mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
98e9d6bdb6
* Fix style of the first ten solutions for Project Euler - Unify the header docstring, and add reference URLs to wikipedia or similar - Fix docstrings to be properly multilined - Add newlines where appropriate - Add doctests where they were missing - Remove doctests that test for the correct solution - fix obvious spelling or grammar mistakes in comments and exception messages - Fix line endings to be UNIX. This makes two of the files seem to have changed completely - no functional changes in any of the solutions were done (except for the spelling fixes mentioned above) * Fix docstrings and main function as per Style Guide
76 lines
1.4 KiB
Python
76 lines
1.4 KiB
Python
"""
|
|
Project Euler Problem 5: https://projecteuler.net/problem=5
|
|
|
|
Smallest multiple
|
|
|
|
2520 is the smallest number that can be divided by each of the numbers
|
|
from 1 to 10 without any remainder.
|
|
|
|
What is the smallest positive number that is _evenly divisible_ by all
|
|
of the numbers from 1 to 20?
|
|
|
|
References:
|
|
- https://en.wiktionary.org/wiki/evenly_divisible
|
|
- https://en.wikipedia.org/wiki/Euclidean_algorithm
|
|
- https://en.wikipedia.org/wiki/Least_common_multiple
|
|
"""
|
|
|
|
|
|
def gcd(x: int, y: int) -> int:
|
|
"""
|
|
Euclidean GCD algorithm (Greatest Common Divisor)
|
|
|
|
>>> gcd(0, 0)
|
|
0
|
|
>>> gcd(23, 42)
|
|
1
|
|
>>> gcd(15, 33)
|
|
3
|
|
>>> gcd(12345, 67890)
|
|
15
|
|
"""
|
|
|
|
return x if y == 0 else gcd(y, x % y)
|
|
|
|
|
|
def lcm(x: int, y: int) -> int:
|
|
"""
|
|
Least Common Multiple.
|
|
|
|
Using the property that lcm(a, b) * gcd(a, b) = a*b
|
|
|
|
>>> lcm(3, 15)
|
|
15
|
|
>>> lcm(1, 27)
|
|
27
|
|
>>> lcm(13, 27)
|
|
351
|
|
>>> lcm(64, 48)
|
|
192
|
|
"""
|
|
|
|
return (x * y) // gcd(x, y)
|
|
|
|
|
|
def solution(n: int = 20) -> int:
|
|
"""
|
|
Returns the smallest positive number that is evenly divisible (divisible
|
|
with no remainder) by all of the numbers from 1 to n.
|
|
|
|
>>> solution(10)
|
|
2520
|
|
>>> solution(15)
|
|
360360
|
|
>>> solution(22)
|
|
232792560
|
|
"""
|
|
|
|
g = 1
|
|
for i in range(1, n + 1):
|
|
g = lcm(g, i)
|
|
return g
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|