*[1*5-1]]
a solution for 1156: 24= 6*[1*5-1]
a solution for 1156: 24= 6*[1*[5-1]]
a solution for 1156: 24= 6*[[1*5]-1]
a solution for 1156: 24= [6/1]*[5-1]
a solution for 1156: 24= 6/[1/[5-1]]
a solution for 1156: 24= [6-1]*5-1
a solution for 1156: 24= [6*[5*1-1]]
a solution for 1156: 24= 6*[5*1-1]
a solution for 1156: 24= 6*[[5*1]-1]
a solution for 1156: 24= [6*[5/1-1]]
a solution for 1156: 24= 6*[5/1-1]
a solution for 1156: 24= 6*[[5/1]-1]
a solution for 1156: 24= [6*[5-1*1]]
a solution for 1156: 24= 6*[5-1]*1
a solution for 1156: 24= 6*[5-1*1]
a solution for 1156: 24= 6*[5-[1*1]]
a solution for 1156: 24= 6*[[5-1]*1]
a solution for 1156: 24= [6*[5-1/1]]
a solution for 1156: 24= 6*[5-1]/1
a solution for 1156: 24= 6*[5-1/1]
a solution for 1156: 24= 6*[5-[1/1]]
a solution for 1156: 24= 6*[[5-1]/1]
47 solutions found for 1156
a solution for 1157: 24= [1+1]*[5+7]
a solution for 1157: 24= [1+1]*[7+5]
a solution for 1157: 24= [1-5]*[1-7]
a solution for 1157: 24= [1-7]*[1-5]
a solution for 1157: 24= [5-1]*[7-1]
a solution for 1157: 24= [5+7]*[1+1]
a solution for 1157: 24= [7-1]*[5-1]
a solution for 1157: 24= [7+5]*[1+1]
8 solutions found for 1157
a solution for 1158: 24= [5-1-1]*8
a solution for 1158: 24= [[5-1-1]*8]
a solution for 1158: 24= 8*[5-[1+1]]
a solution for 1158: 24= [8*[5-1-1]]
a solution for 1158: 24= 8*[5-1-1]
a solution for 1158: 24= 8*[[5-1]-1]
6 solutions found for 1158
No solutions found for 1159
No solutions found for 1161
a solution for 1162: 24= [1+1]*2*6
a solution for 1162: 24= [1+1]*[2*6]
a solution for 1162: 24= [1+1+2]*6
a solution for 1162: 24= [[1+1+2]*6]
a solution for 1162: 24= [1+1]*6*2
a solution for 1162: 24= [1+1]*[6*2]
a solution for 1162: 24= [1+2+1]*6
a solution for 1162: 24= [[1+2+1]*6]
a solution for 1162: 24= 2*[1+1]*6
a solution for 1162: 24= 2*[[1+1]*6]
a solution for 1162: 24= [2+1+1]*6
a solution for 1162: 24= [[2+1+1]*6]
a solution for 1162: 24= [2*6]*[1+1]
a solution for 1162: 24= 2*[6*[1+1]]
a solution for 1162: 24= 6*[1+1]*2
a solution for 1162: 24= 6*[[1+1]*2]
a solution for 1162: 24= [6*[1+1+2]]
a solution for 1162: 24= 6*[1+1+2]
a solution for 1162: 24= 6*[1+[1+2]]
a solution for 1162: 24= 6*[[1+1]+2]
a solution for 1162: 24= [6*[1+2+1]]
a solution for 1162: 24= 6*[1+2+1]
a solution for 1162: 24= 6*[1+[2+1]]
a solution for 1162: 24= 6*[[1+2]+1]
a solution for 1162: 24= [6*2]*[1+1]
a solution for 1162: 24= 6*[2*[1+1]]
a solution for 1162: 24= [6*[2+1+1]]
a solution for 1162: 24= 6*[2+1+1]
a solution for 1162: 24= 6*[2+[1+1]]
a solution for 1162: 24= 6*[[2+1]+1]
30 solutions found for 1162
Ruby
<lang ruby>class TwentyFourGame
EXPRESSIONS = [
'((%dr %s %dr) %s %dr) %s %dr',
'(%dr %s (%dr %s %dr)) %s %dr',
'(%dr %s %dr) %s (%dr %s %dr)',
'%dr %s ((%dr %s %dr) %s %dr)',
'%dr %s (%dr %s (%dr %s %dr))',
]
OPERATORS = [:+, :-, :*, :/].repeated_permutation(3).to_a
def self.solve(digits)
solutions = []
perms = digits.permutation.to_a.uniq
perms.product(OPERATORS, EXPRESSIONS) do |(a,b,c,d), (op1,op2,op3), expr|
# evaluate using rational arithmetic
text = expr % [a, op1, b, op2, c, op3, d]
value = eval(text) rescue next # catch division by zero
solutions << text.delete("r") if value == 24
end
solutions
end
end
- validate user input
digits = ARGV.map do |arg|
begin
Integer(arg)
rescue ArgumentError
raise "error: not an integer: '#{arg}'"
end
end digits.size == 4 or raise "error: need 4 digits, only have #{digits.size}"
solutions = TwentyFourGame.solve(digits) if solutions.empty?
puts "no solutions"
else
puts "found #{solutions.size} solutions, including #{solutions.first}"
puts solutions.sort
end</lang>
- Output:
$ ruby game24_solver.rb 1 1 1 1 no solutions $ ruby game24_solver.rb 1 1 2 7 found 8 solutions, including (1 + 2) * (1 + 7) (1 + 2) * (1 + 7) (1 + 2) * (7 + 1) (1 + 7) * (1 + 2) (1 + 7) * (2 + 1) (2 + 1) * (1 + 7) (2 + 1) * (7 + 1) (7 + 1) * (1 + 2) (7 + 1) * (2 + 1) $ ruby game24_solver.rb 2 3 8 9 found 12 solutions, including (8 / 2) * (9 - 3) ((9 - 3) * 8) / 2 ((9 - 3) / 2) * 8 (8 * (9 - 3)) / 2 (8 / 2) * (9 - 3) (9 - (2 * 3)) * 8 (9 - (3 * 2)) * 8 (9 - 3) * (8 / 2) (9 - 3) / (2 / 8) 8 * ((9 - 3) / 2) 8 * (9 - (2 * 3)) 8 * (9 - (3 * 2)) 8 / (2 / (9 - 3))
Rust
<lang rust>#[derive(Clone, Copy, Debug)] enum Operator {
Sub, Plus, Mul, Div,
}
- [derive(Clone, Debug)]
struct Factor {
content: String, value: i32,
}
fn apply(op: Operator, left: &[Factor], right: &[Factor]) -> Vec<Factor> {
let mut ret = Vec::new();
for l in left.iter() {
for r in right.iter() {
use Operator::*;
ret.push(match op {
Sub if l.value > r.value => Factor {
content: format!("({} - {})", l.content, r.content),
value: l.value - r.value,
},
Plus => Factor {
content: format!("({} + {})", l.content, r.content),
value: l.value + r.value,
},
Mul => Factor {
content: format!("({} x {})", l.content, r.content),
value: l.value * r.value,
},
Div if l.value >= r.value && r.value > 0 && l.value % r.value == 0 => Factor {
content: format!("({} / {})", l.content, r.content),
value: l.value / r.value,
},
_ => continue,
})
}
}
ret
}
fn calc(op: [Operator; 3], numbers: [i32; 4]) -> Vec<Factor> {
fn calc(op: &[Operator], numbers: &[i32], acc: &[Factor]) -> Vec<Factor> {
use Operator::*;
if op.is_empty() {
return Vec::from(acc)
}
let mut ret = Vec::new();
let mono_factor = [Factor {
content: numbers[0].to_string(),
value: numbers[0],
}];
match op[0] {
Mul => ret.extend_from_slice(&apply(op[0], acc, &mono_factor)),
Div => {
ret.extend_from_slice(&apply(op[0], acc, &mono_factor));
ret.extend_from_slice(&apply(op[0], &mono_factor, acc));
},
Sub => {
ret.extend_from_slice(&apply(op[0], acc, &mono_factor));
ret.extend_from_slice(&apply(op[0], &mono_factor, acc));
},
Plus => ret.extend_from_slice(&apply(op[0], acc, &mono_factor)),
}
calc(&op[1..], &numbers[1..], &ret)
}
calc(&op, &numbers[1..], &[Factor { content: numbers[0].to_string(), value: numbers[0] }])
}
fn solutions(numbers: [i32; 4]) -> Vec<Factor> {
use std::collections::hash_set::HashSet;
let mut ret = Vec::new();
let mut hash_set = HashSet::new();
for ops in OpIter(0) {
for o in orders().iter() {
let numbers = apply_order(numbers, o);
let r = calc(ops, numbers);
ret.extend(r.into_iter().filter(|&Factor { value, ref content }| value == 24 && hash_set.insert(content.to_owned())))
}
}
ret
}
fn main() {
let mut numbers = Vec::new();
if let Some(input) = std::env::args().skip(1).next() {
for c in input.chars() {
if let Ok(n) = c.to_string().parse() {
numbers.push(n)
}
if numbers.len() == 4 {
let numbers = [numbers[0], numbers[1], numbers[2], numbers[3]];
let solutions = solutions(numbers);
let len = solutions.len();
if len == 0 {
println!("no solution for {}, {}, {}, {}", numbers[0], numbers[1], numbers[2], numbers[3]);
return
}
println!("solutions for {}, {}, {}, {}", numbers[0], numbers[1], numbers[2], numbers[3]);
for s in solutions {
println!("{}", s.content)
}
println!("{} solutions found", len);
return
}
}
} else {
println!("empty input")
}
}
struct OpIter (usize);
impl Iterator for OpIter {
type Item = [Operator; 3];
fn next(&mut self) -> Option<[Operator; 3]> {
use Operator::*;
const OPTIONS: [Operator; 4] = [Mul, Sub, Plus, Div];
if self.0 >= 1 << 6 {
return None
}
let f1 = OPTIONS[(self.0 & (3 << 4)) >> 4];
let f2 = OPTIONS[(self.0 & (3 << 2)) >> 2];
let f3 = OPTIONS[(self.0 & (3 << 0)) >> 0];
self.0 += 1;
Some([f1, f2, f3])
}
}
fn orders() -> [[usize; 4]; 24] {
[
[0, 1, 2, 3],
[0, 1, 3, 2],
[0, 2, 1, 3],
[0, 2, 3, 1],
[0, 3, 1, 2],
[0, 3, 2, 1],
[1, 0, 2, 3],
[1, 0, 3, 2],
[1, 2, 0, 3],
[1, 2, 3, 0],
[1, 3, 0, 2],
[1, 3, 2, 0],
[2, 0, 1, 3],
[2, 0, 3, 1],
[2, 1, 0, 3],
[2, 1, 3, 0],
[2, 3, 0, 1],
[2, 3, 1, 0],
[3, 0, 1, 2],
[3, 0, 2, 1],
[3, 1, 0, 2],
[3, 1, 2, 0],
[3, 2, 0, 1],
[3, 2, 1, 0]
]
}
fn apply_order(numbers: [i32; 4], order: &[usize; 4]) -> [i32; 4] {
[numbers[order[0]], numbers[order[1]], numbers[order[2]], numbers[order[3]]]
} </lang>
- Output:
$cargo run 5598 solutions for 5, 5, 9, 8 (((5 x 5) - 9) + 8) (((5 x 5) + 8) - 9) (((8 - 5) x 5) + 9) 3 solutions found
Scala
A non-interactive player.
<lang scala>def permute(l: List[Double]): List[List[Double]] = l match {
case Nil => List(Nil)
case x :: xs =>
for {
ys <- permute(xs)
position <- 0 to ys.length
(left, right) = ys splitAt position
} yield left ::: (x :: right)
}
def computeAllOperations(l: List[Double]): List[(Double,String)] = l match {
case Nil => Nil
case x :: Nil => List((x, "%1.0f" format x))
case x :: xs =>
for {
(y, ops) <- computeAllOperations(xs)
(z, op) <-
if (y == 0)
List((x*y, "*"), (x+y, "+"), (x-y, "-"))
else
List((x*y, "*"), (x/y, "/"), (x+y, "+"), (x-y, "-"))
} yield (z, "(%1.0f%s%s)" format (x,op,ops))
}
def hasSolution(l: List[Double]) = permute(l) flatMap computeAllOperations filter (_._1 == 24) map (_._2)</lang>
Example:
val problemsIterator = (
Iterator
continually List.fill(4)(scala.util.Random.nextInt(9) + 1 toDouble)
filter (!hasSolution(_).isEmpty)
)
val solutionIterator = problemsIterator map hasSolution
scala> solutionIterator.next
res8: List[String] = List((3*(5-(3-6))), (3*(5-(3-6))), (3*(5+(6-3))), (3+(6+(3*5))), (3*(6-(3-5))), (3+(6+(5*3))), (3*(
6+(5-3))), (3*(5+(6-3))), (3+(6+(5*3))), (3*(6+(5-3))), (6+(3+(5*3))), (6*(5-(3/3))), (6*(5-(3/3))), (3+(6+(3*5))), (3*(
6-(3-5))), (6+(3+(3*5))), (6+(3+(3*5))), (6+(3+(5*3))))
scala> solutionIterator.next
res9: List[String] = List((4-(5*(5-9))), (4-(5*(5-9))), (4+(5*(9-5))), (4+(5*(9-5))), (9-(5-(4*5))), (9-(5-(5*4))), (9-(
5-(4*5))), (9-(5-(5*4))))
scala> solutionIterator.next
res10: List[String] = List((2*(4+(3+5))), (2*(3+(4+5))), (2*(3+(5+4))), (4*(3-(2-5))), (4*(3+(5-2))), (2*(4+(5+3))), (2*
(5+(4+3))), (2*(5+(3+4))), (4*(5-(2-3))), (4*(5+(3-2))))
scala> solutionIterator.next
res11: List[String] = List((4*(5-(2-3))), (2*(4+(5+3))), (2*(5+(4+3))), (2*(5+(3+4))), (2*(4+(3+5))), (2*(3+(4+5))), (2*
(3+(5+4))), (4*(5+(3-2))), (4*(3+(5-2))), (4*(3-(2-5))))
Scheme
This version outputs an S-expression that will eval to 24 (rather than converting to infix notation).
<lang scheme>
- !r6rs
(import (rnrs)
(rnrs eval)
(only (srfi :1 lists) append-map delete-duplicates iota))
(define (map* fn . lis)
(if (null? lis)
(list (fn))
(append-map (lambda (x)
(apply map*
(lambda xs (apply fn x xs))
(cdr lis)))
(car lis))))
(define (insert x li n)
(if (= n 0)
(cons x li)
(cons (car li) (insert x (cdr li) (- n 1)))))
(define (permutations li)
(if (null? li)
(list ())
(map* insert (list (car li)) (permutations (cdr li)) (iota (length li)))))
(define (evaluates-to-24 expr)
(guard (e ((assertion-violation? e) #f)) (= 24 (eval expr (environment '(rnrs base))))))
(define (tree n o0 o1 o2 xs)
(list-ref (list `(,o0 (,o1 (,o2 ,(car xs) ,(cadr xs)) ,(caddr xs)) ,(cadddr xs)) `(,o0 (,o1 (,o2 ,(car xs) ,(cadr xs)) ,(caddr xs)) ,(cadddr xs)) `(,o0 (,o1 ,(car xs) (,o2 ,(cadr xs) ,(caddr xs))) ,(cadddr xs)) `(,o0 (,o1 ,(car xs) ,(cadr xs)) (,o2 ,(caddr xs) ,(cadddr xs))) `(,o0 ,(car xs) (,o1 (,o2 ,(cadr xs) ,(caddr xs)) ,(cadddr xs))) `(,o0 ,(car xs) (,o1 ,(cadr xs) (,o2 ,(caddr xs) ,(cadddr xs))))) n))
(define (solve a b c d)
(define ops '(+ - * /))
(define perms (delete-duplicates (permutations (list a b c d))))
(delete-duplicates
(filter evaluates-to-24
(map* tree (iota 6) ops ops ops perms))))
</lang>
Example output: <lang scheme> > (solve 1 3 5 7) ((* (+ 1 5) (- 7 3))
(* (+ 5 1) (- 7 3)) (* (+ 5 7) (- 3 1)) (* (+ 7 5) (- 3 1)) (* (- 3 1) (+ 5 7)) (* (- 3 1) (+ 7 5)) (* (- 7 3) (+ 1 5)) (* (- 7 3) (+ 5 1)))
> (solve 3 3 8 8) ((/ 8 (- 3 (/ 8 3)))) > (solve 3 4 9 10) () </lang>
Sidef
With eval():
<lang ruby>var formats = [
'((%d %s %d) %s %d) %s %d', '(%d %s (%d %s %d)) %s %d', '(%d %s %d) %s (%d %s %d)', '%d %s ((%d %s %d) %s %d)', '%d %s (%d %s (%d %s %d))',
]
var op = %w( + - * / ) var operators = op.map { |a| op.map {|b| op.map {|c| "#{a} #{b} #{c}" } } }.flat
loop {
var input = read("Enter four integers or 'q' to exit: ", String)
input == 'q' && break
if (input !~ /^\h*[1-9]\h+[1-9]\h+[1-9]\h+[1-9]\h*$/) {
say "Invalid input!"
next
}
var n = input.split.map{.to_n}
var numbers = n.permutations
formats.each { |format|
numbers.each { |n|
operators.each { |operator|
var o = operator.split;
var str = (format % (n[0],o[0],n[1],o[1],n[2],o[2],n[3]))
eval(str) == 24 && say str
}
}
}
}</lang>
Without eval(): <lang ruby>var formats = [
Hash( func => {|d,e,f,g| ((d.$a(e)).$b(f)).$c(g) }, format => "((%d #{a} %d) #{b} %d) #{c} %d" ) },- Output:
Enter four integers or 'q' to exit: 8 7 9 6 (8 / (9 - 7)) * 6 (6 / (9 - 7)) * 8 (8 * 6) / (9 - 7) (6 * 8) / (9 - 7) 8 / ((9 - 7) / 6) 6 / ((9 - 7) / 8) 8 * (6 / (9 - 7)) 6 * (8 / (9 - 7)) Enter four integers or 'q' to exit: q
Simula
<lang simula>BEGIN
CLASS EXPR; BEGIN
REAL PROCEDURE POP;
BEGIN
IF STACKPOS > 0 THEN
BEGIN STACKPOS := STACKPOS - 1; POP := STACK(STACKPOS); END;
END POP;
PROCEDURE PUSH(NEWTOP); REAL NEWTOP;
BEGIN
STACK(STACKPOS) := NEWTOP;
STACKPOS := STACKPOS + 1;
END PUSH;
REAL PROCEDURE CALC(OPERATOR, ERR); CHARACTER OPERATOR; LABEL ERR;
BEGIN
REAL X, Y; X := POP; Y := POP;
IF OPERATOR = '+' THEN PUSH(Y + X)
ELSE IF OPERATOR = '-' THEN PUSH(Y - X)
ELSE IF OPERATOR = '*' THEN PUSH(Y * X)
ELSE IF OPERATOR = '/' THEN BEGIN
IF X = 0 THEN
BEGIN
EVALUATEDERR :- "DIV BY ZERO";
GOTO ERR;
END;
PUSH(Y / X);
END
ELSE
BEGIN
EVALUATEDERR :- "UNKNOWN OPERATOR";
GOTO ERR;
END
END CALC;
PROCEDURE READCHAR(CH); NAME CH; CHARACTER CH;
BEGIN
IF T.MORE THEN CH := T.GETCHAR ELSE CH := EOT;
END READCHAR;
PROCEDURE SKIPWHITESPACE(CH); NAME CH; CHARACTER CH;
BEGIN
WHILE (CH = SPACE) OR (CH = TAB) OR (CH = CR) OR (CH = LF) DO
READCHAR(CH);
END SKIPWHITESPACE;
PROCEDURE BUSYBOX(OP, ERR); INTEGER OP; LABEL ERR;
BEGIN
CHARACTER OPERATOR;
REAL NUMBR;
BOOLEAN NEGATIVE;
SKIPWHITESPACE(CH);
IF OP = EXPRESSION THEN
BEGIN
NEGATIVE := FALSE;
WHILE (CH = '+') OR (CH = '-') DO
BEGIN
IF CH = '-' THEN NEGATIVE := NOT NEGATIVE;
READCHAR(CH);
END;
BUSYBOX(TERM, ERR);
IF NEGATIVE THEN
BEGIN
NUMBR := POP; PUSH(0 - NUMBR);
END;
WHILE (CH = '+') OR (CH = '-') DO
BEGIN
OPERATOR := CH; READCHAR(CH);
BUSYBOX(TERM, ERR); CALC(OPERATOR, ERR);
END;
END
ELSE IF OP = TERM THEN
BEGIN
BUSYBOX(FACTOR, ERR);
WHILE (CH = '*') OR (CH = '/') DO
BEGIN
OPERATOR := CH; READCHAR(CH);
BUSYBOX(FACTOR, ERR); CALC(OPERATOR, ERR)
END
END
ELSE IF OP = FACTOR THEN
BEGIN
IF (CH = '+') OR (CH = '-') THEN
BUSYBOX(EXPRESSION, ERR)
ELSE IF (CH >= '0') AND (CH <= '9') THEN
BUSYBOX(NUMBER, ERR)
ELSE IF CH = '(' THEN
BEGIN
READCHAR(CH);
BUSYBOX(EXPRESSION, ERR);
IF CH = ')' THEN READCHAR(CH) ELSE GOTO ERR;
END
ELSE GOTO ERR;
END
ELSE IF OP = NUMBER THEN
BEGIN
NUMBR := 0;
WHILE (CH >= '0') AND (CH <= '9') DO
BEGIN
NUMBR := 10 * NUMBR + RANK(CH) - RANK('0'); READCHAR(CH);
END;
IF CH = '.' THEN
BEGIN
REAL FAKTOR;
READCHAR(CH);
FAKTOR := 10;
WHILE (CH >= '0') AND (CH <= '9') DO
BEGIN
NUMBR := NUMBR + (RANK(CH) - RANK('0')) / FAKTOR;
FAKTOR := 10 * FAKTOR;
READCHAR(CH);
END;
END;
PUSH(NUMBR);
END;
SKIPWHITESPACE(CH);
END BUSYBOX;
BOOLEAN PROCEDURE EVAL(INP); TEXT INP;
BEGIN
EVALUATEDERR :- NOTEXT;
STACKPOS := 0;
T :- COPY(INP.STRIP);
READCHAR(CH);
BUSYBOX(EXPRESSION, ERRORLABEL);
IF NOT T.MORE AND STACKPOS = 1 AND CH = EOT THEN
BEGIN
EVALUATED := POP;
EVAL := TRUE;
GOTO NOERRORLABEL;
END;
ERRORLABEL:
EVAL := FALSE;
IF EVALUATEDERR = NOTEXT THEN
EVALUATEDERR :- "INVALID EXPRESSION: " & INP;
NOERRORLABEL:
END EVAL;
REAL PROCEDURE RESULT;
RESULT := EVALUATED;
TEXT PROCEDURE ERR;
ERR :- EVALUATEDERR;
TEXT T;
INTEGER EXPRESSION;
INTEGER TERM;
INTEGER FACTOR;
INTEGER NUMBER;
CHARACTER TAB;
CHARACTER LF;
CHARACTER CR;
CHARACTER SPACE;
CHARACTER EOT;
CHARACTER CH;
REAL ARRAY STACK(0:31);
INTEGER STACKPOS;
REAL EVALUATED;
TEXT EVALUATEDERR;
EXPRESSION := 1;
TERM := 2;
FACTOR := 3;
NUMBER := 4;
TAB := CHAR(9);
LF := CHAR(10);
CR := CHAR(13);
SPACE := CHAR(32);
EOT := CHAR(0);
END EXPR;
INTEGER ARRAY DIGITS(1:4); INTEGER SEED, I; REF(EXPR) E;
INTEGER SOLUTION; INTEGER D1,D2,D3,D4; INTEGER O1,O2,O3; TEXT OPS;
OPS :- "+-*/";
E :- NEW EXPR;
OUTTEXT("ENTER FOUR INTEGERS: ");
OUTIMAGE;
FOR I := 1 STEP 1 UNTIL 4 DO DIGITS(I) := ININT; !RANDINT(0, 9, SEED);
DIGITS ;
FOR D1 := 1 STEP 1 UNTIL 4 DO
FOR D2 := 1 STEP 1 UNTIL 4 DO IF D2 <> D1 THEN
FOR D3 := 1 STEP 1 UNTIL 4 DO IF D3 <> D2 AND
D3 <> D1 THEN
FOR D4 := 1 STEP 1 UNTIL 4 DO IF D4 <> D3 AND
D4 <> D2 AND
D4 <> D1 THEN
|
OPERATORS ;
FOR O1 := 1 STEP 1 UNTIL 4 DO
FOR O2 := 1 STEP 1 UNTIL 4 DO
FOR O3 := 1 STEP 1 UNTIL 4 DO
BEGIN
PROCEDURE P(FMT); TEXT FMT;
BEGIN
INTEGER PLUS;
TRY.SETPOS(1);
WHILE FMT.MORE DO
BEGIN
CHARACTER C;
C := FMT.GETCHAR;
IF (C >= '1') AND (C <= '4') THEN
BEGIN
INTEGER DIG; CHARACTER NCH;
DIG := IF C = '1' THEN DIGITS(D1)
ELSE IF C = '2' THEN DIGITS(D2)
ELSE IF C = '3' THEN DIGITS(D3)
ELSE DIGITS(D4);
NCH := CHAR( DIG + RANK('0') );
TRY.PUTCHAR(NCH);
END
ELSE IF C = '+' THEN
BEGIN
PLUS := PLUS + 1;
OPS.SETPOS(IF PLUS = 1 THEN O1 ELSE
IF PLUS = 2 THEN O2
ELSE O3);
TRY.PUTCHAR(OPS.GETCHAR);
END
ELSE IF (C = '(') OR (C = ')') OR (C = ' ') THEN
TRY.PUTCHAR(C)
ELSE
ERROR("ILLEGAL EXPRESSION");
END;
IF E.EVAL(TRY) THEN
BEGIN
IF ABS(E.RESULT - 24) < 0.001 THEN
BEGIN
SOLUTION := SOLUTION + 1;
OUTTEXT(TRY); OUTTEXT(" = ");
OUTFIX(E.RESULT, 4, 10);
OUTIMAGE;
END;
END
ELSE
BEGIN
IF E.ERR <> "DIV BY ZERO" THEN
BEGIN
OUTTEXT(TRY); OUTIMAGE;
OUTTEXT(E.ERR); OUTIMAGE;
END;
END;
END P;
TEXT TRY;
TRY :- BLANKS(17);
P("(1 + 2) + (3 + 4)");
P("(1 + (2 + 3)) + 4");
P("((1 + 2) + 3) + 4");
P("1 + ((2 + 3) + 4)");
P("1 + (2 + (3 + 4))");
END;
OUTINT(SOLUTION, 0);
OUTTEXT(" SOLUTIONS FOUND");
OUTIMAGE;
END. </lang>
ENTER FOUR INTEGERS: 8 7 9 6 (8 / (9 - 7)) * 6 = 24.0000 8 / ((9 - 7) / 6) = 24.0000 (8 * 6) / (9 - 7) = 24.0000 8 * (6 / (9 - 7)) = 24.0000 (6 * 8) / (9 - 7) = 24.0000 6 * (8 / (9 - 7)) = 24.0000 (6 / (9 - 7)) * 8 = 24.0000 6 / ((9 - 7) / 8) = 24.0000 8 SOLUTIONS FOUND 2 garbage collection(s) in 0.0 seconds. Swift<lang swift> import Darwin import Foundation var solution = "" println("24 Game") println("Generating 4 digits...") func randomDigits() -> [Int] { var result = [Int]()
for i in 0 ..< 4 {
result.append(Int(arc4random_uniform(9)+1))
}
return result
} // Choose 4 digits let digits = randomDigits() print("Make 24 using these digits : ") for digit in digits { print("\(digit) ")
} println() // get input from operator var input = NSString(data:NSFileHandle.fileHandleWithStandardInput().availableData, encoding:NSUTF8StringEncoding)! var enteredDigits = [Double]() var enteredOperations = [Character]() let inputString = input as String // store input in the appropriate table for character in inputString { switch character {
case "1", "2", "3", "4", "5", "6", "7", "8", "9":
let digit = String(character)
enteredDigits.append(Double(digit.toInt()!))
case "+", "-", "*", "/":
enteredOperations.append(character)
case "\n":
println()
default:
println("Invalid expression")
}
} // check value of expression provided by the operator var value = 0.0 if enteredDigits.count == 4 && enteredOperations.count == 3 { value = enteredDigits[0]
for (i, operation) in enumerate(enteredOperations) {
switch operation {
case "+":
value = value + enteredDigits[i+1]
case "-":
value = value - enteredDigits[i+1]
case "*":
value = value * enteredDigits[i+1]
case "/":
value = value / enteredDigits[i+1]
default:
println("This message should never happen!")
}
}
} func evaluate(dPerm: [Double], oPerm: [String]) -> Bool { var value = 0.0
if dPerm.count == 4 && oPerm.count == 3 {
value = dPerm[0]
for (i, operation) in enumerate(oPerm) {
switch operation {
case "+":
value = value + dPerm[i+1]
case "-":
value = value - dPerm[i+1]
case "*":
value = value * dPerm[i+1]
case "/":
value = value / dPerm[i+1]
default:
println("This message should never happen!")
}
}
}
return (abs(24 - value) < 0.001)
} func isSolvable(inout digits: [Double]) -> Bool { var result = false var dPerms = Double() permute(&digits, &dPerms, 0) let total = 4 * 4 * 4 var oPerms = String() permuteOperators(&oPerms, 4, total) for dig in dPerms { for opr in oPerms { var expression = "" if evaluate(dig, opr) { for digit in dig { expression += "\(digit)" } for oper in opr { expression += oper } solution = beautify(expression) result = true } } } return result } func permute(inout lst: [Double], inout res: Double, k: Int) -> Void { for i in k ..< lst.count {
swap(&lst[i], &lst[k])
permute(&lst, &res, k + 1)
swap(&lst[k], &lst[i])
}
if k == lst.count {
res.append(lst)
}
} // n=4, total=64, npow=16 func permuteOperators(inout res: String, n: Int, total: Int) -> Void { let posOperations = ["+", "-", "*", "/"]
let npow = n * n
for i in 0 ..< total {
res.append([posOperations[(i / npow)], posOperations[((i % npow) / n)], posOperations[(i % n)]])
}
} func beautify(infix: String) -> String { let newString = infix as NSString var solution = "" solution += newString.substringWithRange(NSMakeRange(0, 1)) solution += newString.substringWithRange(NSMakeRange(12, 1)) solution += newString.substringWithRange(NSMakeRange(3, 1)) solution += newString.substringWithRange(NSMakeRange(13, 1)) solution += newString.substringWithRange(NSMakeRange(6, 1)) solution += newString.substringWithRange(NSMakeRange(14, 1)) solution += newString.substringWithRange(NSMakeRange(9, 1)) return solution } if value != 24 { println("The value of the provided expression is \(value) instead of 24!")
if isSolvable(&enteredDigits) {
println("A possible solution could have been " + solution)
} else {
println("Anyway, there was no known solution to this one.")
}
} else { println("Congratulations, you found a solution!")
}</lang>
24 Game Generating 4 digits... Make 24 using these digits : 2 4 1 9 2+1*4+9 The value of the provided expression is 21.0 instead of 24! A possible solution could have been 9-2-1*4 24 Game Generating 4 digits... Make 24 using these digits : 2 7 2 3 7-2*2*3 The value of the provided expression is 30.0 instead of 24! A possible solution could have been 3+7+2*2 24 Game Generating 4 digits... Make 24 using these digits : 4 6 3 4 4+4+6+3 The value of the provided expression is 17.0 instead of 24! A possible solution could have been 3*4-6*4 24 Game Generating 4 digits... Make 24 using these digits : 8 8 2 6 8+8+2+6 Congratulations, you found a solution! 24 Game Generating 4 digits... Make 24 using these digits : 6 7 8 9 6+7+8+9 The value of the provided expression is 30.0 instead of 24! Anyway, there was no known solution to this one. TclThis is a complete Tcl script, intended to be invoked from the command line. <lang tcl>package require struct::list
set patterns { {((A x B) y C) z D}
{(A x (B y C)) z D}
{(A x B) y (C z D)}
{A x ((B y C) z D)}
{A x (B y (C z D))}
}
set permutations [struct::list map [struct::list permutations {a b c d}] \ {apply {v {lassign $v a b c d; list A $a B $b C $c D $d}}}]
set operations {+ - * /}
proc find24GameSolutions {values} { global operations patterns permutations
set found {}
# For each possible structure with numbers at the leaves...
foreach pattern $patterns {
foreach permutation $permutations { set p [string map [subst { a [lindex $values 0].0 b [lindex $values 1].0 c [lindex $values 2].0 d [lindex $values 3].0 }] [string map $permutation $pattern]] # For each possible structure with operators at the branches... foreach x $operations { foreach y $operations { foreach z $operations { set e [string map [subst {x $x y $y z $z}] $p] # Try to evaluate (div-zero is an issue!) and add it to # the result if it is 24 catch { if {[expr $e] == 24.0} { lappend found [string map {.0 {}} $e] } } } } } } } return $found }
proc print24GameSolutionFor {values} { set found [lsort -unique [find24GameSolutions $values]]
if {![llength $found]} {
puts "No solution possible" } else {
puts "Total [llength $found] solutions (may include logical duplicates)" puts "First solution: [lindex $found 0]" } } print24GameSolutionFor $argv</lang>
Demonstrating it in use: bash$ tclsh8.4 24player.tcl 3 2 8 9 Total 12 solutions (may include logical duplicates) First solution: ((9 - 3) * 8) / 2 bash$ tclsh8.4 24player.tcl 1 1 2 7 Total 8 solutions (may include logical duplicates) First solution: (1 + 2) * (1 + 7) bash$ tclsh8.4 24player.tcl 1 1 1 1 No solution possible UrsalaThis uses exhaustive search and exact rational arithmetic to enumerate all solutions. The algorithms accommodate data sets with any number of digits and any target value, but will be limited in practice by combinatorial explosion as noted elsewhere. (Rationals are stored as pairs of integers, hence
The
tree_shapes = "n". (@vLPiYo //eql iota "n")*~ (rep"n" ~&iiiK0NlrNCCVSPTs) {0^:<>} with_leaves = ^|DrlDrlK34SPSL/permutations ~& with_roots = ^DrlDrlK35dlPvVoPSPSL\~&r @lrhvdNCBvLPTo2DlS @hiNCSPtCx ~&K0=> value = *^ ~&v?\(@d ~&\1) ^|H\~&hthPX '+-*/'-$<sum,difference,product,quotient> format = *^ ~&v?\-+~&h,%zP@d+- ^H/mat@d *v ~&t?\~& :/`(+ --')' game"n" "d" = format* value==("n",1)*~ with_roots/'+-*/' with_leaves/"d"*-1 tree_shapes length "d"</lang> test program: <lang Ursala>#show+ test_games = mat` * pad` *K7 pad0 game24* <<2,3,8,9>,<5,7,4,1>,<5,6,7,8>></lang> output: 8/(2/(9-3)) 1-(5-(7*4)) 6*(5+(7-8))
8*(9-(2*3)) 1-(5-(4*7)) 6*(7+(5-8))
8*(9-(3*2)) 1+((7*4)-5) 6*(7-(8-5))
8*((9-3)/2) 1+((4*7)-5) 6*(5-(8-7))
(8/2)*(9-3) (7*4)-(5-1) 6*(8/(7-5))
(9-3)/(2/8) (7*4)+(1-5) 8*(6/(7-5))
(9-3)*(8/2) (4*7)-(5-1) 6*((5+7)-8)
(8*(9-3))/2 (4*7)+(1-5) 6*((7+5)-8)
(9-(2*3))*8 (1-5)+(7*4) 6/((7-5)/8)
(9-(3*2))*8 (1-5)+(4*7) 6*((7-8)+5)
((9-3)/2)*8 (7*(5-1))-4 6*((5-8)+7)
((9-3)*8)/2 (1+(7*4))-5 8/((7-5)/6)
(1+(4*7))-5 (5+7)*(8-6)
((7*4)-5)+1 (7+5)*(8-6)
((7*4)+1)-5 (6*8)/(7-5)
((4*7)-5)+1 (8-6)*(5+7)
((4*7)+1)-5 (8-6)*(7+5)
((5-1)*7)-4 (8*6)/(7-5)
(6/(7-5))*8
(5+(7-8))*6
(7+(5-8))*6
(7-(8-5))*6
(5-(8-7))*6
(8/(7-5))*6
((5+7)-8)*6
((7+5)-8)*6
((7-8)+5)*6
((5-8)+7)*6
Yabasic<lang Yabasic>operators$ = "*+-/" space$ = " " sub present() clear screen print "24 Game" print "============\n" print "Computer provide 4 numbers (1 to 9). With operators +, -, * and / you try to\nobtain 24." print "Use Reverse Polish Notation (first operand and then the operators)" print "For example: instead of 2 + 4, type 2 4 +\n\n" end sub repeat present() serie$ = sortString$(genSerie$()) valid$ = serie$+operators$ print "If you give up, press ENTER and the program attempts to find a solution." line input "Write your solution: " input$ if input$ = "" then print "Thinking ... " res$ = explorer$() if res$ = "" print "Can not get 24 with these numbers.." else input$ = delSpace$(input$) inputSort$ = sortString$(input$) if (right$(inputSort$,4) <> serie$) or (len(inputSort$)<>7) then print "Syntax error" else result = evalInput(input$) print "Your solution = ",result," is "; if result = 24 then print "Correct!" else print "Wrong!" end if end if end if print "\nDo you want to try again? (press N for exit, other key to continue)" until(upper$(left$(inkey$(),1)) = "N") exit sub genSerie$() local i, c$, s$ print "The numbers you should use are: "; i = ran() for i = 1 to 4 c$ = str$(int(ran(9))+1) print c$," "; s$ = s$ + c$ next i print return s$ end sub
while(entr$<>"") c$ = left$(entr$,1) entr$ = mid$(entr$,2) if instr(serie$,c$) then i = i + 1 n(i) = val(c$) elseif instr(operators$,c$) then d2 = n(i) n(i) = 0 i = i - 1 if i = 0 return d1 = n(i) n(i) = evaluator(d1, d2, c$) else print "Invalid symbol" return end if wend return n(i) end sub
switch op$ case "+": t = d1 + d2 : break case "-": t = d1 - d2 : break case "*": t = d1 * d2 : break case "/": t = d1 / d2 : break end switch return t end sub
n = token(entr$,t$()," ") for i=1 to n s$ = s$ + t$(i) next i return s$ end sub
fin = len(string$)-1 repeat signal = false for n = 1 to fin if mid$(string$,n,1) > mid$(string$,n+1,1) then signal = true c$ = mid$(string$,n,1) mid$(string$,n,1) = mid$(string$,n+1,1) mid$(string$,n+1,1) = c$ end if next n until(signal = false) return string$ end sub
for d1 = 1 to 4 for d2 = 1 to 4 for o3 = 1 to 4 for x4 = 1 to 8 for x5 = 1 to 8 for x6 = 1 to 8 for o7 = 1 to 4 p$ = mid$(serie$,d1,1)+mid$(serie$,d2,1)+mid$(operators$,o3,1) p$ = p$+mid$(valid$,x4,1)+mid$(valid$,x5,1)+mid$(valid$,x6,1) p$ = p$+mid$(operators$,o7,1) if not instr(solutions$,p$) then if validateInput(p$) then result = evalInput(p$) if result = 24 then solution = solution + 1 print "Solution: ",solution," = "; solutions$ = solutions$ + p$ for n = 1 to 7 print mid$(p$,n,1)," "; next n print end if end if end if next o7 next x6 next x5 next x4 next o3 next d2 next d1 return p$ end sub
inputSort$ = sortString$(e$) if serie$ <> right$(inputSort$,4) return false for n=1 to 3 if not instr(operators$,mid$(inputSort$,n,1)) then return false end if next n return true end sub</lang> zklA brute for search for all solutions. Lexicographical duplicates are removed. File solve24.zkl: <lang zkl>var [const] H=Utils.Helpers; fcn u(xs){ xs.reduce(fcn(us,s){us.holds(s) and us or us.append(s) },L()) } var ops=u(H.combosK(3,"+-*/".split("")).apply(H.permute).flatten()); var fs=T( fcn f0(a,b,c,d,x,y,z){ Op(z)(Op(y)(Op(x)(a,b),c),d) }, // ((AxB)yC)zD
fcn f1(a,b,c,d,x,y,z){ Op(y)(Op(x)(a,b),Op(z)(c,d)) }, // (AxB)y(CzD)
fcn f2(a,b,c,d,x,y,z){ Op(z)(Op(x)(a,Op(y)(b,c)),d) }, // (Ax(ByC))zD
fcn f3(a,b,c,d,x,y,z){ Op(x)(a,Op(z)(Op(y)(b,c),d)) }, // Ax((ByC)zD)
fcn f4(a,b,c,d,x,y,z){ Op(x)(a,Op(y)(b,Op(z)(c,d))) }, // Ax(By(CzD))
); var fts= // format strings for human readable formulas T("((d.d).d).d", "(d.d).(d.d)", "(d.(d.d)).d", "d.((d.d).d)", "d.(d.(d.d))")
.pump(List,T("replace","d","%d"),T("replace",".","%s"));
fcn f2s(digits,ops,f){ fts[f.name[1].toInt()].fmt(digits.zip(ops).flatten().xplode(),digits[3]); } fcn game24Solver(digitsString){ digits:=digitsString.split("").apply("toFloat");
[[(digits4,ops3,f); H.permute(digits); ops; // list comprehension
fs,{ try{f(digits4.xplode(),ops3.xplode()).closeTo(24,0.001) }
catch(MathError){ False } };
{ f2s(digits4,ops3,f) }]];
}</lang> <lang zkl>solutions:=u(game24Solver(ask(0,"digits: "))); println(solutions.len()," solutions:"); solutions.apply2(Console.println);</lang> One trick used is to look at the solving functions name and use the digit in it to index into the formats list.
zkl solve24.zkl 6795 6 solutions: 6+((7-5)*9) 6-((5-7)*9) 6-(9*(5-7)) 6+(9*(7-5)) (9*(7-5))+6 ((7-5)*9)+6 zkl solve24.zkl 1111 0 solutions: zkl solve24.zkl 3388 1 solutions: 8/(3-(8/3)) zkl solve24.zkl 1234 242 solutions: ((1+2)+3)*4 ... |
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