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""" |
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Project Euler Problem 29: Distinct Powers |
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========================================= |
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.. module:: solutions.problem29 |
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:synopsis: My solution to problem #29. |
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The source code for this problem can be |
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`found here <https://bitbucket.org/nekedome/project-euler/src/master/solutions/problem29.py>`_. |
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Problem Statement |
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################# |
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Consider all integer combinations of :math:`a^b` for :math:`2 \\le a \\le 5` and :math:`2 \\le b \\le 5`: |
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15
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.. math:: |
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&2^2=4, &2^3=8, &2^4=16, &2^5=32 \\\\ |
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&3^2=9, &3^3=27, &3^4=81, &3^5=243 \\\\ |
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&4^2=16, &4^3=64, &4^4=256, &4^5=1024 \\\\ |
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&5^2=25, &5^3=125, &5^4=625, &5^5=3125 \\\\ |
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If they are then placed in numerical order, with any repeats removed, we get the following sequence of :math:`15` |
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distinct terms: |
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.. math:: |
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4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125 |
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How many distinct terms are in the sequence generated by :math:`a^b` for :math:`2 \\le a \\le 100` and |
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:math:`2 \\le b \\le 100`? |
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Solution Discussion |
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################### |
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Nothing sophisticated here, explicitly perform the computation. |
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Solution Implementation |
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####################### |
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.. literalinclude:: ../../solutions/problem29.py |
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:language: python |
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:lines: 46- |
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""" |
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from itertools import product |
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def solve(): |
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""" Compute the answer to Project Euler's problem #29 """ |
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upper_bound = 100 |
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terms = set() |
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for a, b in product(range(2, upper_bound + 1), repeat=2): |
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terms.add(a ** b) |
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answer = len(terms) |
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return answer |
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expected_answer = 9183 |
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