iframe-proxy | Sunbelt Computer Software

History

60 lines (48 loc) · 1.97 KB

Raw

"""

Project Euler Problem 75: https://projecteuler.net/problem=75

It turns out that 12 cm is the smallest length of wire that can be bent to form an

integer sided right angle triangle in exactly one way, but there are many more examples.

12 cm: (3,4,5)

24 cm: (6,8,10)

30 cm: (5,12,13)

36 cm: (9,12,15)

40 cm: (8,15,17)

48 cm: (12,16,20)

In contrast, some lengths of wire, like 20 cm, cannot be bent to form an integer sided

right angle triangle, and other lengths allow more than one solution to be found; for

example, using 120 cm it is possible to form exactly three different integer sided

right angle triangles.

120 cm: (30,40,50), (20,48,52), (24,45,51)

Given that L is the length of the wire, for how many values of L ≤ 1,500,000 can

exactly one integer sided right angle triangle be formed?

Solution: we generate all pythagorean triples using Euclid's formula and

keep track of the frequencies of the perimeters.

Reference: https://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple

"""

from collections import defaultdict

from math import gcd

from typing import DefaultDict

def solution(limit: int = 1500000) -> int:

"""

Return the number of values of L <= limit such that a wire of length L can be

formmed into an integer sided right angle triangle in exactly one way.

>>> solution(50)

>>> solution(1000)

112

>>> solution(50000)

5502

"""

frequencies: DefaultDict = defaultdict(int)

euclid_m = 2

while 2 * euclid_m * (euclid_m + 1) <= limit:

for euclid_n in range((euclid_m % 2) + 1, euclid_m, 2):

if gcd(euclid_m, euclid_n) > 1:

continue

primitive_perimeter = 2 * euclid_m * (euclid_m + euclid_n)

for perimeter in range(primitive_perimeter, limit + 1, primitive_perimeter):

frequencies[perimeter] += 1

euclid_m += 1

return sum(1 for frequency in frequencies.values() if frequency == 1)

if __name__ == "__main__":

print(f"{solution() = }")

Sunbelt Computer Software

PL/B Language Development and Support

Navigation Menu

Sunbelt Computer Software

PL/B Language Development and Support

FilesExpand file tree

sol1.py

Latest commit

History

sol1.py

File metadata and controls