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Problem044.py
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Problem044.py
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#!/usr/bin/python3
#coding:utf8
# http://projecteuler.net/problem=44
#
# PROBLEM CONTENT:
# Pentagonal numbers are generated by the formula, Pn = n*(3n-1)/2.
# The first ten pentagonal numbers are:
# 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
#
# It can be seen that P4 + P7 = 22 + 70 = 92 = P8
#
# However, their difference, 70 − 22 = 48, is not pentagonal.
#
# Find the pair of pentagonal numbers, Pj and Pk, for which their sum and
# difference are pentagonal and D = |Pk - Pj| is minimised; what is the value
# of D?
#
# EXPLANATION: There is really no guarantee that the difference is actually
# minimised :( A possible algorithm for this is shown in:
# http://codereview.stackexchange.com/a/93325
import time
from math import sqrt
def pentagonal(maximum):
return [int(n*(3*n-1)/2) for n in range(1,maximum)]
def is_pentagonal(c):
return float((1 + sqrt(1+24*c))/6).is_integer()
def main():
n = 0
computed_pentagonals = pentagonal(10**4)
for indexj, j in enumerate(computed_pentagonals):
for indexk in range(indexj + 1, len(computed_pentagonals)):
diff = computed_pentagonals[indexk] - j
add = computed_pentagonals[indexk] + j
if (is_pentagonal(diff) and is_pentagonal(add)):
print(diff)
return
if __name__ == '__main__':
start = time.time()
main()
elapsed = time.time() - start
print('Solved in %.2f seconds' % elapsed)