56 lines
1.6 KiB
Python
56 lines
1.6 KiB
Python
def fibonacci(n: int) -> int:
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if n in {0, 1}: # Abbruchbedingung
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return n
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return fibonacci(n - 1) + fibonacci(n - 2) # mehrere Rekursionsaufrufe
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def fac(n: int) -> int:
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if n <= 0: # Abbruchbedingung, kein Rekursiver Aufruf mehr!
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return 1
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return n * fac(n - 1) # Rekursiver Aufruf
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def fac2(n: int) -> int:
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num = 1
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for i in range(1, n + 1):
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num *= i
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return num
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def ack(n: int, m: int) -> int:
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match (n, m):
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case (0, _):
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return m + 1
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case (_, 0):
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return ack(n - 1, 1)
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case _:
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return ack(n - 1, ack(n, m - 1))
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def all_fac(max: int) -> list[tuple[int, int]]:
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if max == 0: # Abbruchbedingung
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return [(0, 1)]
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return [(max, fac(max))] + all_fac(max - 1) # Rekursion
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def all_fac_str(min: int, max: int) -> str:
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if min >= max: # Abbruchbedingung
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return f"{fac(min)}"
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return f"{fac(min)} " + all_fac_str(min + 1, max) # Rekursion
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def fib_str(n: int) -> str:
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if n in {0, 1}:
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return str(n)
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return f"({fib_str(n - 1)} + {fib_str(n - 2)})"
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if __name__ == "__main__":
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assert [fibonacci(n) for n in range(15)] == [0, 1, 1, 2,
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3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]
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assert [fac(n) for n in range(11)] == [1, 1, 2, 6, 24,
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120, 720, 5040, 40320, 362880, 3628800]
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assert [fac(n) for n in range(10)] == [fac2(n) for n in range(10)]
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assert list(reversed(all_fac(10))) == [(n, fac(n)) for n in range(11)]
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assert all_fac_str(0, 10) == "1 1 2 6 24 120 720 5040 40320 362880 3628800"
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