47 lines
1.2 KiB
Python
47 lines
1.2 KiB
Python
#!/usr/bin/python3
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# Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:
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#
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# 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
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#
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# It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.
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#
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# Find the pair of pentagonal numbers, Pj and Pk, for which their 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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from math import sqrt
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from timeit import default_timer
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from projecteuler import is_pentagonal
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def main():
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start = default_timer()
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found = 0
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n = 2
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# Check all couples of pentagonal numbers until the right one
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# is found. Use the function implemented in projecteuler.py to
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# check if the sum and difference ot the two numbers is pentagonal.
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while not found:
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pn = n * (3 * n - 1) // 2
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for m in range(1, n):
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pm = m * (3 * m - 1) // 2
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if is_pentagonal(pn+pm) and is_pentagonal(pn-pm):
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found = 1
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break
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n = n + 1
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end = default_timer()
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print('Project Euler, Problem 44')
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print('Answer: {}'.format(pn-pm))
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print('Elapsed time: {:.9f} seconds'.format(end - start))
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if __name__ == '__main__':
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main()
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