mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-22 11:10:14 +00:00
421ace81ed
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.0.285 → v0.0.286](https://github.com/astral-sh/ruff-pre-commit/compare/v0.0.285...v0.0.286) - [github.com/tox-dev/pyproject-fmt: 0.13.1 → 1.1.0](https://github.com/tox-dev/pyproject-fmt/compare/0.13.1...1.1.0) * updating DIRECTORY.md * Fis ruff rules PIE808,PLR1714 --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
42 lines
1.1 KiB
Python
42 lines
1.1 KiB
Python
# Eulers Totient function finds the number of relative primes of a number n from 1 to n
|
|
def totient(n: int) -> list:
|
|
"""
|
|
>>> n = 10
|
|
>>> totient_calculation = totient(n)
|
|
>>> for i in range(1, n):
|
|
... print(f"{i} has {totient_calculation[i]} relative primes.")
|
|
1 has 0 relative primes.
|
|
2 has 1 relative primes.
|
|
3 has 2 relative primes.
|
|
4 has 2 relative primes.
|
|
5 has 4 relative primes.
|
|
6 has 2 relative primes.
|
|
7 has 6 relative primes.
|
|
8 has 4 relative primes.
|
|
9 has 6 relative primes.
|
|
"""
|
|
is_prime = [True for i in range(n + 1)]
|
|
totients = [i - 1 for i in range(n + 1)]
|
|
primes = []
|
|
for i in range(2, n + 1):
|
|
if is_prime[i]:
|
|
primes.append(i)
|
|
for j in range(len(primes)):
|
|
if i * primes[j] >= n:
|
|
break
|
|
is_prime[i * primes[j]] = False
|
|
|
|
if i % primes[j] == 0:
|
|
totients[i * primes[j]] = totients[i] * primes[j]
|
|
break
|
|
|
|
totients[i * primes[j]] = totients[i] * (primes[j] - 1)
|
|
|
|
return totients
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|