77 lines
2.1 KiB
Python
77 lines
2.1 KiB
Python
#!/usr/bin/python3
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# If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
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#
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# {20,48,52}, {24,45,51}, {30,40,50}
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#
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# For which value of p ≤ 1000, is the number of solutions maximised?
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from numpy import zeros
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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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max_ = 0
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savedc = zeros(1000, int)
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# Start with p=12 (the smallest pythagorean triplet is (3,4,5) and 3+4+5=12.
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for p in range(12, 1001):
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count = 0
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a = 0
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b = 0
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c = 0
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m = 2
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# Generate pythagorean triplets.
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while m * m < p:
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for n in range(1, m):
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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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# Increase counter if a+b+c=p and the triplet is new,
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# then save the value of c to avoid counting the same
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# triplet more than once.
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if a + b + c == p and savedc[c] == 0:
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savedc[c] = 1
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count = count + 1
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i = 2
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tmpa = a
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tmpb = b
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tmpc = c
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# Check all the triplets obtained multiplying a, b and c
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# for integer numbers, until the perimeters exceeds p.
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while tmpa + tmpb + tmpc < p:
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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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# Increase counter if the new a, b and c give a perimeter=p.
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if tmpa + tmpb + tmpc == p and savedc[tmpc] == 0:
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savedc[tmpc] = 1
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count = count + 1
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i = i + 1
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m = m + 1
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# If the current value is greater than the maximum,
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# save the new maximum and the value of p.
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if count > max_:
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max_ = count
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res = p
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end = default_timer()
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print('Project Euler, Problem 39')
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print('Answer: {}'.format(res))
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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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