#!/usr/bin/env python

upperlimit = 1000000000

maxcrazy = 9

from math import log10 as log

from itertools import combinations

import signal

import heapq

import shelve

answers = shelve.open("answers2.txt")

from gmpy import is_square

from copy import deepcopy as copy

from pickle import loads, dumps

from fractions import Fraction

factorials = [1]

while len(factorials) < 30:

factorials.append(factorials[-1] * len(factorials))

print factorials

def donothingandlikeit(argument, otherargument = ""):

pass

def jabs(n):

if n >= 0:

return n

return n * n

def isqrt(n):

return x

def score(entry):

return len("".join([str(i) for i in entry]))

queues = []

for i in range(1, maxcrazy + 1):

for j in combinations(range(1, 10), i):

queues.append(([list(j)], "biglist.txt"))

def queueslensort(queueitem):

return len(queueitem[0][0])

queues.sort(key=queueslensort)

for (queue, file) in queues:

answers.clear()

answers.sync()

writefile = open(file, "a")

i = 0

while i < len(queue):

current = queue[i]

for j in range(len(current) - 1):

temp = copy(current)

temp.insert(j, int(str(temp.pop(j)) + str(temp.pop(j))))

good = True

for k in queue:

if dumps(k) == dumps(temp):

good = False

if temp not in queue:

queue.append(temp)

i += 1

for i in range(maxcrazy):

for j in copy(queue):

try:

j[i] *= -1

queue.append(j)

except:

pass

queue = [i for i in queue if len(i) != 1]

for i in queue:

answers[str([(l, 1) for l in i])] = ["(" + str(k) + ")" for k in i]

i = 0

while i < len(queue):

queue[i] = [(j, 1) for j in queue[i]]

queue[i] = (len(queue[i]), queue[i])

i += 1

# for i in queue:

# print i

# print queue

heapq.heapify(queue)

if True:

while len(queue) > 0:

# queue[ii:].sort()

(curscore, current) = heapq.heappop(queue)

# print current

try:

stringrep = answers[str(current)]

except:

stringrep = str(current)

if len(current) == 1:

if current[0][1] == 1:

if current[0][0] >= 0 and current[0][0] <= upperlimit:

i = ([str(k) for k in str([l[0] for l in current]) if k in "1234567890"])

j = ([str(k) for k in str(stringrep) if k in "1234567890"])

while len(i) > 1:

i.insert(0, i.pop(0) + i.pop(0))

while len(j) > 1:

j.insert(0, j.pop(0) + j.pop(0))

# print i, j

if i == j:

print len(queue), str(current[0][0]) + ": " + (answers[str(current)][0]) + "\n",

writefile.write(str(current[0][0]) + ": " + answers[str(current)][0] + "\n")

# print curscore, len(queue), current,

current = [Fraction(i[0], i[1]) for i in current]

# print answers[str([(k.numerator, k.denominator) for k in current])]

for i in range(len(current)):

# sqrt

temp = copy(current)

tempstr = copy(stringrep)

if is_square(temp[i].numerator) and is_square(temp[i].denominator):

temp[i] = Fraction(-isqrt(temp[i].numerator), isqrt(temp[i].denominator))

tempstr.insert(i, "-sqrt(" + tempstr.pop(i) + ")")

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

# Factorial

temp = copy(current)

tempstr = copy(stringrep)

try:

if temp[i].numerator >= 0 and temp[i].numerator < 20 and temp[i].denominator == 1:

temp.insert(i, Fraction(-factorials[temp.pop(i).numerator], 1))

tempstr.insert(i, "-(" + tempstr.pop(i) + ")! ")

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

except:

pass

# sqrt

temp = copy(current)

tempstr = copy(stringrep)

try:

if is_square(temp[i].numerator) and is_square(temp[i].denominator):

temp[i] = Fraction(isqrt(temp[i].numerator), isqrt(temp[i].denominator))

tempstr.insert(i, "sqrt(" + tempstr.pop(i) + ")")

# print temp

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

except:

pass

# Factorial

temp = copy(current)

tempstr = copy(stringrep)

try:

if temp[i].numerator >= 0 and temp[i].numerator < 25 and temp[i].denominator == 1:

temp.insert(i, Fraction(factorials[temp.pop(i).numerator], 1))

tempstr.insert(i, "(" + tempstr.pop(i) + ")! ")

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

except:

pass

for i in range(len(current) - 1):

# Exponents

try:

temp = copy(current)

tempstr = copy(stringrep)

signal.signal(signal.SIGALRM, donothingandlikeit)

signal.alarm(2)

if abs(temp[i + 1]) * log(abs(temp[i])) / log(10) <= log(upperlimit) / log(10) + 1:

if abs(temp[i + 1]) * log(abs(temp[i].denominator)) / log(10) <= log(upperlimit) / log(10) + 1:

temp.insert(i, temp.pop(i) ** temp.pop(i))

tempstr.insert(i, "(" + tempstr.pop(i) + " ^ " + tempstr.pop(i) + ")")

if temp[i].denominator == 1 and abs(temp[i]) <= upperlimit:

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

except BaseException as e:

# print e

pass

signal.alarm(0)

# Division

temp = copy(current)

tempstr = copy(stringrep)

try:

temp.insert(i, temp.pop(i) / temp.pop(i))

tempstr.insert(i, "(" + tempstr.pop(i) + " / " + tempstr.pop(i) + ")")

if temp[i].denominator == 1:

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

except:

pass

# Multiplication

temp = copy(current)

tempstr = copy(stringrep)

temp.insert(i, temp.pop(i) * temp.pop(i))

tempstr.insert(i, "(" + tempstr.pop(i) + " * " + tempstr.pop(i) + ")")

if abs(temp[i]) <= upperlimit:

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

# Subtraction

temp = copy(current)

tempstr = copy(stringrep)

temp.insert(i, temp.pop(i) - temp.pop(i))

tempstr.insert(i, "(" + tempstr.pop(i) + " - " + tempstr.pop(i) + ")")

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

# Addition

temp = copy(current)

tempstr = copy(stringrep)

temp.insert(i, temp.pop(i) + temp.pop(i))

tempstr.insert(i, "(" + tempstr.pop(i) + " + " + tempstr.pop(i) + ")")

if str([(k.numerator, k.denominator) for k in temp]) not in answers:

heapq.heappush(queue, (score(tempstr), [(k.numerator, k.denominator) for k in temp]))

answers[str([(k.numerator, k.denominator) for k in temp])] = tempstr

# else:

# ii += 1

# print "BUHLEETING"

# del queue

# print "PART A DONE"

# for i in copy(answers):

# if len(i) == iii:

# del answers[i]

# print "BUHLEETED"