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@motleytech
Last active June 16, 2023 18:52
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Verbal arithmetic
from pprint import pprint as pp
from time import time
st = time()
def codeForGuess(ch, firsts, indent):
ind = ' '*indent
v1 = """\
%sfor %s in %s:
%s urem(%s)""" % (ind, ch, "udiff(set0)" if ch in firsts else "ucopy()",
ind, ch)
v2 = """%s uadd(%s)""" % (ind, ch)
return (v1, v2)
def codeForVerifySum(chCounts, last, indent, eqIndex):
ind = ' '*indent
sm0, sm1 = "sm%s" % (eqIndex,), "sm%s" % (eqIndex+1,)
st = "%s/10" % (sm0, )
for ch, count in chCounts:
if ch == last:
count -= 1
if count > 1:
st += ' + %s*%s' % (ch, count)
elif count == 1:
st += ' + %s' % (ch, )
c1 = """\
%s%s = %s
%sif %s == %s %% 10:""" % (ind, sm1, st,
ind, last, sm1)
return (c1, None)
def codeForSolve(chs, chCounts, last, indent, eqIndex, firsts):
ind = ' '*indent
sm0, sm1 = "sm%s" % (eqIndex,), "sm%s" % (eqIndex+1,)
st = "%s/10" % (sm0, )
for ch, count in chCounts:
if ch == chs:
continue
elif ch == last:
st += ' + %s*%s' % (ch, count - 1)
else:
if count > 1:
st += ' + %s*%s' % (ch, count)
else:
st += ' + %s' % (ch, )
if chs == last:
c1 = """\
%s%s = %s
%s%s = %s %% 10
%sif %s in unused%s:
%s urem(%s)""" % (ind, sm1, st,
ind, chs, sm1,
ind, chs, (' and %s != 0' % (chs, )) if chs in firsts else '',
ind, chs)
c2 = """%s uadd(%s)""" % (ind, chs)
return c1, c2
else:
c1 = """\
%svalue = %s
%s%s = (%s - value) %% 10
%sif %s in unused%s:
%s urem(%s)
%s %s = value + %s""" % (ind, st,
ind, chs, last,
ind, chs, (' and %s != 0' % (chs, )) if chs in firsts else '',
ind, chs,
ind, sm1, chs)
c2 = """%s uadd(%s)""" % (ind, chs)
return c1, c2
def codeForFinalCheck(eqIndex, chars, indent, prob):
ind = ' '*indent
varDict = "{ " + ", ".join("'%s': %s" % (x, x) for x in chars) + " }"
c1 = """\
%sif %s < 10:
%s values = %s
%s lwords = [str(word2num(v, values)) for v in lhs]
%s rword = str(word2num(rhs, values))
%s return "%%s = %%s" %% (" + ".join(lwords), rword)\n""" % (ind, "sm%s" % (eqIndex + 1),
ind, varDict,
ind,
ind,
ind)
return c1, None
def createProgram(problem):
program1 = """
def word2num(word, values):
num = 0
for c in word:
num = num * 10 + values[c]
return num
def myfunc(words):
unused = set(range(10))
urem = unused.remove
uadd = unused.add
udiff = unused.difference
ucopy = unused.copy
set0 = set([0])
sm0 = 0
lhs = words[:-1]
rhs = words[-1]
"""
program3 = """\
return "not solved"
try:
print myfunc(%s)
except:
from traceback import print_exc
print_exc()
""" % (problem)
problem = [x[::-1] for x in problem]
firsts = set([x[-1] for x in problem])
unused = set()
[unused.union(set(x)) for x in problem]
lhs, rhs = problem[:-1], problem[-1]
equations = []
for i in range(len(rhs)):
equations.append([word[i] if len(word) > i else None for word in problem])
charactersWithOccurenceCount = chOcc = []
unassignedCharsSortedByNumOccurences = unChars = []
characters = set()
for eqn in equations:
used = set([None])
curr = []
for ch in eqn:
characters.add(ch)
if not ch in used:
used.add(ch)
curr.append((ch, eqn.count(ch)))
chOcc.append(curr)
if None in characters:
characters.remove(None)
used = set([None])
for eqn in equations:
curr = []
for ch in eqn:
if not ch in used:
used.add(ch)
curr.append((ch, eqn.count(ch)))
unChars.append(sorted(curr, key=lambda x: x[1], reverse=True))
#pp(chOcc)
#pp(unChars)
indent = 4
c1s, c2s = [], []
for i, (uchs, chCounts) in enumerate(zip(unChars, chOcc)):
luchs = len(uchs)
verifyRequired = True
if luchs == 1:
if uchs[0][1] == 1:
# one unknown which occurs once
# solve for value
# verify its unused and non-zero (if in firsts)
c1, c2 = codeForSolve(uchs[0][0], chCounts, rhs[i], indent, i, firsts)
c1s.append(c1), c2s.append(c2)
indent += 4
verifyRequired = False
else:
# one unknown which occurs multiple times
# for loop to guess values
# verify sum
c1, c2 = codeForGuess(uchs[0][0], firsts, indent)
c1s.append(c1), c2s.append(c2)
indent += 4
elif luchs > 1:
for ch, occ in uchs[:-1]:
c1, c2 = codeForGuess(ch, firsts, indent)
c1s.append(c1), c2s.append(c2)
indent += 4
ch, occ = uchs[-1]
if occ > 1:
c1, c2 = codeForGuess(ch, firsts, indent)
c1s.append(c1), c2s.append(c2)
indent += 4
else:
c1, c2 = codeForSolve(uchs[-1][0], chCounts, rhs[i], indent, i, firsts)
c1s.append(c1), c2s.append(c2)
indent += 4
verifyRequired = False
if verifyRequired:
c1, c2 = codeForVerifySum(chCounts, rhs[i], indent, i)
c1s.append(c1), c2s.append(c2)
indent += 4
c1, c2 = codeForFinalCheck(i, characters, indent, problem)
indent += 4
c1s.append(c1)
c1s = [x for x in c1s if x]
c2s = [x for x in c2s if x]
program = program1 + "\n".join(c1s) + "\n".join(reversed(c2s)) + program3
return program
test_cases = [
["send", "more", "money"],
["zeroes", "ones", "binary"],
["send", "a", "tad", "more", "money"],
["seven", "seven", "six", "twenty"],
["saturn", "uranus", "neptune", "pluto", "planets"],
["donald", "gerald", "robert"],
["fifty", "twenty", "nine", "one", "eighty"],
["forty", "ten", "ten", "sixty"],
["ein", "ein", "ein", "ein", "vier"],
["lets", "solve", "this", "little", "teaser"],
["eleven", "lagers", "revive", "general"],
["she", "will", "wash", "these", "shirts"],
["have", "a", "happy", "happy", "easter"],
["ohio", "hawaii", "kansas", "alaska", "indiana"],
["tonto", "andthe", "lone", "ranger"],
["accentuate", "concertina", "transsonic", "instructor"],
["apolitical", "penicillin", "pickpocket", "knickknack"],
["coincidence", "electrician", "accelerator"],
["compromise", "stretchiest", "microscopic", "homestretch"],
["happy", "holidays", "to", "all", "hohohoho"],
["aries", "leo", "libra", "pisces"],
["gemini", "virgo", "cancer"],
["see", "three", "little", "wolves"],
["earth", "air", "fire", "water", "nature"],
["dclix", "dlxvi", "mccxxv"],
["couple", "couple", "quartet"],
["fish", "n", "chips", "supper"],
["store", "and", "name", "brands"],
["this", "isa", "great", "time", "waster"],
["the", "dog", "got", "her", "on", "the", "hand", "again"],
["when", "i", "really", "want", "a", "thrill"],
["what", "a", "week", "at", "news", "this", "has", "been"],
["this", "it", "seems", "to", "me", "is", "the", "heart", "of", "the", "matter"],
['apperception', 'aristocratic', 'concessionaire', 'conscription',
'inappropriate', 'incapacitate', 'inconsistent',
'interception', 'osteoporosis', 'perspiration', 'prescription',
'proscription', 'prosopopoeia', 'protectorate', 'protestation',
'statistician', 'transoceanic', 'transpiration',
'antiperspirant'],
]
for tc in test_cases:
program = createProgram(tc)
#print program
exec program
et = time() - st
print 'elapsed time : %10.6f' % (et)
print 'average time : %10.6f' % (et / len(test_cases))
# Following is a sample program created by this solution
"""
def word2num(word, values):
num = 0
for c in word:
num = num * 10 + values[c]
return num
def myfunc(words):
unused = set(range(10))
urem = unused.remove
uadd = unused.add
udiff = unused.difference
ucopy = unused.copy
set0 = set([0])
sm0 = 0
lhs = words[:-1]
rhs = words[-1]
for n in ucopy():
urem(n)
for e in ucopy():
urem(e)
for c in udiff(set0):
urem(c)
for t in udiff(set0):
urem(t)
for s in udiff(set0):
urem(s)
value = sm0/10 + n*9 + c*2 + e*4 + t*1 + s
a = (t - value) % 10
if a in unused and a != 0:
urem(a)
sm1 = value + a
for o in udiff(set0):
urem(o)
for i in udiff(set0):
urem(i)
value = sm1/10 + o*8 + i*4 + t*3 + n*1 + a
r = (n - value) % 10
if r in unused:
urem(r)
sm2 = value + r
sm3 = sm2/10 + i*10 + t + a*3 + e*2 + s + n
if a == sm3 % 10:
sm4 = sm3/10 + t*10 + a*3 + i + o*2 + r + c
if r == sm4 % 10:
for p in udiff(set0):
urem(p)
sm5 = sm4/10 + p*6 + r*3 + n + i*2 + s + a*3 + o + e
if i == sm5 % 10:
sm6 = sm5/10 + e*2 + c*3 + o*3 + i*4 + p + r*2 + t*3
if p == sm6 % 10:
sm7 = sm6/10 + c*3 + o*3 + i*3 + r*3 + a + s*3 + p*2
if s == sm7 % 10:
sm8 = sm7/10 + r*3 + t + s*2 + c*3 + p*3 + n + o*2 + e*2 + i
if r == sm8 % 10:
sm9 = sm8/10 + e*3 + s*8 + p + a + o + t*3 + n
if e == sm9 % 10:
sm10 = sm9/10 + p*2 + i + e*2 + n*2 + c*2 + t*2 + r + o*4 + a*2
if p == sm10 % 10:
sm11 = sm10/10 + p + r*7 + c + o + a*2 + n*3 + s + e + t
if i == sm11 % 10:
sm12 = sm11/10 + a*2 + n*2 + c + i*3 + o + p*6 + s + t + r
if t == sm12 % 10:
sm13 = sm12/10 + o + i + t
if n == sm13 % 10:
sm14 = sm13/10 + c
if a == sm14 % 10:
if sm14 < 10:
values = { 'a': a, 'c': c, 'e': e, 'i': i, 'o': o, 'n': n, 'p': p, 's': s, 'r': r, 't': t }
lwords = [str(word2num(v, values)) for v in lhs]
rword = str(word2num(rhs, values))
return "%s = %s" % (" + ".join(lwords), rword)
uadd(p)
uadd(r)
uadd(i)
uadd(o)
uadd(a)
uadd(s)
uadd(t)
uadd(c)
uadd(e)
uadd(n)
return "not solved"
try:
print myfunc(['apperception', 'aristocratic', 'concessionaire', 'conscription', 'inappropriate', 'incapacitate', 'inconsistent', 'interception', 'osteoporosis', 'perspiration', 'prescription', 'proscription', 'prosopopoeia', 'protectorate', 'protestation', 'statistician', 'transoceanic', 'transpiration', 'antiperspirant'])
except:
from traceback import print_exc
print_exc()
"""
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