Python : Cryptogramme Cryptarithm Solver

Résolu
Wubitt -  
Bonjour,

J'essaie de créer un petit programme pour résoudre des Cryptarythmmes, mais je suis bloqué ...

Contrainte :
- Les nombres doivent tous être compris entre 0 et 9, mais on peut les utiliser plusieurs fois... Par exemple A peut être égal à 1, B = 2, ... Mais C peut aussi être égal à 1... etc

J'aimerai :
- Améliorer le processus pour que justement la contrainte chiffre de 0 à 9 soit possible pour plusieurs lettres.
- Intégrer une résolution globale pour que A (par exemple) soit le même chiffre dans l'ensemble des équations.

Est-ce quelqu'un pourrait m'aider s'il vous plaît ?
Je débute dans Python, alors n'hésitez pas à illustrer vos propos avec les lignes de codes.

Par avance merci à tout ceux qui m'aideront.

Voici ce que j'ai déjà fait : 

from time import time

def solve(text):
    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("+")] for s in text.split("=")]
    signs = [1]*len(lhs) + [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("*")] for s in text.split("=")]
    signs = [1]*len(lhs) * [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("-")] for s in text.split("=")]
    signs = [-1]*len(lhs) - [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("/")] for s in text.split("=")]
    signs = [-1]*len(lhs) / [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

testCases=["abcd*ef/ad=ea*dgf/he+ecah",
           "ihbgh*ga/hbl=gf*gjad/di+eeck",
           "eihle*dhc/gi=lc*aijbk/fk+dkigk",
           "bacj*fjg/eid=df*hcli/ai+daeia",
           "lkjek*fb/ddd=c*jikgb/egb+elblc",
           "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
           "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
           "ef+ga-dhc+fjg-fb=gfl",
           "ad+hbl-gi-eid-ddd=dbl",
           "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
           "he+di+fk+ai+egb=gcl",
           "ecah-eeck+dkigk+daeia-elblc=bbfg",
           ]
for test in testCases:
    print(test)
    start=time()
    solution=solve(test)
    print(time()-start, "seconds")
    if solution is None:
        print("No solution exists")
    else:
        result="".join(str(solution.get(c, c)) for c in test)
        for key, value in solution.items():
            print(key, '=', value)
        print(result)
    print(flush=True)

8 réponses

Résumé de la discussion

La discussion porte sur la création d'un petit solveur cryptarithmetic en Python, avec contraintes numériques 0 à 9 réutilisables et cohérence des lettres sur l'ensemble des équations. Plusieurs intervenants examinent des implémentations où résoudre l'addition, la multiplication et d'autres opérations exige une mapping unique des lettres vers des chiffres et un tableau "unused". Le fil aborde des bugs fréquents tels que la duplication de solve_impl, des tests avec des cas simples comme a=b+2, et des améliorations pour éviter des échecs. D'autres échanges insistent sur l'importance de partager le code avec une indentation correcte et proposent des cas de tests variés pour évaluer robustesse et performance.

Bobot (l’IA à votre service)
  2. Wubitt Auteur
    Bonjour yg_be,

    Je fais cela dans le cadre d'un loisir pour résoudre l'énigme qui est dedans :
    "abcd*ef/ad=ea*dgf/he+ecah",
    "ihbgh*ga/hbl=gf*gjad/di+eeck",
    "eihle*dhc/gi=lc*aijbk/fk+dkigk",
    "bacj*fjg/eid=df*hcli/ai+daeia",
    "lkjek*fb/ddd=c*jikgb/egb+elblc",
    "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
    "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
    "ef+ga-dhc+fjg-fb=gfl",
    "ad+hbl-gi-eid-ddd=dbl",
    "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
    "he+di+fk+ai+egb=gcl",
    "ecah-eeck+dkigk+daeia-elblc=bbfg"

    Je n'ai pas vraiment écrit ce code, je l'ai trouvé sur internet pour additionner et je l'ai transformé pour les 4 opérations...

    Du coup, je cherche à l'étoffer pour résoudre mon énigme dont voici la photo.

    Pour les lignes 159 et 160, cela me permet de voir ou je suis bloqué, mais cela n'aura plus d'utilité à la fin si ce programme fonctionne.

    Merci d'avance pour votre aide.
    2. Wubitt Auteur
      @yg_be
      from time import time

def solve(text):
    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("+")] for s in text.split("=")]
    signs = [1]*len(lhs) + [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("*")] for s in text.split("=")]
    signs = [1]*len(lhs) * [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("-")] for s in text.split("=")]
    signs = [-1]*len(lhs) - [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("/")] for s in text.split("=")]
    signs = [-1]*len(lhs) / [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

testCases=["abcd*ef/ad=ea*dgf/he+ecah",
           "ihbgh*ga/hbl=gf*gjad/di+eeck",
           "eihle*dhc/gi=lc*aijbk/fk+dkigk",
           "bacj*fjg/eid=df*hcli/ai+daeia",
           "lkjek*fb/ddd=c*jikgb/egb+elblc",
           "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
           "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
           "ef+ga-dhc+fjg-fb=gfl",
           "ad+hbl-gi-eid-ddd=dbl",
           "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
           "he+di+fk+ai+egb=gcl",
           "ecah-eeck+dkigk+daeia-elblc=bbfg",
           ]
for test in testCases:
    print(test)
    start=time()
    solution=solve(test)
    print(time()-start, "seconds")
    if solution is None:
        print("No solution exists")
    else:
        result="".join(str(solution.get(c, c)) for c in test)
        for key, value in solution.items():
            print(key, '=', value)
        print(result)
    print(flush=True)
    3. Wubitt Auteur
      @yg_beJe l'ai remis... Est-ce mieux ainsi ?
    4. yg_be Contributeur
      @Wubittregarde les lignes 161 et 162: qu'en penses-tu?
    5. Wubitt Auteur
      @yg_beElles ne servent à rien apparemment
  4. Wubitt Auteur
    le voici en plus court : 

    from time import time

def solve(text):
    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("+")] for s in text.split("=")]
    lhs, rhs = [[term[::-1] for term in s.split("*")] for s in text.split("=")]
    lhs, rhs = [[term[::-1] for term in s.split("-")] for s in text.split("=")]
    lhs, rhs = [[term[::-1] for term in s.split("/")] for s in text.split("=")]
    signs = [1]*len(lhs) + [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
   

   
    return True
    return False

testCases=["abcd*ef/ad=ea*dgf/he+ecah",
           "ihbgh*ga/hbl=gf*gjad/di+eeck",
           "eihle*dhc/gi=lc*aijbk/fk+dkigk",
           "bacj*fjg/eid=df*hcli/ai+daeia",
           "lkjek*fb/ddd=c*jikgb/egb+elblc",
           "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
           "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
           "ef+ga-dhc+fjg-fb=gfl",
           "ad+hbl-gi-eid-ddd=dbl",
           "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
           "he+di+fk+ai+egb=gcl",
           "ecah-eeck+dkigk+daeia-elblc=bbfg",
           ]
for test in testCases:
    print(test)
    start=time()
    solution=solve(test)
    print(time()-start, "seconds")
    if solution is None:
        print("No solution exists")
    else:
        result="".join(str(solution.get(c, c)) for c in test)
        for key, value in solution.items():
            print(key, '=', value)
        print(result)
    print(flush=True)
    1. Wubitt Auteur
      Malheureusement cela bug pour la deuxième multiplication :
      et surtout j'ai beaucoup moins de résultats d'égalité qu'auparavant...

      ihbgh*ga/hbl=gf*gjad/di+eeck
      3.552436828613281e-05 seconds
      a = 0
      l = 1
      d = 2
      k = 9
      g = 3
      b = 4
      c = 6
      * = 8
      h = 5
      j = 7
      i5435830/541=3f83702/2i+ee69
    2. yg_be Contributeur
      cela va mieux, il ne reste qu'une erreur avec les lignes 46 et 47.

      cependant, il ne donne pas de résultat utile, même pour un cas simple comme:
      "a=b+2"
    3. Wubitt Auteur
      @yg_bevoilà au plus court possible : 

      from time import time

def solve(text):
    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("+")] for s in text.split("=")]
    signs = [1]*len(lhs) + [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
   
    return True
    return False

testCases=["a=b+2",
           "abcd*ef/ad=ea*dgf/he+ecah",
           "ihbgh*ga/hbl=gf*gjad/di+eeck",
           "eihle*dhc/gi=lc*aijbk/fk+dkigk",
           "bacj*fjg/eid=df*hcli/ai+daeia",
           "lkjek*fb/ddd=c*jikgb/egb+elblc",
           "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
           "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
           "ef+ga-dhc+fjg-fb=gfl",
           "ad+hbl-gi-eid-ddd=dbl",
           "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
           "he+di+fk+ai+egb=gcl",
           "ecah-eeck+dkigk+daeia-elblc=bbfg",
           ]
for test in testCases:
    print(test)
    start=time()
    solution=solve(test)
    print(time()-start, "seconds")
    if solution is None:
        print("No solution exists")
    else:
        result="".join(str(solution.get(c, c)) for c in test)
        for key, value in solution.items():
            print(key, '=', value)
        print(result)
    print(flush=True)


      Mais effectivement, il doit y avoir un problème car cela me donne :

      a=b+2
      5.817413330078125e-05 seconds
      a = 1
      b = 9
      1=9+2

      !!!!!!
    4. yg_be Contributeur
      @Wubittle programme que tu as trouvé sur internet fonctionne-t'il mieux?
      c'est peut-être quand tu l'as transformé qu'il a arrêté de fonctionner.
  6. Wubitt Auteur
    malheureusement, c'est possible, même si 99% de ce qui est écrit ici est le code trouvé
    1. Wubitt Auteur
      voilà, c'est corrigé et cela fonctionne : 

      from time import time

def solve(text):
    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("+")] for s in text.split("=")]
    signs = [1]*len(lhs) + [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("*")] for s in text.split("=")]
    signs = [1]*len(lhs) * [-1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("-")] for s in text.split("=")]
    signs = [-1]*len(lhs) - [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return True
    return False

    text = text.replace(" ", "")
    lhs, rhs = [[term[::-1] for term in s.split("/")] for s in text.split("=")]
    signs = [-1]*len(lhs) / [1]*(len(rhs)-1)
    lhs.extend(rhs[:-1])
    dic = {}
    maxlen = max(len(rhs[-1]), max(map(len, lhs)))
    return dic if solve_impl(lhs, signs, rhs[-1], dic, set(range(10)), 0, 0, 0, maxlen) else None

def solve_impl(lhs, signs, rhs, dic, unused, row, col, carry, maxlen):
    if col==maxlen:
        return carry==0
    if row==len(lhs):
        if col>=len(rhs):
            return carry%10==0 and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if rhs[col] in dic:
            return dic[rhs[col]]==carry%10 and (col<len(rhs)-1 or dic[rhs[col]]!=0)\
                and solve_impl(lhs, signs, rhs, dic, unused, 0, col+1, carry//10, maxlen)
        if carry%10 not in unused:
            return False
        dic[rhs[col]]=carry%10
        if solve_impl(lhs, signs, rhs, dic, unused-{carry%10}, 0, col+1, carry//10, maxlen):
            return True
        del dic[rhs[col]]
        return False
    if col>=len(lhs[row]):
        return solve_impl(lhs, signs, rhs, dic, unused, row+1, col, carry, maxlen)
    if lhs[row][col] in dic:
        return (col<len(lhs[row])-1 or dic[lhs[row][col]]!=0) \
            and solve_impl(lhs, signs, rhs, dic, unused, row+1, col,
                           carry+signs[row]*dic[lhs[row][col]], maxlen)
    for digit in unused:
        if digit!=0 or col<len(lhs[row])-1:
            dic[lhs[row][col]]=digit
            if solve_impl(lhs, signs, rhs, dic, unused-{digit}, row+1, col,
                          carry+signs[row]*digit, maxlen):
                return True
            del dic[lhs[row][col]]
    return False

testCases=["a=b+2",
           "SEND+MORE=MONEY",
           "abcd*ef/ad=ea*dgf/he+ecah",
           "ihbgh*ga/hbl=gf*gjad/di+eeck",
           "eihle*dhc/gi=lc*aijbk/fk+dkigk",
           "bacj*fjg/eid=df*hcli/ai+daeia",
           "lkjek*fb/ddd=c*jikgb/egb+elblc",
           "ekjhl-gfl-dbl=gaaeli-gdhbhb-gcl-bbfg",
           "abcd+ihbgh-eihle-bacj-lkjek=ekjhl",
           "ef+ga-dhc+fjg-fb=gfl",
           "ad+hbl-gi-eid-ddd=dbl",
           "dgf*gjad-aijbk-hcli-jikgb=gdhbhb",
           "he+di+fk+ai+egb=gcl",
           "ecah-eeck+dkigk+daeia-elblc=bbfg",
           ]
for test in testCases:
    print(test)
    start=time()
    solution=solve(test)
    print(time()-start, "seconds")
    if solution is None:
        print("No solution exists")
    else:
        result="".join(str(solution.get(c, c)) for c in test)
        for key, value in solution.items():
            print(key, '=', value)
        print(result)
    print(flush=True)


      réponses données :

      a=b+2
      0.0 seconds
      a = 3
      b = 1
      2 = 2
      3=1+2

      SEND+MORE=MONEY
      0.02094292640686035 seconds
      D = 7
      E = 5
      Y = 2
      N = 6
      R = 8
      O = 0
      S = 9
      M = 1
      9567+1085=10652
      1. Wubitt Auteur
        reste à ajouter l'option que les chiffres peuvent être les mêmes pour deux lettres ou plus différentes.
        1. yg_be Contributeur
          je pense qu'il suffit de ne jamais rien retirer de unused.
        2. Wubitt Auteur
          @yg_beCela ne semble pas suffire.... Une seule autre équation est résolue :

          he+di+fk+ai+egb=gcl
          0.00021886825561523438 seconds
          e = 3
          i = 9
          k = 9
          b = 9
          h = 9
          d = 6
          f = 6
          a = 6
          g = 6
          l = 9
          c = 6
          93+69+69+69+369=669

          et une autre ne l'est plus...
        4. Wubitt Auteur
          @yg_beVoici celle qui a disparu : SEND+MORE=MONEY
        5. yg_be Contributeur
          @Wubittchez moi, elle fonctionne. as-tu encore plusieurs lignes 
          def solve_impl
          ?
          commence par corriger cela.
      2. Wubitt Auteur
        Pouvez-vous me montrer la correction ?
        1. yg_be Contributeur
          je pense que tu progresseras mieux en le faisant toi-même. regarde ce que tu as partagé en #17.
        2. Wubitt Auteur
          @yg_beje ne vois pas ce que je dois corriger...
          le len ?
          le carry ?
        3. yg_be Contributeur
          @Wubittas-tu encore plusieurs lignes 
          def solve_impl
          ?
        5. Wubitt Auteur
          @yg_bej'aurais besoin d'un indice sur ce que je dois corriger, s'il vous plaît... je ne trouve pas l'erreur.

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