48 lines
1.2 KiB
Python
48 lines
1.2 KiB
Python
#!/usr/bin/env python3
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"""
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Created on 30 Aug 2021
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@author: David Doblas Jiménez
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@email: daviddoji@pm.me
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Solution for problem 44 of Project Euler
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https://projecteuler.net/problem=44
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"""
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from itertools import combinations
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from operator import add, sub
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from utils import timeit
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def pentagonal(n):
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return int(n*(3*n-1)/2)
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@timeit("Problem 44")
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def compute():
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"""
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Pentagonal numbers are generated by the formula, Pn=n(3n−1)/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. However, their
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difference, 70 − 22 = 48, is not pentagonal.
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Find the pair of pentagonal numbers, Pj and Pk, for which their
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sum and difference are pentagonal and D = |Pk − Pj| is minimised.
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What is the value of D?
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"""
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dif = 0
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pentagonal_list = set(pentagonal(n) for n in range(1,2500))
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pairs = combinations(pentagonal_list, 2)
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for p in pairs:
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if add(*p) in pentagonal_list and abs(sub(*p)) in pentagonal_list:
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dif = (abs(sub(*p)))
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# the first one found would be the smallest
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break
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return dif
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if __name__ == "__main__":
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print(f"Result for Problem 44: {compute()}") |