mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-05 02:40:16 +00:00
45 lines
1.2 KiB
Python
45 lines
1.2 KiB
Python
|
"""
|
||
|
|
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() = }")
|