mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 17:20:16 +00:00
46 lines
1.2 KiB
Python
46 lines
1.2 KiB
Python
|
# Eulers Totient function finds the number of relative primes of a number n from 1 to n
|
||
|
|
def totient(n: int) -> list:
|
||
|
|
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(0, 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
|
||
|
|
|
||
|
|
|
||
|
|
def test_totient() -> None:
|
||
|
|
"""
|
||
|
|
>>> 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.
|
||
|
|
"""
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
import doctest
|
||
|
|
|
||
|
|
doctest.testmod()
|