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November 5, 2011 15:51
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Ticker solver
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1000 | |
3 4 6 6 6 8 10 | |
2 2 5 5 5 9 15 | |
1 1 2 4 7 9 4 | |
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4 5 5 6 8 8 43 | |
1 3 4 5 8 9 10 | |
4 4 5 5 6 9 22 | |
5 5 5 5 5 6 20 | |
2 2 2 3 3 7 13 | |
1 4 7 8 8 9 23 | |
4 4 6 7 8 9 4 | |
5 5 5 5 8 9 11 | |
1 1 6 6 8 8 17 | |
1 1 3 6 7 9 24 | |
1 1 4 4 5 5 22 | |
1 4 6 8 8 9 5 | |
2 2 6 6 6 7 20 | |
2 4 4 6 6 6 10 | |
3 3 4 4 7 9 8 | |
1 2 5 6 9 9 8 | |
1 5 5 5 7 7 9 | |
4 4 4 5 6 8 26 | |
4 6 8 9 9 9 32 | |
2 2 3 3 4 9 2 | |
4 4 5 5 5 8 1 | |
3 3 3 3 4 5 4 | |
3 7 7 7 7 8 20 | |
2 4 4 4 4 4 14 | |
1 2 3 6 6 9 9 | |
1 3 4 6 9 9 10 | |
4 4 4 6 6 6 55 | |
4 4 5 7 8 9 11 | |
1 1 5 6 7 8 9 | |
4 5 5 5 6 9 4 | |
4 5 5 8 8 8 25 | |
2 4 5 5 6 7 1 | |
1 6 7 9 9 9 18 | |
4 4 5 6 8 9 5 | |
1 1 3 4 5 5 10 | |
1 2 4 4 9 9 23 | |
1 2 2 4 4 9 8 | |
1 1 3 5 5 8 4 | |
4 5 6 7 8 9 6 | |
2 3 3 5 7 8 2 | |
2 5 5 5 9 9 52 | |
4 5 8 9 9 9 10 | |
2 3 3 5 7 7 5 | |
3 4 7 7 8 9 4 | |
2 5 6 6 9 9 18 | |
1 5 6 8 8 8 12 | |
1 1 5 8 9 9 9 | |
1 1 4 4 6 9 7 | |
1 2 4 5 5 8 2 | |
1 1 5 5 8 9 2 | |
2 5 5 5 6 7 9 | |
1 1 2 2 8 9 12 | |
1 2 8 9 9 9 32 | |
2 2 4 9 9 9 10 | |
1 2 2 4 9 9 6 | |
4 4 4 9 9 9 23 | |
1 3 4 4 6 8 1 | |
4 7 8 9 9 9 23 | |
2 3 3 5 8 9 2 | |
2 4 4 6 6 7 4 | |
1 1 2 3 4 9 5 | |
2 2 2 6 6 7 10 | |
2 2 3 3 7 7 29 | |
1 4 4 4 4 5 62 | |
4 4 4 4 5 8 42 | |
2 3 3 4 7 9 2 | |
1 2 2 2 6 8 19 | |
2 2 2 4 5 6 1 | |
1 4 7 7 8 9 23 | |
2 7 7 8 8 8 4 | |
4 6 6 6 8 9 10 | |
2 2 3 3 6 6 4 | |
1 1 2 5 7 7 6 | |
4 6 6 8 9 9 19 | |
1 4 6 6 6 8 11 | |
1 1 1 3 3 9 3 | |
1 3 5 5 9 9 28 | |
2 3 4 4 7 8 4 | |
1 2 2 2 4 8 2 | |
1 1 2 7 7 8 4 | |
2 5 5 6 7 9 9 | |
1 2 2 3 4 8 19 | |
2 2 6 7 7 8 8 | |
2 2 4 6 6 8 33 | |
1 2 3 3 5 7 6 | |
4 4 4 4 4 8 12 | |
3 3 6 7 7 8 2 | |
2 3 3 7 7 8 7 | |
1 3 3 9 9 9 26 | |
2 3 5 7 9 9 4 | |
2 2 4 4 7 8 18 | |
5 5 6 7 7 8 8 | |
1 2 4 4 7 8 1 | |
1 2 4 5 6 9 6 | |
3 3 3 4 5 7 2 | |
4 4 4 6 8 8 53 | |
4 4 4 4 6 8 11 | |
4 4 5 6 9 9 17 | |
3 3 5 5 7 9 5 | |
1 3 4 6 6 9 15 | |
1 3 4 8 8 9 2 | |
1 2 6 6 7 7 13 | |
2 2 5 7 8 9 4 | |
4 5 5 5 5 6 25 | |
1 1 2 3 7 9 6 | |
2 3 7 7 8 9 7 | |
1 1 2 8 9 9 12 | |
3 3 6 6 7 7 4 | |
6 6 8 9 9 9 10 | |
1 1 4 4 9 9 5 | |
1 3 5 6 6 9 7 | |
1 4 5 7 9 9 7 | |
2 3 3 5 5 7 7 | |
3 3 4 7 9 9 8 | |
1 1 2 4 4 4 7 | |
2 5 5 5 7 8 10 | |
1 3 4 5 6 7 6 | |
1 1 1 7 7 8 2 | |
2 7 7 7 7 7 112 | |
1 3 6 8 8 8 4 | |
4 5 5 6 9 9 17 | |
1 2 2 4 4 6 22 | |
2 2 8 8 8 9 2 | |
4 4 4 6 8 9 15 | |
1 3 3 5 5 8 2 | |
2 3 3 5 6 8 3 | |
4 4 4 5 5 9 22 | |
1 3 3 5 7 9 27 | |
2 4 4 9 9 9 28 | |
1 3 3 3 7 7 4 | |
2 6 7 7 8 9 5 | |
1 1 1 1 5 5 15 | |
3 4 5 5 6 7 9 | |
1 5 6 7 8 9 12 | |
3 5 6 7 9 9 4 | |
1 3 3 3 4 8 20 | |
1 2 2 2 3 7 6 | |
4 4 7 8 8 9 2 | |
1 1 2 5 6 9 9 | |
1 1 2 4 5 9 14 | |
1 2 4 7 7 7 2 | |
2 3 5 6 7 7 10 | |
3 3 3 4 4 5 23 | |
1 2 2 5 5 5 20 | |
2 2 3 4 8 9 7 | |
2 4 6 6 7 7 1 | |
2 3 5 7 8 8 5 | |
2 2 5 5 5 5 218 | |
1 3 5 6 8 9 21 | |
2 2 6 8 8 8 24 | |
2 2 4 4 5 8 17 | |
3 5 5 6 6 8 14 | |
2 3 4 5 5 5 99 | |
1 5 5 6 6 9 8 | |
1 1 1 4 7 9 40 | |
3 3 4 6 9 9 5 | |
1 2 2 5 7 8 14 | |
2 3 3 6 7 9 2 | |
3 3 3 4 4 9 1 | |
1 2 3 6 8 9 2 | |
4 5 5 5 6 6 15 | |
2 3 3 4 6 7 7 | |
2 2 3 3 8 9 11 | |
4 5 6 7 7 8 2 | |
2 4 4 7 7 8 2 | |
1 2 2 7 8 8 4 | |
2 3 4 6 6 9 2 | |
5 6 8 8 8 9 10 | |
1 5 5 6 7 9 19 | |
2 2 7 7 8 8 36 | |
3 3 3 6 6 8 34 | |
2 2 2 4 8 9 12 | |
1 1 2 4 8 9 5 | |
1 2 5 6 8 9 15 | |
3 3 6 7 8 8 6 | |
1 3 3 3 5 6 6 | |
1 4 4 5 9 9 20 | |
1 6 6 6 9 9 25 | |
2 4 4 5 5 7 2 | |
6 6 7 8 8 9 2 | |
1 1 3 3 4 5 4 | |
1 1 3 3 7 8 1 | |
2 4 4 6 6 8 28 | |
4 5 7 8 8 9 8 | |
2 2 2 5 5 8 9 | |
2 5 6 6 6 6 4 | |
1 2 3 3 3 6 1 | |
2 3 3 3 4 4 19 | |
1 1 4 4 4 9 18 | |
1 3 6 6 7 7 7 | |
1 4 5 8 8 8 5 | |
4 4 4 4 4 9 50 | |
1 4 5 5 6 7 14 | |
4 5 6 8 8 9 2 | |
2 2 2 5 6 8 6 | |
2 2 5 7 7 9 27 | |
1 4 4 9 9 9 3 | |
3 4 4 6 7 7 8 | |
2 2 2 7 7 7 40 | |
2 2 2 6 6 8 2 | |
4 4 5 5 9 9 19 | |
4 4 5 6 6 8 28 | |
4 4 4 5 9 9 26 | |
5 5 6 7 8 9 21 | |
1 4 4 8 8 9 2 | |
1 6 7 7 8 8 17 | |
2 3 3 4 6 9 5 | |
1 3 3 3 5 8 2 | |
3 4 6 6 9 9 14 | |
2 2 2 2 4 7 4 | |
1 1 1 1 5 9 1 | |
1 2 3 3 5 9 10 | |
3 5 6 6 6 7 4 | |
3 4 5 6 8 8 10 | |
2 2 3 3 5 6 4 | |
2 5 6 8 8 8 6 | |
3 3 4 4 8 9 6 | |
2 3 3 5 8 8 10 | |
5 6 6 6 7 9 18 | |
3 4 4 6 8 8 10 | |
4 7 8 8 8 8 5 | |
3 4 5 5 8 8 2 | |
1 4 5 6 7 9 6 | |
2 4 6 7 8 8 12 | |
3 3 6 7 7 7 4 | |
3 3 6 6 6 7 8 | |
2 2 2 2 2 8 12 | |
1 2 5 7 8 9 4 | |
3 5 5 7 9 9 15 | |
4 4 5 5 8 9 4 | |
1 1 2 3 7 8 2 | |
1 1 4 4 5 9 6 | |
3 5 5 7 7 7 2 | |
4 4 7 7 7 7 4 | |
3 5 5 9 9 9 20 | |
2 2 2 3 4 4 41 | |
1 5 5 6 8 8 7 | |
3 3 3 4 4 4 25 | |
2 2 2 3 3 8 6 | |
2 3 7 7 7 9 34 | |
1 3 3 4 5 6 12 | |
1 3 4 5 5 9 7 | |
1 1 1 2 4 9 1 | |
1 1 2 2 3 9 4 | |
1 5 7 7 8 9 19 | |
4 5 5 6 7 9 22 | |
1 4 4 6 7 7 8 | |
2 2 3 6 6 8 30 | |
1 1 4 6 6 9 5 | |
2 3 5 5 6 9 7 | |
4 6 7 7 8 8 25 | |
4 5 5 7 7 7 25 | |
1 1 2 2 5 7 5 | |
1 2 5 5 8 9 12 | |
1 4 5 5 6 6 64 | |
1 4 4 4 8 8 6 | |
4 6 6 6 7 9 33 | |
3 3 3 3 7 7 6 | |
3 7 8 8 8 9 6 | |
1 3 3 6 9 9 8 | |
5 7 7 9 9 9 12 | |
4 5 6 7 7 7 14 | |
1 3 4 4 6 7 1 | |
4 4 5 6 8 8 17 | |
1 4 5 6 8 8 5 | |
2 2 2 2 7 9 6 | |
1 1 3 5 5 6 2 | |
1 6 6 7 8 9 7 | |
2 3 5 6 6 7 10 |
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#!/usr/bin/env python | |
from itertools import product, groupby | |
import sys | |
def LeftBracketIndexes(n): | |
"""Algorithm N of Knuth's TAoCP 4D""" | |
g = [None] | |
z = [None] | |
for j in range(1, n + 1): | |
z.append(2 * j - 1) | |
g.append(2 * j - 2) | |
while True: | |
yield z[1::] | |
j = n | |
while z[j] == g[j]: | |
g[j] = g[j] ^ 1 | |
j = j - 1 | |
if (g[j] - z[j]) % 2 == 0: | |
z[j] = z[j] + 2 | |
else: | |
t = z[j] - 2 | |
if t < 0: | |
break | |
else: | |
if t < z[j - 1]: | |
t = t + 3 | |
elif t == z[j - 1]: | |
t = t + 1 | |
z[j] = t | |
def MakeStack(indexes, operations): | |
stack = [] | |
operationIndex = 0 | |
digitIndex = 0 | |
for index in range(0, len(indexes) + len(operations) + 1): | |
if operationIndex < len(operations) and index + 1 == indexes[operationIndex]: | |
stack.append(operations[operationIndex]) | |
operationIndex += 1 | |
elif digitIndex < len(indexes) + 1: | |
stack.append('d') | |
digitIndex += 1 | |
return stack | |
def MapStack(digits, stack): | |
digitIndex = 0 | |
mapped = [] | |
for item in stack: | |
if item == 'd': | |
mapped.append(digits[digitIndex]) | |
digitIndex += 1 | |
else: | |
mapped.append(item) | |
return mapped | |
def EvalStack(stack): | |
buffer = [] | |
while len(stack) > 0: | |
item = stack.pop() | |
if item == '+' or item == '-' or item == '*': | |
a = buffer.pop() | |
b = buffer.pop() | |
if item == '+': | |
buffer.append(a + b) | |
elif item == '-': | |
buffer.append(a - b) | |
elif item == '*': | |
buffer.append(a * b) | |
else: | |
buffer.append(item) | |
return buffer.pop() | |
def ReadTests(): | |
tests = [] | |
for line in sys.stdin: | |
test = map(lambda digit: int(digit), line.strip('\n').split(' ')) | |
answer = test.pop() | |
if len(test) > 0 and answer != None: | |
tests.append((test, answer)) | |
return tests | |
size = 6 | |
target = 100 | |
indexesSet = list(LeftBracketIndexes(size - 1)) | |
operationsSet = list(product('+-*', repeat=size - 1)) | |
tests = ReadTests() | |
stacks = [] | |
for indexes in indexesSet: | |
for operations in operationsSet: | |
stack = MakeStack(indexes, operations) | |
stacks.append(([], stack)) | |
experimental = 15 | |
for ticket, answer in tests[:experimental]: | |
targets = 0 | |
for guesses, stack in stacks: | |
guess = EvalStack(MapStack(ticket, stack)) | |
guesses.append(guess) | |
if guess == target: | |
targets += 1 | |
print targets == answer | |
stacks = sorted(map(lambda s: (str(s[0]), s[1]), stacks), key=lambda a: a[0]) | |
distinctStacks = [] | |
for _, group in groupby(stacks, key=lambda a: a[0]): | |
_, stack = next(group) | |
distinctStacks.append((stack, len(list(group)) + 1)) | |
for ticket, answer in tests[experimental:]: | |
targets = 0 | |
for stack, same in distinctStacks: | |
guess = EvalStack(MapStack(ticket, stack)) | |
if guess == target: | |
targets += same | |
print targets == answer | |
# 10206 stacks | |
# 2595 distinct stacks | |
# On all stacks | |
# real 4m48.268s | |
# user 4m44.367s | |
# sys 0m0.601s | |
# On ditinct stacks | |
# real 1m4.194s | |
# user 1m3.181s | |
# sys 0m0.178s |
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