70 lines
1.6 KiB
Python
70 lines
1.6 KiB
Python
#!/usr/bin/python3
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# A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
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#
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# a2 + b2 = c2
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#
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# For example, 32 + 42 = 9 + 16 = 25 = 52.
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#
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# There exists exactly one Pythagorean triplet for which a + b + c = 1000.
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#
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# Find the product abc.
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from math import gcd
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from timeit import default_timer
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def main():
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start = default_timer()
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found = 0
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m = 2
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# Brute force approach: generate all the Pythagorean triplets using
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# Euclid's formula, until the one where a+b+c=1000 is found.
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while not found:
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for n in range(1, m):
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if found == 1:
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break
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if gcd(m, n) == 1 and (m % 2 == 0 and n % 2 != 0 or m % 2 != 0 and n % 2 == 0):
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a = m * m - n * n
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b = 2 * m * n
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c = m * m + n * n
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if a + b + c == 1000:
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found = 1
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break
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i = 2
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while True:
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tmpa = a * i
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tmpb = b * i
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tmpc = c * i
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if tmpa + tmpb + tmpc == 1000:
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a = tmpa
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b = tmpb
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c = tmpc
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found = 1
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break
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if tmpa + tmpb + tmpc > 1000:
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break
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i = i + 1
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m = m + 1
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end = default_timer()
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print('Project Euler, Problem 9')
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print('Answer: {}'.format(a * b * c))
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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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