added tut07

Tutorium/tut07/src/tutorium_07.py

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