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65 lines
1.6 KiB
Python
65 lines
1.6 KiB
Python
#!/usr/bin/env python
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'''
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Created on 21 oct. 2012
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@author: Julien Lengrand-Lambert
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DESCRIPTION: Solves problem 44 of Project Euler
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Pentagonal numbers are generated by the formula, Pn=n(3n1)/2.
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The first ten pentagonal numbers are:
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1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
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It can be seen that P4 + P7 = 22 + 70 = 92 = P8.
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However, their difference, 70 22 = 48, is not pentagonal.
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Find the pair of pentagonal numbers, Pj and Pk,
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for which their sum and difference is pentagonal
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and D = |Pk - Pj| is minimised; what is the value of D?
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'''
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penta_vals = []
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def is_pentagonal(val):
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"""
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Returns True if val is a pentagonal number
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"""
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global penta_vals
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return (val in penta_vals)
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def pent(val):
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"""
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Returns the pentagonal number created using val
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Pentagonal numbers are defined by Pn=n(3n-1)/2
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"""
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return (val * (3 * val - 1) / 2)
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def create_pentagonal(ite=1000):
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"""
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Returns a list of ite pentagonal numbers
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default is 1000
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Pentagonal numbers are defined by Pn=n(3n1)/2
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"""
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temp = range(1, ite + 1)
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return [pent(val) for val in temp]
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def find_pair(ite=1000):
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"""
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Finds the pair of pentagonal numbers such as
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Pj + Pk and Pj - Pk are also pentagonal
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Returns minimised |Pk - Pj|
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"""
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global penta_vals
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penta_vals = create_pentagonal(ite)
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for val_j in penta_vals:
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for val_k in penta_vals:
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if is_pentagonal(val_k + val_j) and is_pentagonal(val_k - val_j):
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return min(abs(val_j - val_k), abs(val_k - val_j))
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if __name__ == '__main__':
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print "Answer : %d " % (find_pair(10000)) # 10000 is just a rude guess
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