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45 lines
1.2 KiB
Python
45 lines
1.2 KiB
Python
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"""
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Project Euler Problem 94: https://projecteuler.net/problem=94
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It is easily proved that no equilateral triangle exists with integral length sides and
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integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square
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units.
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We shall define an almost equilateral triangle to be a triangle for which two sides are
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equal and the third differs by no more than one unit.
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Find the sum of the perimeters of all almost equilateral triangles with integral side
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lengths and area and whose perimeters do not exceed one billion (1,000,000,000).
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"""
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def solution(max_perimeter: int = 10**9) -> int:
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"""
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Returns the sum of the perimeters of all almost equilateral triangles with integral
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side lengths and area and whose perimeters do not exceed max_perimeter
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>>> solution(20)
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16
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"""
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prev_value = 1
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value = 2
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perimeters_sum = 0
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i = 0
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perimeter = 0
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while perimeter <= max_perimeter:
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perimeters_sum += perimeter
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prev_value += 2 * value
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value += prev_value
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perimeter = 2 * value + 2 if i % 2 == 0 else 2 * value - 2
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i += 1
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return perimeters_sum
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if __name__ == "__main__":
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print(f"{solution() = }")
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