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>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 sorted lowercased words of 3 to 9 characters" words = urllib.request.urlopen(url).read().decode().strip().lower().split() return sorted(set(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.
<lang perl6>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;
};
print { qq:to/END/; Using $dict, minimum $min letters. \t┌───┬───┬───┐ \t│ $^a │ $^b │ $^c │ \t├───┼───┼───┤ \t│ $^d │ $^e │ $^f │ \t├───┼───┼───┤ \t│ $^g │ $^h │ $^i │ \t└───┴───┴───┘ END }( |$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