Python/project_euler/problem_094/sol1.py

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