Word wheel
A "word wheel" is a type of word game commonly found on the "puzzle" page of newspapers. You are presented with nine letters arranged in a circle or 3x3 grid. The objective is to find as many words as you can using only the letters contained in the wheel or grid. Each word must contain the letter in the centre of the wheel or grid. Usually there will be a minimum word length of 3 or 4 characters. Each letter may only be used as many times as it appears in the wheel or grid.
For example:
N D E O K G E L W
- Task
Write a program to solve the above "word wheel" puzzle. Specifically:
- Find all words of 3 or more letters using only the letters in the string "ndeokgelw".
- All words must contain the central letter "k".
- Each letter may be used only as many times as it appears in the string.
- For this task we'll use lowercase English letters exclusively.
A "word" is defined to be any string contained in the file located at http://wiki.puzzlers.org/pub/wordlists/unixdict.txt. If you prefer to use a different
dictionary please state which one you have used.
C++
The puzzle parameters are hard-coded but could easily be replaced by e.g. command line arguments. <lang cpp>#include <array>
- include <iostream>
- include <fstream>
- include <map>
- include <string>
- include <vector>
// A multiset specialized for strings consisting of lowercase // letters ('a' to 'z'). class letterset { public:
explicit letterset(const std::string& str) {
count_.fill(0);
for (char c : str) {
if (c >= 'a' && c <= 'z')
++count_[c - 'a' + 1];
else
++count_[0];
}
}
bool contains(const letterset& set) const {
for (size_t i = 0; i < count_.size(); ++i) {
if (set.count_[i] > count_[i])
return false;
}
return true;
}
unsigned int count(char c) const {
if (c >= 'a' && c <= 'z')
return count_[c - 'a' + 1];
return 0;
}
bool is_valid() const {
return count_[0] == 0;
}
private:
// elements 1..26 contain the number of times each lowercase // letter occurs in the word // element 0 is the number of other characters in the word std::array<unsigned int, 27> count_;
};
template <typename iterator, typename separator> std::string join(iterator begin, iterator end, separator sep) {
std::string result;
if (begin != end) {
result += *begin++;
for (; begin != end; ++begin) {
result += sep;
result += *begin;
}
}
return result;
}
int main(int argc, char** argv) {
const int min_length = 3;
const char* letters = "ndeokgelw";
const char central_letter = 'k';
const char* dict(argc == 2 ? argv[1] : "unixdict.txt");
std::ifstream in(dict);
if (!in) {
std::cerr << "Cannot open file " << dict << '\n';
return 1;
}
letterset set(letters);
std::string word;
std::map<size_t, std::vector<std::string>> words;
while (getline(in, word)) {
if (word.size() < min_length)
continue;
letterset subset(word);
if (subset.count(central_letter) > 0 && set.contains(subset)) {
words[word.size()].push_back(word);
}
}
for (const auto& p : words) {
const auto& v = p.second;
auto n = v.size();
std::cout << "Found " << n << " " << (n == 1 ? "word" : "words")
<< " of length " << p.first << ": "
<< join(v.begin(), v.end(), ", ") << '\n';
}
return 0;
}</lang>
- Output:
Found 5 words of length 3: eke, elk, keg, ken, wok Found 10 words of length 4: keel, keen, keno, knee, knew, know, kong, leek, week, woke Found 1 word of length 5: kneel Found 1 word of length 9: knowledge
Factor
<lang factor>USING: assocs io.encodings.ascii io.files kernel math math.statistics prettyprint sequences sorting ;
! Only consider words longer than two letters and words that ! contain elt.
- pare ( elt seq -- new-seq )
[ [ member? ] keep length 2 > and ] with filter ;
- words ( input-str path -- seq )
[ [ midpoint@ ] keep nth ] [ ascii file-lines pare ] bi* ;
- ?<= ( m n/f -- ? ) dup f = [ nip ] [ <= ] if ;
! Can we make sequence 1 with the elements in sequence 2?
- can-make? ( seq1 seq2 -- ? )
[ histogram ] bi@ [ swapd at ?<= ] curry assoc-all? ;
- solve ( input-str path -- seq )
[ words ] keepd [ can-make? ] curry filter ;
"ndeokgelw" "unixdict.txt" solve [ length ] sort-with .</lang>
- Output:
{
"eke"
"elk"
"keg"
"ken"
"wok"
"keel"
"keen"
"keno"
"knee"
"knew"
"know"
"kong"
"leek"
"week"
"woke"
"kneel"
"knowledge"
}
Julia
<lang julia>using Combinatorics
const tfile = download("http://wiki.puzzlers.org/pub/wordlists/unixdict.txt") const wordlist = Dict(w => 1 for w in split(read(tfile, String), r"\s+"))
function wordwheel(wheel, central)
returnlist = String[]
for combo in combinations([string(i) for i in wheel])
if central in combo && length(combo) > 2
for perm in permutations(combo)
word = join(perm)
if haskey(wordlist, word) && !(word in returnlist)
push!(returnlist, word)
end
end
end
end
return returnlist
end
println(wordwheel("ndeokgelw", "k"))
</lang>
- Output:
["ken", "keg", "eke", "elk", "wok", "keno", "knee", "keen", "knew", "kong", "know", "woke", "keel", "leek", "week", "kneel", "knowledge"]
Python
<lang python>import urllib.request from collections import Counter
GRID = """
N D E
O K G
E L W
"""
def getwords(url='http://wiki.puzzlers.org/pub/wordlists/unixdict.txt'):
"Return lowercased words of 3 to 9 characters" words = urllib.request.urlopen(url).read().decode().strip().lower().split() return (w for w in words if 2 < len(w) < 10)
def solve(grid, dictionary):
gridcount = Counter(grid)
mid = grid[4]
return [word for word in dictionary
if mid in word and not (Counter(word) - gridcount)]
if __name__ == '__main__':
chars = .join(GRID.strip().lower().split())
found = solve(chars, dictionary=getwords())
print('\n'.join(found))</lang>
- Output:
eke elk keel keen keg ken keno knee kneel knew know knowledge kong leek week wok woke
Raku
Everything is adjustable through command line parameters.
Defaults to task specified wheel, unixdict.txt, minimum 3 letters.
Using Terminal::Boxer from the Raku ecosystem.
<lang perl6>use Terminal::Boxer;
my %*SUB-MAIN-OPTS = :named-anywhere;
unit sub MAIN ($wheel = 'ndeokgelw', :$dict = './unixdict.txt', :$min = 3);
my $must-have = $wheel.comb[4].lc;
my $has = $wheel.comb».lc.Bag;
my %words; $dict.IO.slurp.words».lc.map: {
next if not .contains($must-have) or .chars < $min;
%words{.chars}.push: $_ if .comb.Bag ⊆ $has;
};
say "Using $dict, minimum $min letters.";
print rs-box :3col, :3cell, :indent("\t"), $wheel.comb».uc;
printf "%d letters: %s\n", .key, .value.sort.join(', ') for %words.sort; </lang>
- Output:
<lang>raku word-wheel.raku</lang>
Using ./unixdict.txt, minimum 3 letters. ╭───┬───┬───╮ │ N │ D │ E │ ├───┼───┼───┤ │ O │ K │ G │ ├───┼───┼───┤ │ E │ L │ W │ ╰───┴───┴───╯ 3 letters: eke, elk, keg, ken, wok 4 letters: keel, keen, keno, knee, knew, know, kong, leek, week, woke 5 letters: kneel 9 letters: knowledge
- Larger dictionary
Using the much larger dictionary words.txt file from https://github.com/dwyl/english-words
<lang>raku word-wheel.raku --dict=./words.txt</lang>
Using ./words.txt, minimum 3 letters. ╭───┬───┬───╮ │ N │ D │ E │ ├───┼───┼───┤ │ O │ K │ G │ ├───┼───┼───┤ │ E │ L │ W │ ╰───┴───┴───╯ 3 letters: dkg, dkl, eek, egk, eke, ekg, elk, gok, ked, kee, keg, kel, ken, keo, kew, kln, koe, kol, kon, lek, lgk, nek, ngk, oke, owk, wok 4 letters: deek, deke, doek, doke, donk, eked, elke, elko, geek, genk, gonk, gowk, keel, keen, keld, kele, kend, keno, keon, klee, knee, knew, know, koel, koln, kone, kong, kwon, leek, leke, loke, lonk, okee, oken, week, welk, woke, wolk, wonk 5 letters: dekle, dekow, gleek, kedge, kendo, kleon, klong, kneed, kneel, knowe, konde, oklee, olnek, woken 6 letters: gowked, keldon, kelwen, knowle, koleen 8 letters: weeklong 9 letters: knowledge
- Exercise adjustable parameters
<lang>raku word-wheel.raku iuymslleb --dict=./words.txt --min=4</lang>
Using ./words.txt, minimum 4 letters. ╭───┬───┬───╮ │ I │ U │ Y │ ├───┼───┼───┤ │ M │ S │ L │ ├───┼───┼───┤ │ L │ E │ B │ ╰───┴───┴───╯ 4 letters: bels, beys, bise, blus, bmus, bsem, bsie, bslm, bsme, bums, busy, buys, byes, eisb, elis, ells, elms, elsi, elsy, elys, emus, emys, ills, ilse, imsl, isle, islm, islu, ismy, leis, leys, libs, lies, lise, lues, luis, lums, lyes, lyse, mels, mibs, mils, mise, misy, msie, musb, muse, sbli, sell, semi, siey, sile, sill, sime, sium, slbm, sleb, sley, slim, slub, slue, slum, suey, suiy, sull, sumi, sumy, syli, syll, uims 5 letters: belis, bells, belus, bemis, biles, bills, bisme, blues, bulls, bulse, busey, buyse, eblis, ellis, embus, emuls, eulis, ileus, illus, ilyse, isbel, iseum, lesiy, lesli, lesly, lieus, liles, limbs, limes, limsy, lisle, lubes, luise, lusby, lyles, melis, mells, miles, mills, misly, mlles, mules, mulls, mulse, musie, musil, myles, mysel, sebum, selby, selim, selli, selly, sibel, sible, sibyl, silly, silyl, simul, slily, slime, slimy, smell, smile, smily, sully, sybil, syble, yells, yills, ylems, yules, yusem 6 letters: bellis, bisley, bluesy, blueys, bluism, blumes, bulies, bullis, busily, elymus, embusy, illyes, imbues, libels, libuse, limbus, limeys, milles, milsey, muesli, muleys, musily, mysell, sibell, sibley, simule, slimly, smelly, smiley, umbels, umbles 7 letters: besully, bullies, bullism, elysium, illumes, mulleys, sibylle, silybum, sublime, sybille 8 letters: bullyism, semibull 9 letters: sublimely
REXX
Quite a bit of boilerplate was included in this REXX example.
No assumption was made as the "case" of the words (upper/lower/mixed case). Duplicate words were detected and
eliminated (god and God), as well as words that didn't contain all Roman (Latin) letters.
The number of minimum letters can be specified, as well as the dictionary fileID and the letters in the word wheel (grid).
Additional information is also provided. <lang rexx>/*REXX pgm finds (dictionary) words which can be found in a specified word wheel (grid).*/ parse arg grid mLen iFID . /*obtain optional arguments from the CL*/ if grid==|grid=="," then grid= 'ndeokgelw' /*Not specified? Then use the default.*/ if mLen==|mLen=="," then mLen= 3 /* " " " " " " */ if iFID==|iFID=="," then iFID= 'UNIXDICT.TXT' /* " " " " " " */ omLen= mLen; mLen= abs(mLen) /*if negative, then don't show a list. */ gridU= grid; upper gridU; guAir= inflate(gridU) /*get an uppercase version of the grid.*/ Lg= length(grid); Hg= Lg%2 c= substr(grid, Hg+1,1 ); upper c /*get uppercase center letter in grid. */ wrds= 0 /*# words that are in the dictionary. */ wees= 0 /*" " " " too short. */ dups= 0 /*" " " " duplicates. */ ills= 0 /*" " " contain not letters.*/ good= 0 /*" " " contain center letter. */ say ' Reading the file: ' iFID @.= . /*uppercase non─duplicated dict. words.*/ $= /*the list of dictionary words in grid.*/
do recs=1 while lines(iFID)\==0 /*process all words in the dictionary. */
_= linein(iFID) /*read a word (line of text) from dict.*/
u= space(_, 0); upper u; L= length(u) /*elide superfluous blanks from a word.*/
L= length(u) /*obtain the length of the word. */
if @.u\==. then do; dups= dups+1; iterate; end /*is this a duplicate? */
if L<mLen then do; wees= wees+1; iterate; end /*is the word too short? */
if \datatype(u,'U') then do; ills= ills+1; iterate; end /*has word non─letters? */
@.u= /*signify that U is a dictionary word*/
wrds= wrds + 1 /*bump the number of "good" dist. words*/
if pos(c, u)==0 then iterate /*word doesn't have center grid letter.*/
good= good + 1 /*bump # center─letter words in dict. */
if verify(u, gridU)\==0 then iterate /*word contains a letter not in grid. */
air= inflate(u) /*insert "air" (blanks) between letters*/
if \deflate(air, guAir) then iterate /*have all the letters been found ? */
$= $ u /*add this word to the "found" list. */
end /*recs*/
say say ' number of records (lines) in the dictionary: ' right( commas(recs), 9) say ' number of ill─formed words in the dictionary: ' right( commas(ills), 9) say ' number of duplicate words in the dictionary: ' right( commas(dups), 9) say ' number of too─small words in the dictionary: ' right( commas(wees), 9) say ' number of acceptable words in the dictionary: ' right( commas(wrds), 9) say ' number center─letter words in the dictionary: ' right( commas(good), 9) say ' the minimum length of words that can be used: ' right( commas(mLen), 9) say ' the word wheel (grid) being used: ' grid say ' center of the word wheel (grid) being used: ' right('↑', Hg+1) say; #= words($); $= strip($) say ' number of word wheel words in the dictionary: ' right( commas(# ), 9) if #==0 | omLen<0 then exit # say say ' The list of word wheel words found:'; say copies('─', length($)); say lower($) exit # /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ lower: arg aa; @='abcdefghijklmnopqrstuvwxyz'; @u=@; upper @u; return translate(aa,@,@U) commas: parse arg _; do jc=length(_)-3 to 1 by -3; _=insert(',', _, jc); end; return _ inflate: procedure; arg z 1 a 2; do m=2 to length(z); a= a substr(z,m,1); end; return a /*──────────────────────────────────────────────────────────────────────────────────────*/ deflate: procedure; arg aa,guA; Laa= length(aa)
do n=1 to Laa by 2; p= wordpos( substr(aa,n,1), guA); if p==0 then return 0
guA= delword(guA, p, 1)
end /*n*/; return 1</lang>
- output when using the default inputs:
Reading the file: UNIXDICT.TXT
number of records (lines) in the dictionary: 25,105
number of ill─formed words in the dictionary: 126
number of duplicate words in the dictionary: 0
number of too─small words in the dictionary: 159
number of acceptable words in the dictionary: 24,819
number center─letter words in the dictionary: 1,834
the minimum length of words that can be used: 3
the word wheel (grid) being used: ndeokgelw
center of the word wheel (grid) being used: ↑
number of word wheel words in the dictionary: 17
The list of word wheel words found:
─────────────────────────────────────────────────────────────────────────────────────
eke elk keel keen keg ken keno knee kneel knew know knowledge kong leek week wok woke
- output when using the inputs: satRELion -3
(I am trying for a maximum word wheel count for the UNIXDICT dictionary;
the negative minimum word length indicates to not list the words found.)
Reading the file: UNIXDICT.TXT
number of records (lines) in the dictionary: 25,105
number of ill─formed words in the dictionary: 126
number of duplicate words in the dictionary: 0
number of too─small words in the dictionary: 159
number of acceptable words in the dictionary: 24,819
number center─letter words in the dictionary: 14,755
the minimum length of words that can be used: 3
the word wheel (grid) being used: satRELion
center of the word wheel (grid) being used: ↑
number of word wheel words in the dictionary: 212