algorithms.py

def fibonacci(n: int) -> int:
    # The n:th Fibonacci number F(n) with the value of n provided by the user.
    # https://en.wikipedia.org/wiki/Fibonacci_number
    # https://en.wikipedia.org/wiki/Fibonacci_number#Sequence_properties
    match n:
        case n if not isinstance(n, int):
            raise TypeError(f"n must be an int, not {type(n).__name__}")
        case n if 1 >= n >= 0:
            # F(0) = 0, F(1) = 1
            return n
        case n if n > 1:
            # F(n) = F(n-1) + F(n-2)
            return fibonacci(n - 1) + fibonacci(n - 2)
        case n if n < 0:
            # F(-n) = (-1)^(n+1)F(n)
            return int((-1) ** (n + 1) * fibonacci(-n))


def ackermann(m: int, n: int) -> int:
    # The Ackermann function A(m,n) with values of m and n provided by the user.
    # The factorial n! of a non-negative integer n provided by the user.
    # https://en.wikipedia.org/wiki/Ackermann_function
    match (m, n):
        case (m, _) if not isinstance(m, int):
            raise TypeError(f"m must be an int, not {type(m).__name__}")
        case (_, n) if not isinstance(n, int):
            raise TypeError(f"n must be an int, not {type(n).__name__}")
        case (m, _) if m < 0:
            raise ValueError(f"m must be a non-negative number, got {m!r}")
        case (_, n) if n < 0:
            raise ValueError(f"n must be a non-negative number, got {n!r}")
        case (0, n):
            # A(0, n) = n + 1
            return n + 1
        case (m, 0) if m > 0:
            # A(m,0) = A(m - 1,1)
            return ackermann(m - 1, 1)
        case (m, n) if m > 0 and n > 0:
            # A(m,n) = A(m - 1,A(m, n - 1)
            return ackermann(m - 1, ackermann(m, n - 1))


def factorial(n: int) -> int:
    # The factorial n! of a non-negative integer n provided by the user.
    # https://en.wikipedia.org/wiki/Factorial
    match n:
        case n if not isinstance(n, int):
            raise TypeError(f"n must be an int, not {type(n).__name__}")
        case n if n < 0:
            raise ValueError(f"n must be a non-negative number, got {n!r}")
        case 0:
            # F(0) = 1
            return 1
        case n:
            # F(n) = n * f(n-1) * f(n-2) ...
            return n * factorial(n - 1)