Scralphabet

Kantung normal ubin Scrabble berisi huruf-huruf berikut ( ?adalah ubin kosong, yang dapat digunakan untuk huruf lain):

AAAAAAAAABBCCDDDDEEEEEEEEEEEEFFGGGHHIIIIIIIIIJKLLLLMMNNNNNNOOOOOOOOPPQRRRRRRSSSSTTTTTTUUUUVVWWXYYZ??

Surat-surat memiliki nilai berikut:

{"A": 1,"B": 3,"C": 3,"D": 2,"E": 1,"F": 4,"G": 2,"H": 4,"I": 1,"J": 8,"K": 5,"L": 1,"M": 3,"N": 1,"O": 1,"P": 3,"Q": 10,"R": 1,"S": 1,"T": 1,"U": 1,"V": 4,"W": 4,"X": 8,"Y": 4,"Z": 10,"?": 0}

Diberikan kantong normal ubin Scrabble, buat kumpulan kata-kata non-berpotongan dengan skor tertinggi (yaitu, kata-kata individual, bukan pada papan Scrabble) dengan ketentuan sebagai berikut:

• Skor untuk setiap kata adalah sum(letter_values) * length(word).
• Anda hanya dapat memasukkan maksimal satu kata yang dimulai dengan setiap huruf alfabet (jadi, maksimal 26 kata).
• Hanya kata-kata Scrabble yang valid (dari kamus ini ) yang dapat dimasukkan. Anda dapat membaca kamus dari suatu file, mengkode-kodenya (ugh), atau mengikisnya dari situs web.
• Anda tidak perlu menggunakan setiap ubin, tetapi semua ubin yang tidak digunakan membentuk satu kata, mencetak dengan cara yang sama, yang mengurangi skor Anda.

Jika diinginkan, kode Anda dapat menerima dua input: isi tas sebagai string, dan nilai huruf dalam beberapa format yang mirip dengan python dict(seperti di atas); sebagai alternatif, Anda dapat membuat hard-code isi tas dan nilai huruf. Seharusnya menampilkan kata-kata dalam set Anda, skor masing-masing, dan skor total Anda, dalam beberapa format yang masuk akal.

Kumpulan kata dengan skor tertinggi menang, dengan ikatan akan dikirim lebih dulu.

C, 2765 (optimal)

Edit

Sekarang semua dalam satu file C. Ini hanya menemukan semua solusi optimal. Mereka semua harus memiliki 6 kata 15 huruf dan satu kata 10 huruf yang terdiri dari 8 huruf bernilai 1 dan dua kosong. Untuk itu saya hanya perlu memuat sebagian kecil dari kamus dan saya tidak perlu mencari 15 kata kata dengan kosong. Kode adalah pencarian mendalam-pertama lengkap sederhana.

#include <stdio.h>
#include <stdint.h>
#include <string.h>
struct w {
    struct lc { uint64_t hi,lo; } lc;
    char w[16];
} w15[6000], w10[40000];
int n15,n10;
struct lc pool = { 0x12122464612, 0x8624119232c4229 };
int pts[27] = {0,1,3,3,2,1,4,2,4,1,8,5,1,3,1,1,3,10,1,1,1,1,4,4,8,4,10};
int f[27],fs[26], w15c[27],w15l[27][6000];
int count(struct lc a, int l) { return (l < 16 ? a.lo << 4 : a.hi) >> 4*(l&15) & 15; }
int matches_val(uint64_t a, uint64_t b) {
    uint64_t mask = 0x1111111111111111ll;
    return !((a - b ^ a ^ b) & mask);
}
int matches(struct lc all, struct lc a) { return matches_val(all.hi,a.hi) && matches_val(all.lo,a.lo); }
int picks[10];
void try(struct lc cur, int used, int level) {
    int c, i, must;
    if (level == 6) {
    for (i = 0; i<27; i++) if (count(cur, i) && pts[i]>1) return;
    for (i = 0; i < n10; i++) if(!(used & (1 << (w10[i].w[0] & 31))) && matches(w10[i].lc, cur)) {
        for (c = 0; c<level; c++) printf("%s ",w15[picks[c]].w);
        printf("%s\n",w10[i].w);
    }
    return;
    }
    for (i = 0; i < 26;i++) if (count(cur,fs[i])) break;
    must = fs[i];
    for (c = 0; c < w15c[must]; c++) { i = w15l[must][c]; if(!(used & (1 << (w15[i].w[0] & 31))) && matches(cur, w15[i].lc)) {
    struct lc b = { cur.hi - w15[i].lc.hi, cur.lo - w15[i].lc.lo };
    picks[level] = i;
    try(b, used + (1 << (w15[i].w[0] & 31)), level+1);
    }}
}
int cmpfs(int *a, int *b){return f[*a]-f[*b];}
void ins(struct w*w, char *s, int c) {
    int i;
    strcpy(w->w,s);
    for (;*s;s++)
    if (*s&16) w->lc.hi += 1ll << 4*(*s&15); else w->lc.lo += 1ll << 4*(*s&15) - 4;
    if (c) for (i = 0; i < 27;i++) if (count(w->lc,i)) f[i]++, w15l[i][w15c[i]++] = w-w15;
}
int main() {
    int i;
    char s[20];
    while(scanf("%s ",s)>0) {
    if (strlen(s) == 15) ins(w15 + n15++,s,1);
    if (strlen(s) == 10) ins(w10 + n10++,s,0);
    }
    for (i = 0; i < 26;i++) fs[i] = i+1;
    qsort(fs, 26, sizeof(int), cmpfs);
    try(pool, 0, 0);
}

Pemakaian:

$time ./scrab <sowpods.txt
cc -O3    scrab.c   -o scrab
JUXTAPOSITIONAL DEMISEMIQUAVERS ACKNOWLEDGEABLY WEATHERPROOFING CONVEYORIZATION FEATHERBEDDINGS LAURUSTINE
JUXTAPOSITIONAL DEMISEMIQUAVERS ACKNOWLEDGEABLY WEATHERPROOFING CONVEYORIZATION FEATHERBEDDINGS LUXURIATED
JUXTAPOSITIONAL DEMISEMIQUAVERS ACKNOWLEDGEABLY WEATHERPROOFING CONVEYORIZATION FEATHERBEDDINGS LUXURIATES
JUXTAPOSITIONAL DEMISEMIQUAVERS ACKNOWLEDGEABLY WEATHERPROOFING CONVEYORIZATION FEATHERBEDDINGS ULTRAQUIET
JUXTAPOSITIONAL DEMISEMIQUAVERS ACKNOWLEDGEABLY WEATHERPROOFING CONVEYORIZATION FEATHERBEDDINGS UTRICULATE
JUXTAPOSITIONAL DEMISEMIQUAVERS WEATHERPROOFING ACKNOWLEDGEABLY CONVEYORIZATION FEATHERBEDDINGS LAURUSTINE
JUXTAPOSITIONAL DEMISEMIQUAVERS WEATHERPROOFING ACKNOWLEDGEABLY CONVEYORIZATION FEATHERBEDDINGS LUXURIATED
JUXTAPOSITIONAL DEMISEMIQUAVERS WEATHERPROOFING ACKNOWLEDGEABLY CONVEYORIZATION FEATHERBEDDINGS LUXURIATES
JUXTAPOSITIONAL DEMISEMIQUAVERS WEATHERPROOFING ACKNOWLEDGEABLY CONVEYORIZATION FEATHERBEDDINGS ULTRAQUIET
JUXTAPOSITIONAL DEMISEMIQUAVERS WEATHERPROOFING ACKNOWLEDGEABLY CONVEYORIZATION FEATHERBEDDINGS UTRICULATE
OVERADJUSTMENTS QUODLIBETARIANS ACKNOWLEDGEABLY WEATHERPROOFING EXEMPLIFICATIVE HYDROGENIZATION RUBIACEOUS
OVERADJUSTMENTS QUODLIBETARIANS WEATHERPROOFING ACKNOWLEDGEABLY EXEMPLIFICATIVE HYDROGENIZATION RUBIACEOUS

real    0m1.754s
user    0m1.753s
sys 0m0.000s

Perhatikan bahwa setiap solusi dicetak dua kali karena ketika menambahkan 15 huruf 'W' kata 2 pesanan dibuat karena ada 2 ubin 'W'.

Solusi pertama yang ditemukan dengan pemecahan titik:

JUXTAPOSITIONAL 465
DEMISEMIQUAVERS 480
ACKNOWLEDGEABLY 465
WEATHERPROOFING 405
CONVEYORIZATION 480
FEATHERBEDDINGS 390
LAURUSTINE (LAURU?TI?E) 80
no tiles left

Edit: penjelasan

Apa yang memungkinkan pencarian seluruh ruang? Sambil menambahkan kata baru saya hanya memperhitungkan kata-kata akun yang memiliki huruf sisa paling langka. Surat ini harus dalam beberapa kata (dan kata 15 huruf karena ini akan menjadi surat yang tidak bernilai 1, meskipun saya tidak memeriksanya). Jadi saya mulai dengan kata-kata yang mengandung J, Q, W, W, X, Zyang diperhitungkan 50, 100, 100, 100, 200, 500. Pada level yang lebih rendah saya mendapatkan lebih banyak cutoff karena beberapa kata dihilangkan oleh kurangnya huruf. Luasnya pohon pencarian di setiap tingkat:

0: 1
1: 49
2: 3046
3: 102560
4: 724040
5: 803959
6: 3469

Tentu saja banyak cutoff diperoleh dengan tidak memeriksa solusi yang tidak optimal (kosong dalam 15 kata kata atau kata-kata pendek). Jadi sangat beruntung bahwa 2765 solusi dapat dicapai dengan kamus ini (tapi sudah dekat, hanya 2 kombinasi dari 15 kata kata memberikan sisa yang masuk akal). Di sisi lain, mudah untuk memodifikasi kode untuk menemukan kombinasi skor yang lebih rendah di mana tidak semua 10 huruf sisanya bernilai 1, meskipun akan lebih sulit untuk membuktikan ini akan menjadi solusi yang optimal.

Juga kode menunjukkan kasus klasik optimasi prematur. Versi matchesfungsi ini membuat kode hanya 30% lebih lambat:

int matches(struct lc all, struct lc a) {
    int i;
    for (i = 1; i < 27; i++) if (count(a, i) > count(all, i)) return 0;
    return 1;
}

Saya bahkan menemukan cara untuk membuat perbandingan paralel bit ajaib lebih pendek daripada di kode asli saya (nibble tertinggi tidak dapat digunakan dalam kasus ini, tetapi ini bukan masalah, karena saya hanya perlu 26 dari 32 nibble):

int matches_val(uint64_t a, uint64_t b) {
    uint64_t mask = 0x1111111111111111ll;
    return !((a - b ^ a ^ b) & mask);
}

Tapi itu memberi keuntungan nol.

Edit

Menulis penjelasan di atas, saya menyadari bahwa sebagian besar waktu dihabiskan untuk memindai daftar kata-kata untuk mereka yang mengandung huruf tertentu yang tidak ada dalam matchesfungsi. Menghitung daftar di muka memberi kecepatan 10x.

Python 2, skor: 1840 2162

Program ini pertama-tama menemukan kata skor terbaik yang tersedia dengan ubin yang diberikan (tanpa menggunakan wildcard), kemudian membuat 10.000 upaya untuk memasukkan kata-kata acak yang memenuhi batasan karakter pertama yang unik dan memiliki ubin yang tersedia. Dengan konstanta saat ini, program ini membutuhkan 27 detik untuk berjalan di mesin saya. Menggunakan konstanta yang lebih besar mungkin akan menemukan kombinasi kata yang lebih tinggi.

UPDATE: Sekarang menggunakan algoritma pemilihan 2 tahap, sehingga ia menemukan yang terbaik dari 50 kata di setiap tahap pilih. Skor penalti sekarang digunakan dalam algoritma evaluasi juga.

from random import *

tilelist = ('AAAAAAAAABBCCDDDDEEEEEEEEEEEEFFGGGHHIIIIIIIIIJKLLLLMM'
        'NNNNNNOOOOOOOOPPQRRRRRRSSSSTTTTTTUUUUVVWWXYYZ??')
maintiles = dict((t, tilelist.count(t)) for t in set(tilelist))
value = {"A": 1,"B": 3,"C": 3,"D": 2,"E": 1,"F": 4,"G": 2,"H": 4,"I": 1,
        "J": 8,"K": 5,"L": 1,"M": 3,"N": 1,"O": 1,"P": 3,"Q": 10,"R": 1,
        "S": 1,"T": 1,"U": 1,"V": 4,"W": 4,"X": 8,"Y": 4,"Z": 10,"?": 0}
words = open('words.txt', 'rt').read().split()

def sumpoints(word):
    return len(word) * sum(value[c] for c in word)

ranked = sorted((sumpoints(w),w) for w in words)[::-1]
for points,word in ranked:
    if all(word.count(ch) <= maintiles[ch] for ch in word):
        firstword = word
        break

def findwordset(first):
    tiles = maintiles.copy()
    startletter = set(tilelist) - {'?'}
    startletter.discard(first[0])
    result = [ (first, sumpoints(first)) ]
    thistotal = sumpoints(first)
    for ch in first:
        tiles[ch] -= 1
    for i in range(30):
        best = None
        for word in sample(words, 50):
            if word[0] in startletter:
                if all(word.count(ch) <= tiles[ch] for ch in word):
                    points = sumpoints(word)
                    if best == None or points > best:
                        best, bestword = points, word
        if best:
            thistotal += best
            result.append( (bestword,best) )
            startletter.discard(bestword[0])
            for ch in bestword:
                tiles[ch] -= 1
    penaltyword = ''.join(c*n for c,n in tiles.items())
    penalty = sumpoints(penaltyword)
    return thistotal - penalty, result, tiles

best = None
for attempt in range(10000):
    wordset = findwordset(firstword)
    if best == None or wordset > best:
        best = wordset

total, result, tiles = best
penaltyword = ''.join(c*n for c,n in tiles.items())
penalty = sumpoints(penaltyword)
for word,points in result:
    print '%20s%6s' % (word, points)
print 'Remaining word "%s" penalty = %s' % (penaltyword, -penalty)
print 'Total score = %s' % total

Di sini saya sertakan yang terbaik dari beberapa proses:

$ python s.py 
 OXYPHENBUTAZONE   615
   LIQUEFACTIONS   351
  DETERMINATIVES   280
   FAMILIARISERS   234
     JUNKETEERED   253
      WOODPIGEON   170
           GAYAL    45
         CLAUGHT    91
       BRIARWOOD   135
Remaining word "V??" penalty = -12
Total score = 2162

Perhatikan bahwa saya tidak menggunakan kartu liar dan membayar penalti yang lebih besar (karena panjang kata). Peningkatan di masa mendatang mungkin termasuk penggunaan wildcard.

Simulated annealing (skor 2246)

180     ADDITIVELY
338     ERYTHROPHOBIA
345     FLAGELLOMANIACS
435     INTERSUBJECTIVE
171     KOWTOWERS
390     QUADRINGENARIES
250     WEAPONIZED
200     XENOGAMOUS
-9      for blank used as S
-9      for blank used as W
-18     FTU unused
Total score: 2246

Sayangnya ini tidak deterministik. Saya akan mencoba memperbaikinya dan menemukan benih deterministik yang memberikan nilai lebih baik.

import java.io.*;
import java.util.*;

public class PPCG50219 {
    // Plus two wildcards
    private static String CHAR_FREQ  = "9224<232911426821646422121";
    private static String CHAR_VALUE = "1332142418513113:11114484:";

    private static List<List<String>> WORDS;

    public static void main(String[] args) {
        init();

        Random rnd = new Random(1);
        FeasibleSolution initial = new FeasibleSolution();
        List<List<String>> shuffledByLetter = new ArrayList<List<String>>(WORDS);
        Collections.shuffle(shuffledByLetter,  rnd);
        for (List<String> list : shuffledByLetter) {
            Collections.shuffle(list, rnd);
            for (String word : list) {
                if (initial.canUse(word)) {
                    initial.use(word);
                    break;
                }
            }
        }

        FeasibleSolution best = anneal(initial, rnd);
        System.out.println(best.toStringDetailed());
    }

    private static void init() {
        try {
            WORDS = new ArrayList<List<String>>(26);
            for (int i = 0; i < 26; i++) WORDS.add(new ArrayList<String>());

            // Take dictionary from stdin with fallback to hard-coded path.
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in, "ISO-8859-1"));
            if (!br.ready()) {
                br.close();
                br = new BufferedReader(new InputStreamReader(new FileInputStream("/home/pjt33/notes/dict/sowpods"), "ISO-8859-1"));
            }

            String line;
            FeasibleSolution soln = new FeasibleSolution();
            while ((line = br.readLine()) != null) WORDS.get(line.charAt(0) - 'A').add(line);
            br.close();
        }
        catch (IOException ioe) {
            throw new RuntimeException(ioe);
        }
    }

    public static FeasibleSolution anneal(FeasibleSolution feasibleSolution, Random rnd)
    {
        //Random rnd = new Random();

        FeasibleSolution best = feasibleSolution;
        int bestScore = best.score();
        double temperature = bestScore / 10;

        FeasibleSolution current = best;
        int currentScore = bestScore;

        for (int i = 0; i < 1024; i++)
        {
            // Try out some random changes, and then adjust the temperature according to the results.
            FeasibleSolution bestAtT = current;
            for (int j = 0; j < 256; j++)
            {
                FeasibleSolution neighbour = current.randomNeighbour(rnd);
                int score = neighbour.score();

                // Use a simple threshold rather than a Boltzmann probability
                if (score >= currentScore - temperature)
                {
                    current = neighbour;
                    currentScore = score;
                    temperature *= 0.95;
                }
                if (score > bestScore)
                {
                    best = neighbour;
                    bestScore = score;
                }
            }

            if (current == bestAtT) temperature *= 1.01;
            if (temperature < 1E-6 * bestScore) break;
        }

        return best;
    }

    static class FeasibleSolution {
        private final String[] words;
        private int blanksUsed;
        private final int[] counts;

        private FeasibleSolution(String[] words) {
            this.words = words;

            counts = new int[26];
            for (String word : words) {
                if (word == null) continue;
                for (char ch : word.toCharArray()) counts[ch - 'A']++;
            }
            for (int i = 0; i < 26; i++) {
                int limit = CHAR_FREQ.charAt(i) - '0';
                if (counts[i] > limit) blanksUsed += counts[i] - limit;
            }
            if (blanksUsed > 2) throw new IllegalArgumentException("Required " + blanksUsed + " blanks");
        }

        public FeasibleSolution() {
            this(new String[26]);
        }

        public FeasibleSolution(FeasibleSolution copy) {
            this(copy.words.clone());
        }

        public boolean canUse(String word) {
            int offset = word.charAt(0) - 'A';

            String current = clear(offset);
            boolean rv = set(offset, word);

            clear(offset);
            if (!set(offset, current)) throw new IllegalStateException();

            return rv;
        }

        public void use(String word) {
            int offset = word.charAt(0) - 'A';
            clear(offset);
            if (!set(offset, word)) throw new IllegalArgumentException();
        }

        private boolean set(int offset, String word) {
            if (words[offset] != null) throw new IllegalStateException();

            if (word != null) {
                for (char ch : word.toCharArray()) {
                    int limit = CHAR_FREQ.charAt(ch - 'A') - '0';
                    counts[ch - 'A']++;
                    if (counts[ch - 'A'] > limit) blanksUsed++;
                }
            }

            words[offset] = word;
            return blanksUsed <= 2;
        }

        private String clear(int offset) {
            String word = words[offset];
            if (word != null) {
                for (char ch : word.toCharArray()) {
                    int limit = CHAR_FREQ.charAt(ch - 'A') - '0';
                    if (counts[ch - 'A'] > limit) blanksUsed--;
                    counts[ch - 'A']--;
                }
            }

            words[offset] = null;
            return word;
        }

        public int score() {
            int score = 0;

            List<List<Integer>> lengths = new ArrayList<List<Integer>>();
            for (int i = 0; i < 26; i++) lengths.add(new ArrayList<Integer>());
            int unused = 100;

            for (String word : words) {
                if (word == null) continue;
                for (char ch : word.toCharArray()) lengths.get(ch - 'A').add(word.length());
                unused -= word.length();
            }

            for (int i = 0; i < 26; i++) {
                int limit = CHAR_FREQ.charAt(i) - '0';
                int off = 0;
                List<Integer> l = lengths.get(i);
                if (l.size() > limit) {
                    off = l.size() - limit;
                    Collections.sort(l);
                }
                else if (l.size() < limit) {
                    int surplus = limit - l.size();
                    l.add(-surplus * unused);
                }
                for (; off < l.size(); off++) score += l.get(off) * (CHAR_VALUE.charAt(i) - '0');
            }
            return score;
        }

        public FeasibleSolution randomNeighbour(Random rnd) {
            FeasibleSolution soln = new FeasibleSolution(this);

            // Shake things up.
            List<Integer> used = new ArrayList<Integer>();
            int totalCount = 0;
            for (int i = 0; i < words.length; i++) {
                if (words[i] == null) continue;
                used.add(i);
                totalCount += words[i].length();
            }
            if (totalCount > 50) {
                int offset = used.get(rnd.nextInt(used.size()));
                soln.clear(offset);
            }

            // TODO We can probably get better results by biasing the shuffle.
            List<List<String>> shuffledByLetter = new ArrayList<List<String>>(WORDS);
            String theBitThatMatters = Arrays.toString(counts);
            Collections.shuffle(shuffledByLetter,  rnd);
            for (List<String> list : shuffledByLetter) {
                Collections.shuffle(list, rnd);
                for (String word : list) {
                    if (word.equals(soln.words[word.charAt(0) - 'A'])) continue;
                    if (soln.canUse(word)) {
                        soln.use(word);
                        if (!theBitThatMatters.equals(Arrays.toString(soln.counts))) return soln;
                    }
                }

                // To avoid getting trapped in a local oscillation.
                int off = list.get(0).charAt(0) - 'A';
                if (soln.words[off] != null) {
                    soln.clear(off);
                    return soln;
                }
            }

            throw new RuntimeException("This really shouldn't be reachable");
        }

        @Override
        public String toString() {
            StringBuilder sb = new StringBuilder();
            for (String word : words) {
                if (word == null) continue;
                if (sb.length() > 0) sb.append(", ");
                sb.append(word);
            }

            return sb.toString();
        }

        private static int wordScore(String word) {
            int wordScore = 0;
            for (char ch : word.toCharArray()) {
                if (ch != '?') wordScore += (CHAR_VALUE.charAt(ch - 'A') - '0');
            }
            return wordScore * word.length();
        }

        public String toStringDetailed() {
            int score = 0;

            List<List<Integer>> lengths = new ArrayList<List<Integer>>();
            for (int i = 0; i < 26; i++) lengths.add(new ArrayList<Integer>());
            int unused = 100;

            StringBuilder surplusChars = new StringBuilder();
            int unusedBlanks = 2;

            StringBuilder sb = new StringBuilder();
            for (String word : words) {
                if (word == null) continue;
                for (char ch : word.toCharArray()) lengths.get(ch - 'A').add(word.length());
                unused -= word.length();
                sb.append(wordScore(word)).append("\t").append(word).append("\n");
            }

            for (int i = 0; i < 26; i++) {
                int limit = CHAR_FREQ.charAt(i) - '0';
                int off = 0;
                List<Integer> l = lengths.get(i);
                if (l.size() > limit) {
                    off = l.size() - limit;
                    unusedBlanks -= off;
                    Collections.sort(l);
                }
                while (l.size() < limit) {
                    surplusChars.append((char)('A' + i));
                    l.add(-unused);
                }
                for (int j = 0; j < off; j++) sb.append(-l.get(j)).append("\tfor blank used as ").append((char)('A' + i)).append("\n");
                for (; off < l.size(); off++) score += l.get(off) * (CHAR_VALUE.charAt(i) - '0');
            }

            while (unusedBlanks > 0) {
                surplusChars.append('?');
                unusedBlanks--;
            }
            sb.append(-wordScore(surplusChars.toString())).append("\t").append(surplusChars).append(" unused\n");

            sb.append("Total score: ").append(score());
            return sb.toString();
        }
    }
}

Python, skor 2638 2675 2676 2689 2699 2717

Hasil:

OXYPHENBUTAZONE for 615
MICROEARTHQUAKE for 525
FLAVOURDYNAMICS for 435
ADJUSTABILITIES for 375
PREINTERVIEWING for 360
WATERFLOODINGS for 308
EAGLE?OOD? for 100
Left-over word: E
2717

Kode:

import time
from multiprocessing import Pool

start_tiles = "AAAAAAAAABBCCDDDDEEEEEEEEEEEEFFGGGHHIIIIIIIIIJKLLLLMMNNNNNNOOOOOOOOPPQRRRRRRSSSSTTTTTTUUUUVVWWXYYZ??"
start_tiles = {l: start_tiles.count(l) for l in set(start_tiles)}
values = {"A": 1,"B": 3,"C": 3,"D": 2,"E": 1,"F": 4,"G": 2,"H": 4,"I": 1,"J": 8,"K": 5,"L": 1,"M": 3,"N": 1,"O": 1,"P": 3,"Q": 10,"R": 1,"S": 1,"T": 1,"U": 1,"V": 4,"W": 4,"X": 8,"Y": 4,"Z": 10,"?": 0}
with open("sowpods.txt") as f:
    full_dictionary = list(l.strip() for l in f if l.strip())

def num_wilds_needed(word, tiles):
    return sum(max(0, word.count(l) - tiles[l]) for l in word)

def word_is_possible(word, tiles):
    # never replace 1st letter with wild, for simplicity
    if tiles[word[0]] <= 0:
        return False

    return num_wilds_needed(word, tiles) <= tiles['?']

def word_score(word):
    return sum(values[c] for c in word) * len(word)

def final_score(words, tiles_left, print_leftover=False):
    left_over_word = ""
    for tile, counts in tiles_left.iteritems():
        left_over_word += tile * counts
    if print_leftover:
        print "Left-over word: %s" % (left_over_word,)
    return sum(word_score(word) for word in words) - word_score(left_over_word)

def filter_dictionary(dictionary, tiles_left, start_letters):
    return [word for word in dictionary
            if word[0] in start_letters and word_is_possible(word, tiles_left)]

def pick_word(next_word, start_letters, tiles_left, dictionary):
    if not word_is_possible(next_word, tiles_left):
        raise ValueError("Using word that is impossible: %s" % (next_word,))

    next_letters = set(start_letters)
    next_letters.remove(next_word[0])
    next_tiles = dict(tiles_left)
    for c in next_word:
        next_tiles[c] -= 1

    next_dictionary = filter_dictionary(dictionary, next_tiles, next_letters)

    return next_letters, next_tiles, next_dictionary

class FakeResult:
    def __init__(self, value):
        self.value = value
    def get(self, timeout=None):
        return self.value

class FakePool:
    def apply_async(self, f, args):
        res = f(*args)
        return FakeResult(res)

def proc_next_word(next_word,
                   start_letters, tiles_left, filtered_sorted_dictionary,
                   depth, picks, prefix):
    score = word_score(next_word)
    next_letters, next_tiles, next_dictionary = pick_word(
        next_word, start_letters, tiles_left, filtered_sorted_dictionary)

    if len(prefix) / 2 < 5:
        print "%sDepth %d: ?, %s for %d, %d possible words left" % (
            prefix, len(prefix) / 2, next_word, score, len(filtered_sorted_dictionary))

    next_words, next_score = search(FakePool(), next_letters, next_tiles, next_dictionary,
                                    depth-1, picks, prefix + "  ")

    if len(prefix) / 2 < 5:
        print "%sDepth %d: %d, %s for %d" % (
            prefix, len(prefix) / 2, score + next_score, next_word, score)

    return [next_word] + next_words, score + next_score

def wildify(word, tiles_left):
    # replace missing letters with wilds
    while True:
        for c in word:
            if tiles_left[c] < word.count(c):
                word = word[0] + word[1:].replace(c, '?',  word.count(c) - tiles_left[c])
                break
        else:
            break

    return word

def search(pool, start_letters, tiles_left, filtered_sorted_dictionary, depth, picks, prefix=""):
    if not filtered_sorted_dictionary:
        # no words left - penalize for tiles left
        return [], final_score([], tiles_left)

    if depth == 0:
        raise ValueError("Hit depth 0")

    if tiles_left['?'] > 0:
        # proc top few and re-calculate score based on wildcarding
        best_word_candidates = [wildify(w, tiles_left) for w in filtered_sorted_dictionary[:10000]]
        best_word_candidates.sort(key=word_score, reverse=True)
    else:
        # no wildification needed
        best_word_candidates = filtered_sorted_dictionary

    best_words = best_word_candidates[:picks]
    if depth == 1:
        # only look at 1 word since depth 0 will do nothing
        best_words = [best_words[0]]

    results = [pool.apply_async(proc_next_word, (next_word,
                                                 start_letters, tiles_left, filtered_sorted_dictionary,
                                                 depth, picks, prefix))
               for next_word in best_words]
    results = [result.get() for result in results]

    return max(results, key=lambda (words, result): result)

if __name__ == "__main__":
    start_letters = set("ABCDEFGHIJKLMNOPQRSTUVWXYZ")
    tiles_left = dict(start_tiles)
    print "Preparing word list..."
    dictionary = filter_dictionary(full_dictionary, tiles_left, start_letters)
    dictionary.sort(key=word_score, reverse=True)
    print "Starting search..."
    pool = Pool(8)
    words, _ = search(pool, start_letters, tiles_left, dictionary, 666, 5)

    for word in words:
        for c in word:
            if tiles_left[c] <= 0:
                raise ValueError("Invalid word list")
            tiles_left[c] -= 1

    print
    print "\n".join(("%s for %s" % (word, word_score(word)) for word in words))
    print final_score(words, tiles_left, True)

Penjelasan:

Pencarian mendalam pertama yang mencari seluruh pohon, memilih antara pickskata-kata terbaik di setiap tahap

Saya mengurutkan seluruh daftar kata satu kali dengan skor di awal. Setelah memilih setiap kata, untuk iterasi berikutnya saya menyaring semua kata yang sekarang tidak mungkin lagi, menjaga urutan, jadi saya tidak perlu mengurutkan daftar pada setiap langkah. Untuk berurusan dengan wildcard, jika ada kemungkinan kartu wild diperlukan, saya memilih 10.000 kandidat teratas, mengganti surat yang hilang dengan wildcard jika diperlukan, dan mengurutkan kembali berdasarkan skor baru (lebih rendah).

Output ini untuk picks=5dan 8m01sperlu dijalankan pada mesin 8-core saya.

Java 8, skor 2641 2681

Program dimulai dengan mengambil 40 kata terbaik. Untuk setiap kata, ia menemukan 40 kata terbaik untuk diikuti. Dari 1600 kombinasi, program mengambil 40 terbaik. Untuk setiap kombinasi, 40 kata terbaik ditemukan, dan siklus berulang.

Ketika hanya beberapa ubin yang tersisa, huruf-huruf yang tersisa digabungkan dengan dua kosong untuk kata terakhir.

Memperbarui

Saya meningkatkan ambang batas ke 50 kata terbaik. Juga, setiap kombinasi hanya menambahkan kata-kata yang kurang dari yang sudah ada. Ini mencegah banyak permutasi dari grup yang sama.

OXYPHENBUTAZONE: 615
MICROEARTHQUAKE: 525
INTERSUBJECTIVE: 435
DAFFADOWNDILLY: 406
PREINTERVIEWING: 360
AUTOALLOGAMIES: 238
GOODSIRES: 99
?A?: 3             (ZAX)
---
Total: 2681

Program:

import java.io.File;
import java.io.IOException;
import java.nio.file.Files;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.stream.Collectors;

public class Scrabble {

    static final int[] scores = new int[]{1, 3, 3, 2, 1, 4, 2, 4, 1, 8, 5, 1, 3, 1, 1, 3, 10, 1, 1, 1, 1, 4, 4, 8, 4, 10, 0};
    static final int[] freqs = new int[]{9, 2, 2, 4, 12, 2, 3, 2, 9, 1, 1, 4, 2, 6, 8, 2, 1, 6, 4, 6, 4, 2, 2, 1, 2, 1, 2};

    static final int MAX = 50;

    public static void main(String[] args) throws IOException {
        List<String> words = Files.readAllLines(new File("C:/Users/Ypnypn/scrabble.txt").toPath());
        words.sort((s, t) -> score(t) - score(s));
        words.removeIf(w -> !works(w));

        List<List<String>> last = words.stream().map(Arrays::asList).collect(Collectors.toList()),
                finalList = new ArrayList();

        for (int i = 0; i < 10; i++) {
            List<List<String>> next = new ArrayList();
            for (int j = 0; j < MAX && j < last.size(); j++) {
                List<String> group = last.get(j);
                Object[] thirds = words.stream().filter(word -> workTogether(group, word) && least(word, group)).toArray();
                for (int k = 0; k < MAX && k < thirds.length; k++) {
                    List<String> newList = new ArrayList(group);
                    newList.add((String) thirds[k]);
                    next.add(newList);
                }
            }
            last = next;
            last.sort((s, t) -> t.stream().mapToInt(Scrabble::score).sum()
                                - s.stream().mapToInt(Scrabble::score).sum());
            for (List<String> l : last) {
                if (l.stream().mapToInt(String::length).sum() > 90) {
                    finalList.add(l);
                }
            }
        }
        finalList.forEach(g -> {
            List<Integer> chars = new ArrayList();
            int[] counts = new int[26];
            g.forEach(str -> str.chars().forEach(c -> counts[c - 'A']++));
            for (int i = 0; i < 26; i++) {
                while (counts[i] < freqs[i]) {
                    chars.add('A' + i);
                    counts[i]++;
                }
            }
            String end = words.stream()
                    .filter(w -> w.length() == chars.size() + 2)
                    .filter(w -> g.stream().noneMatch(s -> s.charAt(0) == w.charAt(0)))
                    .filter(w -> {
                        List<Integer> copy = new ArrayList(chars);
                        int _1 = 0, _2 = 0;
                        for (char c : w.toCharArray()) {
                            if (copy.contains((int) c)) {
                                copy.remove((Integer) (int) c);
                            } else if (_1 == 0) {
                                _1 = c;
                            } else if (_2 == 0) {
                                _2 = c;
                            } else {
                                return false;
                            }
                        }
                        return true;
                    }).findAny().orElse("");
            if (end.equals("")) {
                return;
            }
            char[] arr = end.toCharArray();
            for (int i = 0; i < arr.length; i++) {
                if (chars.contains((int) arr[i])) {
                    chars.remove((Integer) (int) arr[i]);
                } else {
                    arr[i] = '?';
                }
            }
            g.add(new String(arr));
        });

        finalList.removeIf(g -> g.stream().mapToInt(String::length).sum() < 100);
        finalList.sort((s, t) -> t.stream().mapToInt(Scrabble::score).sum()
                                 - s.stream().mapToInt(Scrabble::score).sum());
        List<String> answer = finalList.get(0);
        for (String str : answer) {
            System.out.print(str + ": " + score(str));
            if (str.contains("?")) {
                String actual = words.stream().filter(s -> s.matches("^" + str.replace('?', '.') + "$")).findAny().get();
                System.out.print("             (" + actual + ")");
            }
            System.out.println();
        }
        System.out.println("---");
        System.out.println("Total: " + answer.stream().mapToInt(Scrabble::score).sum());
    }

    static boolean works(String str) {
        int[] counts = new int[26];
        for (char c : str.toCharArray()) {
            counts[c - 'A']++;
        }
        for (int i = 0; i < 26; i++) {
            if (counts[i] > freqs[i]) {
                return false;
            }
        }
        return true;
    }

    static boolean workTogether(List<String> strs, String str) {
        if (strs.stream().anyMatch(s -> s.charAt(0) == str.charAt(0))) {
            return false;
        }
        int[] counts = new int[26];
        strs.stream().forEach(s -> s.chars().forEach(c -> counts[c - 'A']++));
        str.chars().forEach(c -> counts[c - 'A']++);
        for (int i = 0; i < 26; i++) {
            if (counts[i] > freqs[i]) {
                return false;
            }
        }
        return true;
    }

    static boolean least(String str, List<String> strs) {
        int score = score(str);
        return strs.stream().allMatch(s -> score(s) >= score);
    }

    static int score(String word) {
        int score = 0;
        for (char c : word.toCharArray()) {
            if (c != '?') {
                score += scores[c - 'A'];
            }
        }
        return score * word.length();
    }
}

Perl, skor: 2655 2630

#!perl -l
%p = qw{A 1 B 3 C 3 D 2 E 1 F 4 G 2 H 4 I 1 J 8 K 5 L 1 M 3 N 1 O 1 P 3 Q 10 R 1 S 1 T 1 U 1 V 4 W 4 X 8 Y 4 Z 10 x 0};
/[A-Z]+/,push @R,$& for <>;
@R = sort{length($b)<=>length($a)}@R;
for(@R) {push@W,$_;push@W,"$`x$'" while /./g;push@O,($_)x(1+length)}
$l = "AAAAAAAAABBCCDDDDEEEEEEEEEEEEFFGGGHHIIIIIIIIIJKLLLLMMNNNNNNOOOOOOOOPPQRRRRRRSSSSTTTTTTUUUUVVWWXYYZxx";
@S = map {$r='';for$x(A..Z,'x'){$r.="${x}{".(1*s/$x//g).",}"};"^$r\$"} map{"$_"}@W;
sub score{$r=0;$r+=$p{$_}for split'',$rr=pop;$r*length$rr}
@X = map{score$_}@W;
$f = 'x';
for(;;) {
$best = -1; $besti = 0;
for ($i=0;$i<@S;$i++) {
    next if $X[$i] < $best;
    if ($O[$i]!~/^[$f]/ && $l=~$S[$i]) {
    $best = $X[$i];
    $besti = $i;
    }
}
if($best < 0){
    $ls = score$l;
    print "left: $l (-$ls)";
    $tot -= $ls;
    print "total: $tot";
    exit;
}
$l=~s/$_// for $W[$besti]=~/./g;
$O[$besti]=~/./; $f .= $&;
print "$W[$besti]/$O[$besti] ($X[$besti])";
$tot += $X[$besti];
}

Menggunakan:

$ perl ./scrab.pl <~/sowpods.txt
OXYPHENBUTAZONE/OXYPHENBUTAZONE (615)
MICROEARTHQUAKE/MICROEARTHQUAKE (525)
NONOBJECTIVISMS/NONOBJECTIVISMS (465)
DAFFADOWNDILLY/DAFFADOWNDILLY (406)
PREINTERVIEWIxG/PREINTERVIEWING (345)
LITURGIOLOGxSTS/LITURGIOLOGISTS (240)
URDEE/URDEE (30)
EE/EE (4)
AA/AA (4)
left: AA (-4)
total: 2630

Penggunaan blanko sebenarnya tidak memberikan banyak sementara secara signifikan memperlambat eksekusi:

$ perl ./scrab.pl <~/sowpods.txt 
OXYPHENBUTAZONE/OXYPHENBUTAZONE (615)
MICROEARTHQUAKE/MICROEARTHQUAKE (525)
NONOBJECTIVISMS/NONOBJECTIVISMS (465)
DAFFADOWNDILLY/DAFFADOWNDILLY (406)
PREINTERVIEWED/PREINTERVIEWED (322)
LITURGIOLOGISTS/LITURGIOLOGISTS (255)
RUGAE/RUGAE (30)
EE/EE (4)
AA/AA (4)
left: Axx (-3)
total: 2623

Setelah menambahkan beberapa heuristik:

$ time perl ./scrab.pl <~/sowpods.txt 
OXYPHENBUTAZONE/OXYPHENBUTAZONE (615)
MICROEARTHQUAKE/MICROEARTHQUAKE (525)
NONOBJECTIVISMS/NONOBJECTIVISMS (465)
PREFIGURATIVELY/PREFIGURATIVELY (405)
DOWNREGULATIONS/DOWNREGULATIONS (300)
FORGEAxILITIES/FORGEABILITIES (238)
ADWAxDED/ADWARDED (104)
EA/EA (4)
left: L (-1)
total: 2655

real    3m58.517s
user    3m57.832s
sys 0m0.512s

Python 3, skor 2735

(Skor optimal 2765, "6 kata dari 15 huruf dan satu kata 10 huruf yang terdiri dari 8 huruf bernilai 1 dan dua kosong" telah dicapai oleh nutki .)

Saya menggunakan pendekatan serakah yang mirip dengan yang lain:

Saya mulai dengan daftar satu elemen yang berisi kata-kata dengan skor tertinggi yang berisi Q's.

Di setiap langkah untuk setiap elemen daftar saya membuat k = 800daftar baru dengan kata-kata hukum terbaik untuk daftar. Dari daftar daftar agregat, saya menyimpan kdaftar penilaian teratas dan mengulangi prosesnya 10 kali.

Perhatikan bahwa Anda bisa mendapatkan kelemen teratas dari ndaftar-panjang di O (n + k * log n) yang O (n) jika k<<nseperti dalam kasus kami ( k = 800, n ~= 250000) dengan antrian tumpukan. Saya kira metode ini tidak digunakan dalam kiriman lain maka nilai yang lebih kecil k.

Saya menggunakan wildcard sepanjang jalan jika diperlukan untuk kata-kata.

Runtime adalah beberapa menit untuk k = 800. Nilai yang lebih besar dan optimasi lainnya belum menghasilkan hasil yang lebih baik.

Hasil:

DEMISEMIQUAVERS for 480
OXYPHENBUTAZONE for 615
ACKNOWLEDGEABLY for 465
FLASHFORWARDING for 435
INTERJACULATING for 375
COOPERATIVITIES for 330
METEOROID for 108
? is C for -45
? is M for -27
Left U for -1
Total score of 2735

Saya bereksperimen dengan produk Descartes dari kata-kata terbaik yang mengandung Q, J dan X karena surat-surat ini jarang berbagi kata-kata. Skor terbaik saya dengan startegy ini adalah 2723 ( DEMISEMIQUAVERS OXYPHENBUTAZONE INTERSUBJECTIVE FLASHFORWARDING KNOWLEDGABILITY RADIOPROTECTION ANALOGUE EA).

Kode spageti rumit yang tidak perlu (dengan jejak eksperimen dengan metode lain):

import sys,heapq as hq

def score(s):
    r=0
    for c in s:
        r+=ord('1332142418513113:11114484:0'[ord(c)-65])-48
    return r*len(s)

def score_wl(rwl):
    ac=a[:] 
    ssd=0    
    for rwle in rwl:
        ac,sd=decr(ac,rwle)
        ssd+=sd
    return sum([score(rw) for rw in rwl])-ssd

def decr(av,nw):
    nav=av[:]
    scd=0
    for c in nw:
        if nav[ord(c)-65]>0:
            nav[ord(c)-65]-=1
        else:
            nav[ord('[')-65]-=1
            scd+=(ord('1332142418513113:11114484:'[ord(c)-65])-48)*len(nw)
    return (nav,scd)

def bestwordlist(w,ac,sw,count):
    stl=[swe[0] for swe in sw]
    sl=[]
    for we in w:
        if we[0] not in stl:
            acn,sd=decr(ac,we)
            if min(acn)>=0:
                sl+=[(we,score(we)-sd)]
    mw=hq.nlargest(count,sl,key=lambda p:p[1])
    res=[mwe[0] for mwe in mw]
    return res

def bestword(w,ac,sw):
    ms=0
    mw=''
    stl=[swe[0] for swe in sw]
    for we in w:
        if we[0] not in stl:
            acn,sd=decr(ac,we)
            if min(acn)>=0 and score(we)-sd>ms:
                ms=score(we)-sd
                mw=we
    return mw

def search(t,lev,av,sw):
    if lev>=len(t) and min(av)>=0:
        return [sw]
    if min(av)<0:
        return []
    r=[]
    stl=[swe[0] for swe in sw]
    if av[ord(tl[lev])-65]>0:
        for i in range(1,maxch):
            nw=t[lev][-i][0]
            if nw[0] not in stl:
                nav=decr(av,nw)[0]
                swn=sw[:]+[nw]       
                r+=search(t,lev+1,nav,swn)
    else:
        r+=[sw]
    if len(r)<10000:
        return r
    else:
        return hq.nlargest(10000,r,key=score_wl)

args=sys.argv
maxch=300#int(args[1])
maxch2=800#int(args[2])

w=[]
with open('scr_words.txt','r') as f:
    for l in f:
        w+=[l[:-1]]

a=[ord(c)-48  for c in '9224<2329114268216464221212']
                       #ABCDEFGHIJKLMNOPQRSTUVWXYZ?

t=[]
tl='Q'
for c in tl:
    tp=[]
    wl=[(x,score_wl([x])) for x in w if c in x]
    wl=sorted(wl,key=lambda p:p[1])
    t+=[wl]

r=search(t,0,a,[])

rt=sorted(r,key=score_wl)[-maxch2:]

ms=0
res='-'

for i in range(10-len(tl)):
    rtn=[]
    for sw in rt:

        ac=a[:] 
        for swe in sw:        
            ac,sd=decr(ac,swe)

        bwl=bestwordlist(w,ac,sw,maxch2)

        if not bwl:
            rtn+=[sw]
        for bwle in bwl:
            rtn+=[sw+[bwle]]

    rt=sorted(rtn,key=score_wl)[-maxch2:]
    print(rt[-1],score_wl(rt[-1]),'- left')
    sys.stdout.flush()

ms=-1000000
for sw in rt:    
    ssd=0
    ac=a[:]
    for swe in sw:
        ac,sd=decr(ac,swe)
        ssd+=sd
    sc=sum([score(swe) for swe in sw])-ssd
    left=''.join([chr(i+65)*v for i,v in enumerate(ac)])
    sc-=score(left)
    if sc>ms:
        ms=sc
        res=(sw,left)

fsw,left=res        
print('\n\nres =',ms,' '.join(fsw),'left',left)
    v