31 lines
579 B
Python
31 lines
579 B
Python
import math
|
|
from functools import cache
|
|
|
|
|
|
def factorial(n: int) -> int:
|
|
"""
|
|
n! = 1 * 2 * 3 * 4 * ... * n
|
|
1, 1, 2, 6, 24, 120, 720, ...
|
|
"""
|
|
return math.factorial(n)
|
|
|
|
|
|
@cache
|
|
def fibonacci(n: int) -> int:
|
|
"""
|
|
F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1
|
|
0, 1, 1, 2, 3, 5, 8, 13, 21, ...
|
|
"""
|
|
if n < 2:
|
|
return n
|
|
|
|
return fibonacci(n - 1) + fibonacci(n - 2)
|
|
|
|
|
|
def triangular(n: int) -> int:
|
|
"""
|
|
a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n
|
|
0, 1, 3, 6, 10, 15, ...
|
|
"""
|
|
return int(n * (n + 1) / 2)
|