53 lines
1.2 KiB
Python
53 lines
1.2 KiB
Python
#!/usr/bin/env python3
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# The points P(x1,y1) and Q(x2,y2) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.
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#
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# There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive;
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# that is, 0<=x1,y1,x2,y2<=2.
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#
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# Given that 0<=x1,y1,x2,y2<=50, how many right triangles can be formed?
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from itertools import product
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from projecteuler import timing
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N = 50
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def check_triangle(p1, p2, p3):
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a = int((p2[0] - p1[0]) ** 2 + (p2[1] - p1[1]) ** 2)
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b = int((p3[0] - p2[0]) ** 2 + (p3[1] - p2[1]) ** 2)
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c = int((p3[0] - p1[0]) ** 2 + (p3[1] - p1[1]) ** 2)
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if ((a > 0 and b > 0 and c > 0) and
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(a == (b + c) or b == (a + c) or
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c == (a + b))):
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return True
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return False
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@timing
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def p091():
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combinations = []
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for i in range(N + 1):
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for j in range(N + 1):
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combinations.append((i, j))
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prods = product(combinations, repeat=2)
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count = 0
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for p in prods:
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if check_triangle((0, 0), p[0], p[1]):
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count += 1
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print('Project Euler, Problem 91')
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print(f'Answer: {int(count / 2)}')
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if __name__ == '__main__':
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p091()
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