From d147717c39ebee8ea16ee2d9af7a0ac8aac6cfbb Mon Sep 17 00:00:00 2001
From: Nils Pukropp <nils@narl.io>
Date: Fri, 1 Dec 2023 08:35:08 +0100
Subject: [PATCH] added tut07

---
 Tutorium/tut07/README.md                      | 169 ++++++++++++++++++
 Tutorium/tut07/img/ws2022-notenverteilung.png | Bin 0 -> 11778 bytes
 Tutorium/tut07/img/ws2022-studienleistung.png | Bin 0 -> 10468 bytes
 .../src/solutions-exercise-06/mastermind.py   |  57 ++++++
 .../src/solutions-exercise-06/typevars.py     |  35 ++++
 Tutorium/tut07/src/trees.py                   |  36 ++++
 Tutorium/tut07/src/tutorium_07.py             |  55 ++++++
 7 files changed, 352 insertions(+)
 create mode 100644 Tutorium/tut07/img/ws2022-notenverteilung.png
 create mode 100644 Tutorium/tut07/img/ws2022-studienleistung.png
 create mode 100644 Tutorium/tut07/src/solutions-exercise-06/mastermind.py
 create mode 100644 Tutorium/tut07/src/solutions-exercise-06/typevars.py
 create mode 100644 Tutorium/tut07/src/trees.py
 create mode 100644 Tutorium/tut07/src/tutorium_07.py

diff --git a/Tutorium/tut07/README.md b/Tutorium/tut07/README.md
index e69de29..33ce71c 100644
--- a/Tutorium/tut07/README.md
+++ b/Tutorium/tut07/README.md
@@ -0,0 +1,169 @@
+# Tutorium 07 - 01.12.2023
+
+## Execrise 06
+
+- Korrektur wieder am Samstag
+
+### Problematik ChatGPT und Plagiate
+
+- ChatGPT ist ein tolles Tool, warum?
+    - Manchmal liefert es andere Lösungen zu Problemen
+    - Grundverständnis bei neuen Problemen
+    - integriert in die IDE (z.B. Github Copilot):
+        - schneller Code schreiben
+            <details>
+            <summary>Wie viele Zeilen Code schreibt ein Entwickler durchschnittlich am Tag?</summary>
+            10 bis 50 Codezeilen
+            </details>
+        - Leichtsinnsfehler ausbessern
+    - Kurz: Es nimmt einen repetetive Arbeit ab
+
+#### Die Problematik?
+
+- Ein EidP soll das Grundverständnis von Programmieren vermittelt werden
+    - Denkweise
+    - Konzepte in der theoretischen Informatik
+    - Konzepte in Programmiersprachen
+    - Übung
+- Um ChatGPT sinnvoll zu nutzen müsst ihr diese Grundverständnis bereits besitzen
+- Auch Studierende mit Vorwissen profitieren davon die Übung sinnvoll zu bearbeiten
+    - Wenn Ihr für die Aufgaben ChatGPT verwendet, dann habt ihr nicht genug Vorwissen
+
+<details>
+<summary>Studienleistung WS2022</summary>
+<img src="./img/ws2022-studienleistung.png" width=833 height=auto>
+</details>
+<details>
+<summary>Notenverteilung WS2022</summary>
+<img src="./img/ws2022-notenverteilung.png" width=833 height=auto>
+</details>
+
+
+#### Also, macht eure Aufgaben selber!
+
+----
+
+## Wichtiges/Hilfreiches für Exercise-07
+
+### Rekursion
+
+- Rekursion in Python sind Funktionen die sich selbst aufrufen
+    ```python
+    def fac(n: int) -> int:
+        if n <= 1: # Abbruchbedingung, kein Rekursiver Aufruf mehr!
+            return 1
+        return n * fac(n - 1) # Rekursiver Aufruf
+    ```
+- Eine Rekursion braucht eine **Abbruchbedingung**
+- primitive Rekursionen können auch einfach iterative gelöst werden
+    ```python
+    def fac2(n: int) -> int:
+        fac = 1
+        for i in range(1, n + 1):
+            fac *= i
+        return fac
+    ```
+- Eine Rekursion kann mehrere Rekursionspfade haben! (Kaskadenförmige Rekursion), welche auch primitiv berechenbar sind!
+    ```python
+    def fib(n: int) -> int:
+        if n in {0, 1}: # Abbruchbedingung
+            return n
+        return fib(n - 1) + fib(n - 2) # mehrere Rekursionsaufrufe
+    ```
+- Wie Funktioniert das?
+    -  Es wird ein Rekursionsbaum aufgebaut
+    -  Wenn dieser Fertig ist wird berechnet
+    -  Z.b. `fac`:
+        ```
+        fac(5) 
+        5 * fac(4) 
+        5 * 4 * fac(3) 
+        5 * 4 * 3 * fac(2)
+        5 * 4 * 3 * 2 * fac(1)
+        5 * 4 * 3 * 2 * 1
+        120
+        ```
+
+        ```
+        fib(4)
+        fib(3)                          + fib(2)
+        (fib(2)             + fib(1))   + (fib(0) + fib(1))
+        ((fib(0) + fib(1))  + fib(1))   + (fib(0) + fib(1))
+        ((0 + 1)            + 1)        + (0 + 1)
+        3
+        ```
+- Gibt es Rekursionen die nicht iterative berechenbar sind?
+    - $\mu$-Rekursionen oder partiell Rekursionen
+    - erste partiell rekursive Funktion von Wilhelm Ackermann 1926, die "Ackermannfunktion"
+        $\alpha(0, m) = m + 1$
+        $\alpha(n, 0) = \alpha(n - 1, 1)$
+        $\alpha(n, m) = \alpha(n, \alpha(n, m - 1))$
+
+        ```python
+        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))
+        ```
+
+#### Tipp:
+
+Man kann alles rekursiv Aufbauen mit Operatoren (`+, -, *, /, %, //, &&, and, ...`), also auch Listen oder Strings
+
+```python
+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}: # Abbruchbedingung
+        return str(n)
+    return f"({fib_str(n - 1)} + {fib_str(n - 2)})" # Rekursion
+```
+
+### Rekursion in Bäumen
+
+- Drei möglichkeiten einen Baum *abzulaufen*
+    - **Pre-Order**: Knoten, links, rechts
+        ```python
+        def preorder[T](tree: BTree[T]):
+            match tree:
+                case Node(value, left, right):
+                    print(value)
+                    preorder(left)
+                    preorder(right)
+                case _:
+                    return
+        ```
+    - **Post-Order**: links, rechts, Knoten
+        ```python
+        def postorder[T](tree: BTree[T]):
+            match tree:
+                case Node(value, left, right):
+                    postorder(left)
+                    postorder(right)
+                    print(value)
+                case _:
+                    return
+        ```
+    - **In-Order**: links, Knoten, rechts
+        ```python
+        def inorder[T](tree: BTree[T]):
+            match tree:
+                case Node(value, left, right):
+                    inorder(left)
+                    print(value)
+                    inorder(right)
+                case _:
+                    return
+        ```
\ No newline at end of file
diff --git a/Tutorium/tut07/img/ws2022-notenverteilung.png b/Tutorium/tut07/img/ws2022-notenverteilung.png
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diff --git a/Tutorium/tut07/src/solutions-exercise-06/mastermind.py b/Tutorium/tut07/src/solutions-exercise-06/mastermind.py
new file mode 100644
index 0000000..7d8dbf6
--- /dev/null
+++ b/Tutorium/tut07/src/solutions-exercise-06/mastermind.py
@@ -0,0 +1,57 @@
+import random
+
+
+def remove_char(string: str, c: str) -> str:
+    for i, s in enumerate(string):
+        if s == c:
+            return string[:i] + string[i + 1:]
+    return string
+
+
+def perfect_chars(inp: str, sol: str) -> str:
+    chars = ""
+    for c, s in zip(inp, sol):
+        if c == s:
+            chars = chars + c
+    return chars
+
+
+def correct_chars(inp: str, sol: str) -> str:
+    res = ""
+    for c in inp:
+        if c in sol:
+            res += c
+            sol = remove_char(sol, c)
+    return res
+
+
+def compare(inp: str, sol: str) -> tuple[int, int]:
+    perfect = len(perfect_chars(inp, sol))
+    correct = len(correct_chars(inp, sol))
+    return perfect, correct - perfect
+
+
+def compare_alt(inp: str, sol: str) -> tuple[int, int]:
+    perfect = perfect_chars(inp, sol)
+    for c in perfect:
+        sol = remove_char(sol, c)
+        inp = remove_char(inp, c)
+    correct = correct_chars(inp, sol)
+    return len(perfect), len(correct)
+
+
+def game(length: int, symbols: str):
+    solution = "".join(random.choices(symbols, k=length))
+    print("Länge:", length, "Zeichen:", symbols)
+    result = (0, 0)
+    while result != (length, 0):
+        c = input()
+        if len(c) != length:
+            print("Try again!")
+            continue
+        result = compare(c, solution)
+        print("Antwort:", result[0] * "X" + result[1] * "-")
+
+
+if __name__ == '__main__':
+    game(5, "ABCDE")
diff --git a/Tutorium/tut07/src/solutions-exercise-06/typevars.py b/Tutorium/tut07/src/solutions-exercise-06/typevars.py
new file mode 100644
index 0000000..2c79ae1
--- /dev/null
+++ b/Tutorium/tut07/src/solutions-exercise-06/typevars.py
@@ -0,0 +1,35 @@
+from typing import Optional
+
+
+def head[T](xs: list[T]) -> Optional[T]:
+    if not xs:
+        return None
+    return xs[0]
+
+
+def tail[T](xs: list[T]) -> Optional[list[T]]:
+    if not xs:
+        return None
+    return xs[1:]
+
+
+def concat[T](xss: list[list[T]]) -> list[T]:
+    outer = list()
+    for xs in xss:
+        outer += xs
+    return outer
+
+
+def zip[T, U](xs: list[T], ys: list[U]) -> list[tuple[T, U]]:
+    out = list()
+    for i, x in enumerate(xs):
+        if i >= len(ys):
+            return out
+        else:
+            out += [(x, ys[i])]
+    return out
+
+
+def assoc[T, U, V](t: tuple[tuple[T, U], V]) -> tuple[T, tuple[U, V]]:
+    (x, y), z = t
+    return (x, (y, z))
diff --git a/Tutorium/tut07/src/trees.py b/Tutorium/tut07/src/trees.py
new file mode 100644
index 0000000..fcc4c52
--- /dev/null
+++ b/Tutorium/tut07/src/trees.py
@@ -0,0 +1,36 @@
+@dataclass
+class Node[T]:
+    value: T
+    left: Optional['Node[T]'] = None
+    right: Optional['Node[T]'] = None
+    
+type BTree[T] = Node[T] | None
+
+def preorder[T](tree: BTree[T]):
+    match tree:
+        case Node(value, left, right):
+            print(value)
+            preorder(left)
+            preorder(right)
+        case _:
+            return
+        
+        
+def postorder[T](tree: BTree[T]):
+    match tree:
+        case Node(value, left, right):
+            postorder(left)
+            postorder(right)
+            print(value)
+        case _:
+            return
+        
+        
+def inorder[T](tree: BTree[T]):
+    match tree:
+        case Node(value, left, right):
+            inorder(left)
+            print(value)
+            inorder(right)
+        case _:
+            return
\ No newline at end of file
diff --git a/Tutorium/tut07/src/tutorium_07.py b/Tutorium/tut07/src/tutorium_07.py
new file mode 100644
index 0000000..71356f0
--- /dev/null
+++ b/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"