Init

2026-03-27 17:19:51 +01:00 · 2026-03-27 17:19:51 +01:00 · 4f5a78ac05
commit 4f5a78ac05
55 changed files with 14110 additions and 0 deletions
--- a/data/elektro.txt
+++ b/data/elektro.txt
@ -0,0 +1,8 @@
+"Höhleneingang";"Ost/West-Passage";5
+"Höhleneingang";"Nord/Süd-Passage";3
+"Nord/Süd-Passage";"Nebelraum";7
+"Steiniger Pfad";"Ost/West-Passage";2
+"Ost/West-Passage";"Schwefelgewölbe";4
+"Schwefelgewölbe";"Steiniger Pfad";1
+"Schatzkammer";"Nebelraum";2
+"Steiniger Pfad";"Schatzkammer";6
--- a/data/hoehle.txt
+++ b/data/hoehle.txt
@ -0,0 +1,8 @@
+"Höhleneingang" <> "Ost/West-Passage"
+"Höhleneingang" <> "Nord/Süd-Passage"
+"Nord/Süd-Passage" <> "Nebelraum"
+"Steiniger Pfad" > "Ost/West-Passage"
+"Ost/West-Passage" <> "Schwefelgewölbe"
+"Schwefelgewölbe" > "Steiniger Pfad"
+"Schatzkammer" > "Nebelraum"
+"Steiniger Pfad" > "Schatzkammer"
--- a/data/labyrinth.txt
+++ b/data/labyrinth.txt
@ -0,0 +1,9 @@
+xxxxxxxxxxxxxxxxxxxxx
+x                   x
+x        S          x
+x                   x
+x      xxxxxxxx     x
+x                   x
+x                   x
+x            A      x
+xxxxxxxxxxxxxxxxxxxxx
--- a/data/labyrinth1.txt
+++ b/data/labyrinth1.txt
@ -0,0 +1,5 @@
+xxxxxAxxxxxxxxx
+x           xSx
+xxxxxxxxxx xx x
+x             x
+xxxxxxxxxxxxxxx
--- a/data/seq0.txt
+++ b/data/seq0.txt
@ -0,0 +1,14 @@
+-59
+52
+46
+14
+-50
+58
+-87
+-77
+34
+15
+50
+47
+51
+48
--- a/data/seq1.txt
+++ b/data/seq1.txt
@ -0,0 +1,100 @@
+56
+13
+97
+14
+5
+40
+33
+20
+51
+98
+52
+89
+31
+33
+47
+59
+47
+75
+11
+39
+0
+79
+33
+57
+5
+1
+28
+87
+77
+54
+35
+21
+24
+97
+96
+94
+6
+31
+-45
+53
+-98
+-44
+85
+-76
+-48
+-90
+-99
+47
+-11
+16
+-98
+98
+-23
+57
+27
+-35
+23
+65
+-54
+96
+71
+99
+81
+30
+-7
+76
+-22
+43
+62
+-49
+73
+59
+75
+36
+39
+15
+51
+-51
+63
+69
+1
+1
+-25
+-18
+88
+86
+93
+33
+71
+-95
+56
+2
+4
+11
+-55
+28
+60
+-55
+-69
+-97
--- a/data/seq2.txt
+++ b/data/seq2.txt
--- a/data/seq3.txt
+++ b/data/seq3.txt
--- a/requirements.txt
+++ b/requirements.txt
@ -0,0 +1,4 @@
+matplotlib
+numpy
+pygame
+graphviz
--- a/utils/init.py
+++ b/utils/init.py
--- a/utils/constants.py
+++ b/utils/constants.py
@ -0,0 +1,5 @@
+from utils.literal import Literal
+
+MAX_VALUE = Literal(99999999999999999999)
+MIN_VALUE = Literal(-99999999999999999999)
+
--- a/utils/game.py
+++ b/utils/game.py
@ -0,0 +1,53 @@
+import pygame
+
+class Game:
+
+    def __init__(self, title, fps=60, size=(640, 400)):
+        self.title = title
+        self.fps = fps
+        self.size = size
+        self.clock = pygame.time.Clock()
+        self.dt = 0
+        self.screen = None
+
+    def init_game(self):
+        pygame.init()
+        pygame.display.set_caption(self.title)
+        self.screen = pygame.display.set_mode(self.size)
+
+
+    def game_loop(self):
+        while True:
+            # Berechnung der Zeitdifferenz seit dem letzten Frame
+            self.dt = self.clock.tick(self.fps) / 1000
+            if self.event_handling() == False:
+                break
+            if self.update_game() == False:
+                break
+            self.draw_game()
+
+    def exit_game(self):
+        pygame.quit()
+
+    def event_handling(self):  # bleibt in der Unterklasse unverändert
+        for event in pygame.event.get():
+            if not self.handle_event(event):
+                return False
+        return True
+
+    def handle_event(self, event):  # wird in der Unterklasse überschrieben
+        if event.type == pygame.QUIT:
+            return False
+        return True
+
+    def update_game(self):
+        return True
+
+    def draw_game(self):
+        pygame.display.flip()
+
+    def run(self):
+        self.init_game()
+        self.game_loop()
+        self.exit_game()
+
--- a/utils/literal.py
+++ b/utils/literal.py
@ -0,0 +1,103 @@
+
+class Literal:
+    def __init__(self, value):
+        """Initialisiert Literal."""
+        if isinstance(value, Literal):
+            self.value = value.value
+        else:
+            self.value = value
+        self.read_count = 0
+        self.compare_count = 0
+
+    def reset_counters(self):
+        """Setzt alle Zähler auf 0 zurück."""
+        self.read_count = 0
+        self.compare_count = 0
+
+    def get(self):
+        """Liest den Wert aus."""
+        self.read_count += 1
+        return self.value
+
+    def __eq__(self, other):
+        """Vergleicht den Wert mit einem anderen Wert."""
+        if other is None:
+            return False
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value == other.value
+
+    def __ne__(self, other):
+        """Vergleicht den Wert der Speicherzelle mit einem anderen Wert."""
+        if other is None:
+            return True
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value != other.value
+
+    def __lt__(self, other):
+        """Vergleicht den Wert der Speicherzelle mit einem anderen Wert."""
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value < other.value
+
+    def __le__(self, other):
+        """Vergleicht den Wert der Speicherzelle mit einem anderen Wert."""
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value <= other.value
+
+    def __gt__(self, other):
+        """Vergleicht den Wert der Speicherzelle mit einem anderen Wert."""
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value > other.value
+
+    def __ge__(self, other):
+        """Vergleicht den Wert der Speicherzelle mit einem anderen Wert."""
+        assert isinstance(other, Literal), "Can only compare with Literal or MemoryCell"
+        self.compare_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return self.value >= other.value
+
+    def __str__(self):
+        """Repräsentation des Werts."""
+        return f"{self.value}"
+
+    def __repr__(self):
+        """Repräsentation des Werts für Debugging-Zwecke."""
+        return f"Literal(value={self.value}, reads={self.read_count})"
+
+    def get_read_count(self):
+        """Gibt zurück, wie oft der Wert gelesen wurde."""
+        return self.read_count
+
+    def __int__(self):
+        """Gibt den Wert als Integer zurück."""
+        self.read_count += 1
+        return int(self.value)
+
+    def succ(self):
+        return Literal(self.value+1)
+
+    def pred(self):
+        return Literal(self.value-1)
+
+
+if __name__ == "__main__":
+    l1 = Literal(5)
+    l2 = Literal(3)
+    print(l1 == l2)
+    print(l1 > l2)
+
--- a/utils/memory_array.py
+++ b/utils/memory_array.py
@ -0,0 +1,126 @@
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.project_dir import get_path
+from random import randint
+
+class MemoryArray:
+
+    def __init__(self, parm):
+        if isinstance(parm, Literal):
+            self.init_with_size(parm)
+        elif isinstance(parm, list):
+            self.size = len(parm)
+            self.cells = [MemoryCell(value) for value in parm]
+        else:
+            raise ValueError("Invalid parameter type")
+
+    def init_with_size(self, size):
+        """Initialisiert ein Speicherarray mit einer bestimmten Größe."""
+        assert isinstance(size, Literal), "Size must be a Literal or MemoryCell"
+        assert isinstance(size.value, int), "Size must be an int"
+        assert size.value > 0, "Size must be positive"
+        self.size = size.value
+        self.cells = [MemoryCell() for _ in range(self.size)]
+
+    def __getitem__(self, index):
+        """Gibt den Wert einer Speicherzelle zurück."""
+        assert isinstance(index, Literal), "Index must be a Literal or MemoryCell"
+        assert isinstance(index.value, int), "Index value must be an int"
+        assert 0 <= index.value < self.size, "Index out of bounds"
+        return self.cells[index.value]
+
+    def __setitem__(self, index, value):
+        """Setzt den Wert einer Speicherzelle."""
+        assert isinstance(index, Literal), "Index must be a Literal or MemoryCell"
+        assert isinstance(index.value, int), "Index value must be an int"
+        assert 0 <= index.value < self.size, "Index out of bounds"
+        assert isinstance(value, Literal), "Value must be a Literal or MemoryCell"
+        self.cells[index.value].set(value.value)
+
+    def __len__(self):
+        """Gibt die Größe des Speicherarrays zurück."""
+        return self.size
+
+    def __str__(self):
+        """Gibt eine Liste der Speicherzellen zurück."""
+        return str([cell.value for cell in self.cells])
+
+    def __iter__(self):
+        """Gibt einen Iterator über die Speicherzellen zurück."""
+        return iter(self.cells)
+
+    def indices(self):
+        """Gibt eine Liste der Indizes der Speicherzellen zurück."""
+        return [Literal(i) for i in range(self.size)]
+
+    def length(self):
+        """Gibt die Größe des Speicherarrays zurück."""
+        return Literal(self.size)
+
+    def count_compares(self):
+        return sum([cell.compare_count for cell in self.cells])
+
+
+    def reset_counters(self):
+        """Setzt alle Zähler auf 0 zurück."""
+        for cell in self.cells:
+            cell.reset_counters()
+
+    @staticmethod
+    def create_random_array(count, min_value, max_value):
+        """Erzeugt ein zufälliges Speicherarray."""
+        size = Literal(count)
+        a = MemoryArray(size)
+        for i in a.indices():
+            a[i] = Literal(randint(min_value, max_value))
+        a.reset_counters()
+        return a
+
+    @staticmethod
+    def create_sorted_array(count):
+        """Erzeugt ein sortiertes Speicherarray."""
+        a = MemoryArray(list(range(count)))
+        a.reset_counters()
+        return a
+
+
+    @staticmethod
+    def create_array_from_file(filename, limit=None):
+        """Erzeugt ein Speicherarray aus einer Datei."""
+        filename = get_path(filename)
+        with open(filename) as f:
+            lines = f.readlines()
+        if limit is not None:
+            lines = lines[:limit]
+        size = Literal(len(lines))
+        a = MemoryArray(size)
+        for i, line in enumerate(lines):
+            a[Literal(i)] = Literal(int(line))
+        a.reset_counters()
+        return a
+
+    def __str__(self):
+        result = "[ "
+        for cell in self.cells:
+            result += str(cell) + ", "
+        result += "]"
+        return result
+
+
+if __name__ == "__main__":
+    import random
+    size = Literal(5)
+    a = MemoryArray(size)
+    for i in a.indices():
+        a[i] = Literal(random.randint(1,100))
+    print(a)
+    s = MemoryCell(0)
+    for cell in a.cells:
+        s += cell
+    print(s)
+    print(f"Anzahl der Additionen: {MemoryManager.count_adds()}")
+
+    a = MemoryArray.create_array_from_file("data/seq0.txt")
+    print(a)
+
--- a/utils/memory_cell.py
+++ b/utils/memory_cell.py
@ -0,0 +1,194 @@
+from utils.memory_manager import MemoryManager
+from utils.literal import Literal
+
+class MemoryCell (Literal):
+
+    def __new__(cls, *args, **kwargs):
+        """Erstellt eine neue Instanz von MemoryCell."""
+        instance = MemoryManager().acquire_cell()
+        if instance is None:
+            instance = super().__new__(cls)
+            MemoryManager().register_cell(instance)
+        return instance
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        MemoryManager().release_cell(self)
+
+    def __init__(self, value=None):
+        """Initialisiert eine Speicherzelle mit optionalem Startwert."""
+        super().__init__(value)
+        self.write_count = 0
+        self.add_count = 0
+        self.sub_count = 0
+        self.mul_count = 0
+        self.div_count = 0
+        self.bitop_count = 0
+        if value is not None:
+            self.write_count +=1
+        else:
+            self.value = 0
+
+    def reset_counters(self):
+        """Setzt alle Zähler auf 0 zurück."""
+        super().reset_counters()
+        self.write_count = 0
+        self.add_count = 0
+        self.sub_count = 0
+        self.mul_count = 0
+        self.div_count = 0
+        self.bitop_count = 0
+
+    def set(self, new_value):
+        """Schreibt einen neuen Wert in die Speicherzelle und erhöht den Schreibzähler."""
+        self.write_count += 1
+        if isinstance(new_value, Literal):
+            self.value = new_value.value
+        else:
+            self.value = new_value
+
+    def add(self, other):
+        """Addiert den Wert der Speicherzelle mit einem anderen Wert."""
+        self.set((self + other).value)
+
+    def sub(self, other):
+        """Subtrahiert den Wert der Speicherzelle mit einem anderen Wert."""
+        self.set((self - other).value)
+
+    def mul(self, other):
+        """Multipliziert den Wert der Speicherzelle mit einem anderen Wert."""
+        self.set((self * other).value)
+
+    def div(self, other):
+        """Dividiert den Wert der Speicherzelle durch einen anderen Wert."""
+        self.set((self // other).value)
+
+    def modulo(self, other):
+        """Berechnet den Modulo des Wertes der Speicherzelle durch einen anderen Wert."""
+        self.set((self % other).value)
+
+    def lshift(self, other):
+        """Verschiebt den Wert der Speicherzelle um eine bestimmte Anzahl von Bits nach links."""
+        assert isinstance(other, Literal), "Can only lshift Literal or MemoryCell by MemoryCell"
+        self.bitop_count += 1
+        self.read_count += 1
+        self.write_count += 1
+        other.read_count += 1
+        self.value <<= other.value
+
+    def rshift(self, other):
+        """Verschiebt den Wert der Speicherzelle um eine bestimmte Anzahl von Bits nach rechts."""
+        assert isinstance(other, Literal), "Can only rshift Literal or MemoryCell by MemoryCell"
+        self.bitop_count += 1
+        self.read_count += 1
+        self.write_count += 1
+        other.read_count += 1
+        self.value >>= other.value
+
+    def and_op(self, other):
+        """Führt ein Bitweise AND auf den Wert der Speicherzelle mit einem anderen Wert aus."""
+        assert isinstance(other, Literal), "Can only and Literal or MemoryCell with MemoryCell"
+        self.bitop_count += 1
+        self.read_count += 1
+        self.write_count += 1
+        other.read_count += 1
+        self.value &= other.value
+
+    def or_op(self, other):
+        """Führt ein Bitweise OR auf den Wert der Speicherzelle mit einem anderen Wert aus."""
+        assert isinstance(other, Literal), "Can only or Literal or MemoryCell with MemoryCell"
+        self.bitop_count += 1
+        self.read_count += 1
+        self.write_count += 1
+        other.read_count += 1
+        self.value |= other.value
+
+    def xor_op(self, other):
+        """Führt ein Bitweise XOR auf den Wert der Speicherzelle mit einem anderen Wert aus."""
+        assert isinstance(other, Literal), "Can only xor Literal or MemoryCell with MemoryCell"
+        self.bitop_count += 1
+        self.read_count += 1
+        self.write_count += 1
+        other.read_count += 1
+        self.value ^= other.value
+
+    def get_write_count(self):
+        """Gibt zurück, wie oft der Wert geschrieben wurde."""
+        return self.write_count
+
+    def __repr__(self):
+        """Repräsentation der Speicherzelle für Debugging-Zwecke."""
+        return f"MemoryCell(value={self.value}, reads={self.read_count}, writes={self.write_count})"
+
+    def __add__(self, other):
+        assert isinstance(other, Literal), "Can only add Literal or MemoryCell to MemoryCell"
+        self.add_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value + other.value)
+
+    def __sub__(self, other):
+        assert isinstance(other, Literal), "Can only add Literal or MemoryCell to MemoryCell"
+        self.sub_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value - other.value)
+
+    def __mul__(self, other):
+        assert isinstance(other, Literal), "Can only mul Literal or MemoryCell with MemoryCell"
+        self.mul_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value * other.value)
+
+    def __truediv__(self, other):
+        assert isinstance(other, Literal), "Can only div Literal or MemoryCell by MemoryCell"
+        self.div_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value / other.value)
+
+    def __floordiv__(self, other):
+        assert isinstance(other, Literal), "Can only div Literal or MemoryCell by MemoryCell"
+        self.div_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value // other.value)
+
+    def __mod__(self, other):
+        assert isinstance(other, Literal), "Can only div Literal or MemoryCell by MemoryCell"
+        self.div_count += 1
+        self.read_count += 1
+        other.read_count += 1
+        return Literal(self.value % other.value)
+
+    def __iadd__(self, other):
+        self.add(other)
+        return self
+
+    def __isub__(self, other):
+        self.sub(other)
+        return self
+
+    def __imul__(self, other):
+        self.mul(other)
+        return self
+
+    def __itruediv__(self, other):
+        self.set(self // other)
+        return self
+
+    def __ifloordiv__(self, other):
+        self.div(other)
+        return self
+
+
+if __name__ == "__main__":
+    a = MemoryCell(5)
+    b = MemoryCell(3)
+    a += b
+    print(f"Ergebnis: {a}")
+    print(f"a wurde {a.get_read_count()} mal gelesen und {a.get_write_count()} mal geschrieben.")
+    print(f"b wurde {b.get_read_count()} mal gelesen und {b.get_write_count()} mal geschrieben.")
--- a/utils/memory_manager.py
+++ b/utils/memory_manager.py
@ -0,0 +1,148 @@
+import matplotlib.pyplot as plt
+import queue
+
+
+class MemoryManager:
+
+    _instance = None
+    stats = {}
+
+    def __new__(cls, *args, **kwargs):
+        """Erstellt eine einzige Instanz von MemoryManager."""
+        if cls._instance is None:
+            cls._instance = super().__new__(cls)
+            cls._instance._initialize()  # Eigene Init-Methode, damit __init__ nicht mehrfach läuft
+        return cls._instance
+
+    def _initialize(self):
+        """Initialisiert die Speicherverwaltung (einmalig)."""
+        self.cells = []
+        self._pool = queue.Queue()
+        self._finalizers = {}
+
+
+    @staticmethod
+    def count_cells():
+        return len(MemoryManager().cells)
+
+
+    @staticmethod
+    def count_reads():
+        return sum([cell.read_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_writes():
+        return sum([cell.write_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_compares():
+        return sum([cell.compare_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_adds():
+        return sum([cell.add_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_subs():
+        return sum([cell.sub_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_muls():
+        return sum([cell.mul_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_divs():
+        return sum([cell.div_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def count_bitops():
+        return sum([cell.bitop_count for cell in MemoryManager().cells])
+
+    @staticmethod
+    def reset():
+        manager = MemoryManager()
+        for cell in manager.cells:
+            cell.reset_counters()
+
+    @staticmethod
+    def purge():
+        MemoryManager._instance = None
+
+    @staticmethod
+    def save_stats(count):
+        data = {    "cells": MemoryManager.count_cells(),
+                    "reads": MemoryManager.count_reads(),
+                    "writes": MemoryManager.count_writes(),
+                    "compares": MemoryManager.count_compares(),
+                    "adds": MemoryManager.count_adds(),
+                    "subs": MemoryManager.count_subs(),
+                    "muls": MemoryManager.count_muls(),
+                    "divs": MemoryManager.count_divs(),
+                    "bitops": MemoryManager.count_bitops()  }
+        MemoryManager.stats[count] = data
+
+    @staticmethod
+    def plot_stats(labels):
+        data = MemoryManager.stats
+        x = list(data.keys())
+
+        fig, axes = plt.subplots(len(labels), 1, figsize=(8, 4 * len(labels)), sharex=True)
+
+        if len(labels) == 1:
+            axes = [axes]  # Falls nur ein Plot vorhanden ist, in eine Liste umwandeln
+
+        for ax, l in zip(axes, labels):
+            y = [data[k][l] for k in x]
+            ax.plot(x, y, label=l)
+            ax.set_ylabel(l)
+            ax.legend()
+
+        plt.xlabel("n")
+        plt.show()
+
+
+    def acquire_cell(self):
+        try:
+            return self._pool.get_nowait()
+        except queue.Empty:
+            return None
+
+    def register_cell(self, cell):
+        self.cells.append(cell)
+
+    def release_cell(self, cell):
+        self._pool.put(cell)
+
+
+class Testcell:
+
+    def __new__(cls, *args, **kwargs):
+        instance = MemoryManager().acquire_cell()
+        if instance is None:
+            instance = super().__new__(cls)
+            MemoryManager().register_cell(instance)
+        return instance
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_val, exc_tb):
+        MemoryManager().release_cell(self)
+
+
+if __name__ == "__main__":
+
+    # Einfaches Anlegen einer Zelle
+    a = Testcell()
+    print(MemoryManager.count_cells())
+
+    # Anlegen einer Zelle und Beenden des Scopes
+    with Testcell() as b:
+        print(MemoryManager.count_cells())
+
+    print(MemoryManager.count_cells())
+
+    # Reuse einer Zelle
+    c = Testcell()
+    print(MemoryManager.count_cells())
+
--- a/utils/memory_range.py
+++ b/utils/memory_range.py
@ -0,0 +1,29 @@
+from utils.literal import Literal
+
+# a generator that yields items instead of returning a list
+def mrange(parm1, parm2=None, parm3=None):
+    if parm2 is None:
+        start = 0
+        stop = int(parm1)
+        step = 1
+    elif parm3 is None:
+        start = int(parm1)
+        stop = int(parm2)
+        step = 1
+    else:
+        start = int(parm1)
+        stop = int(parm2)
+        step = int(parm3)
+    num = start
+    if step > 0:
+        while num < stop:
+            yield Literal(num)
+            num += step
+    else:
+        while num > stop:
+            yield Literal(num)
+            num += step
+
+if __name__ == "__main__":
+    for l in mrange(10):
+        print(l)
--- a/utils/priority_queue.py
+++ b/utils/priority_queue.py
@ -0,0 +1,40 @@
+import heapq
+
+class PriorityQueue:
+    def __init__(self):
+        self.heap = []
+        self.entry_finder = {}  # map: item -> [priority, item]
+        self.REMOVED = '<removed>'
+        self.counter = 0  # unique sequence count to break ties
+
+    def add_or_update(self, item, priority):
+        if item in self.entry_finder:
+            self.remove(item)
+        count = self.counter
+        entry = [priority, count, item]
+        self.entry_finder[item] = entry
+        heapq.heappush(self.heap, entry)
+        self.counter += 1
+
+    def remove(self, item):
+        entry = self.entry_finder.pop(item)
+        entry[-1] = self.REMOVED  # mark as removed
+
+    def pop(self):
+        while self.heap:
+            priority, count, item = heapq.heappop(self.heap)
+            if item != self.REMOVED:
+                del self.entry_finder[item]
+                return item, priority
+        return None
+
+if __name__ == "__main__":
+    pq = PriorityQueue()
+    pq.add_or_update('task1', 1)
+    pq.add_or_update('task2', float('inf'))
+    pq.add_or_update('task3', float('inf'))
+
+    print(pq.pop())  # Should print ('task1', 1)
+    pq.add_or_update('task2', 0)  # Update priority of 'task1'
+    print(pq.pop())  # Should print ('task2', 0)
+    print(pq.pop())  # Should print ('task3', 3)
--- a/utils/project_dir.py
+++ b/utils/project_dir.py
@ -0,0 +1,13 @@
+from pathlib import Path
+
+def get_path(filename) -> Path:
+    this_dir = Path(__file__).resolve().parent
+    project_dir = this_dir.parent
+    return project_dir / filename
+
+if __name__ == "__main__":
+    filename = get_path("data/seq0.txt")
+    print(filename)
+    print(filename.resolve())
+    print(filename.is_file())
+    print(filename.exists())
--- a/utils/test_memory_array.py
+++ b/utils/test_memory_array.py
@ -0,0 +1,47 @@
+from unittest import TestCase
+from utils.literal import Literal
+from utils.memory_array import MemoryArray
+import random
+
+class TestMemoryArray(TestCase):
+
+    def test_create_array(self):
+        l = random.randint(5,10)
+        size = Literal(l)
+        a = MemoryArray(size)
+        self.assertEqual(len(a), l)
+
+    def test_set_item(self):
+        l = random.randint(5,10)
+        size = Literal(l)
+        a = MemoryArray(size)
+        i = Literal(random.randint(0,l-1))
+        v = Literal(random.randint(1,100))
+        a[i] = v
+        self.assertEqual(a[i].value, v.value)
+
+    def test_get_item(self):
+        l = random.randint(5,10)
+        values = [random.randint(1,100) for _ in range(l)]
+        a = MemoryArray(values)
+        for pos, i in enumerate(a.indices()):
+            self.assertEqual(a[i].value, values[pos])
+
+    def test_reset_counters(self):
+        l = random.randint(5,10)
+        values = [random.randint(1,100) for _ in range(l)]
+        a = MemoryArray(values)
+        for i in a.indices():
+            self.assertEqual(a[i].write_count, 1)
+        a.reset_counters()
+        for i in a.indices():
+            self.assertEqual(a[i].write_count, 0)
+
+    def test_create_random_array(self):
+        a = MemoryArray.create_random_array(10, 1, 100)
+        self.assertEqual(len(a), 10)
+
+    def test_create_array_from_file(self):
+        a = MemoryArray.create_array_from_file("data/seq0.txt")
+        self.assertEqual(len(a), 14)
+
--- a/utils/test_memory_cell.py
+++ b/utils/test_memory_cell.py
@ -0,0 +1,166 @@
+from unittest import TestCase
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+import random
+
+
+class TestMemoryCell(TestCase):
+
+    def test_create_cell(self):
+        v = random.randint(1, 100)
+        cell = MemoryCell(v)
+        self.assertEqual(cell.value, v)
+        self.assertEqual(cell.read_count, 0)
+        self.assertEqual(cell.write_count, 1)
+        self.assertEqual(cell.add_count, 0)
+        self.assertEqual(cell.sub_count, 0)
+        self.assertEqual(cell.mul_count, 0)
+        self.assertEqual(cell.div_count, 0)
+        self.assertEqual(cell.bitop_count, 0)
+
+    def test_cast_cell(self):
+        v = random.randint(1, 100)
+        cell = MemoryCell(v)
+        self.assertEqual(int(cell), v)
+        self.assertEqual(cell.read_count, 1)
+        self.assertEqual(cell.write_count, 1)
+        self.assertEqual(cell.add_count, 0)
+        self.assertEqual(cell.sub_count, 0)
+        self.assertEqual(cell.mul_count, 0)
+        self.assertEqual(cell.div_count, 0)
+        self.assertEqual(cell.bitop_count, 0)
+
+    def test_add(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+
+        # "in place" Addition zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        cell1 += cell2
+        self.assertEqual(cell1.value, v1 + v2)
+        self.assertEqual(cell1.add_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(cell1, MemoryCell))
+        self.assertTrue(isinstance(cell2, MemoryCell))
+
+        # Freie Addition zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        result = cell1 + cell2
+
+        self.assertEqual(result.value, v1 + v2)
+        self.assertEqual(cell1.add_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(result, Literal))
+
+    def test_sub(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+
+        # "in place" Subtraktion zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        cell1 -= cell2
+
+        self.assertEqual(cell1.value, v1 - v2)
+        self.assertEqual(cell1.sub_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(cell1, MemoryCell))
+        self.assertTrue(isinstance(cell2, MemoryCell))
+
+        # Freie Subtraktion zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        result = cell1 - cell2
+        self.assertEqual(result.value, v1 - v2)
+        self.assertEqual(cell1.sub_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(result, Literal))
+
+    def test_mul(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+
+        # "in place" Multiplikation zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        cell1 *= cell2
+
+        self.assertEqual(cell1.value, v1 * v2)
+        self.assertEqual(cell1.mul_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(cell1, MemoryCell))
+        self.assertTrue(isinstance(cell2, MemoryCell))
+
+        # Freie Multiplikation zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        result = cell1 * cell2
+        self.assertEqual(result.value, v1 * v2)
+        self.assertEqual(cell1.mul_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(result, Literal))
+
+    def test_div(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+
+        # "in place" Division zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        cell1 //= cell2
+
+        self.assertEqual(cell1.value, v1 // v2)
+        self.assertEqual(cell1.div_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(cell1, MemoryCell))
+        self.assertTrue(isinstance(cell2, MemoryCell))
+
+        # Freie Division zweier MemoryCells
+        cell1 = MemoryCell(v1)
+        cell2 = MemoryCell(v2)
+        result = cell1 // cell2
+        self.assertEqual(result.value, v1 // v2)
+        self.assertEqual(cell1.div_count, 1)
+        self.assertEqual(cell1.read_count, 1)
+        self.assertEqual(cell2.read_count, 1)
+        self.assertTrue(isinstance(result, Literal))
+
+    def test_reset_counters(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+        cell = MemoryCell(v1)
+        cell += Literal(v2)
+
+        self.assertEqual(cell.value, v1+v2)
+        self.assertEqual(cell.read_count, 1)
+        self.assertEqual(cell.add_count, 1)
+        self.assertEqual(cell.write_count, 2)
+
+        cell.reset_counters()
+
+        self.assertEqual(cell.value, v1+v2)
+        self.assertEqual(cell.read_count, 0)
+        self.assertEqual(cell.add_count, 0)
+        self.assertEqual(cell.write_count, 0)
+
+
+    def test_set(self):
+        v1 = random.randint(1, 100)
+        v2 = random.randint(1, 100)
+
+        cell = MemoryCell(v1)
+        cell.set(v2)
+
+        self.assertEqual(cell.value, v2)
+        self.assertEqual(cell.read_count, 0)
+        self.assertEqual(cell.write_count, 2)
+
--- a/vorlesung/L01_grundlagen/euklid.py
+++ b/vorlesung/L01_grundlagen/euklid.py
@ -0,0 +1,13 @@
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+
+x = MemoryCell(int(input("Erste Zahl: ")))
+y = MemoryCell(int(input("Zweite Zahl: ")))
+
+while x > Literal(0):
+    if x < y:
+        x, y = y, x
+    x -= y
+print(y)
+
+print(f"Insgesamt gab es {x.sub_count + y.sub_count} Subtraktionen.")
--- a/vorlesung/L02_elementares_sortieren/bubble_game.py
+++ b/vorlesung/L02_elementares_sortieren/bubble_game.py
@ -0,0 +1,41 @@
+import random
+import pygame
+from utils.game import Game
+from utils.memory_array import MemoryArray
+from bubble_sorting import bubble_sort_stepwise
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+
+class BubbleGame(Game):
+
+    def __init__(self):
+        super().__init__("Bubble Game", fps=60, size=(400, 400))
+        random.seed()
+        l =list(range(1, 101))
+        random.shuffle(l)
+        self.z = MemoryArray(l)
+        self.finished = False
+        self.sort_generator = bubble_sort_stepwise(self.z)
+
+    def update_game(self):
+        if not self.finished:
+            try:
+                next(self.sort_generator)
+            except StopIteration:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        for i, cell in enumerate(self.z):
+            x = 50 + i*3
+            y = 350 - cell.value * 3
+            pygame.draw.rect(self.screen, BLUE, (x, y, 3, 3))
+        super().draw_game()
+
+
+if __name__ == "__main__":
+    b = BubbleGame()
+    b.run()
+
--- a/vorlesung/L02_elementares_sortieren/bubble_sorting.py
+++ b/vorlesung/L02_elementares_sortieren/bubble_sorting.py
@ -0,0 +1,83 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+def bubble_sort_stepwise(z: MemoryArray):
+    n = z.length()
+    for i in mrange(n.pred()):
+        for j in mrange(n.pred(), i, -1):
+            if z[j.pred()] > z[j]:
+                swap(z, j, j.pred())
+                yield z
+
+
+def bubble_sort2_stepwise(z: MemoryArray):
+    n = MemoryCell(z.length())
+    true = Literal(1)
+    false = Literal(0)
+    sortiert = MemoryCell()
+    while True:
+        sortiert.set(true)
+        for i in mrange(n.pred()):
+            if z[i] > z[i.succ()]:
+                swap(z, i, i.succ())
+                sortiert.set(false)
+                yield z
+        n -= Literal(1)
+        if sortiert == true or n <= Literal(1):
+            break
+
+
+def bubble_sort(z: MemoryArray):
+    sort_generator = bubble_sort_stepwise(z)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+
+def bubble_sort2(z: MemoryArray):
+    sort_generator = bubble_sort2_stepwise(z)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+
+def sort_file(filename, sort_func):
+    z = MemoryArray.create_array_from_file(filename)
+    sort_func(z)
+    return z
+
+def analyze_complexity(sort_func, sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sort_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size)
+        else:
+            random_array = MemoryArray.create_random_array(size, -100, 100)
+        sort_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+if __name__ == '__main__':
+        analyze_complexity(bubble_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+#        analyze_complexity(bubble_sort2, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+#        analyze_complexity(bubble_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], True)
+#        analyze_complexity(bubble_sort2, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], True)
--- a/vorlesung/L02_elementares_sortieren/insert_game.py
+++ b/vorlesung/L02_elementares_sortieren/insert_game.py
@ -0,0 +1,41 @@
+import random
+import pygame
+from utils.game import Game
+from utils.memory_array import MemoryArray
+from insert_sorting import insert_sort_stepwise
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+
+class InsertGame(Game):
+
+    def __init__(self):
+        super().__init__("Insert Game", fps=60, size=(400, 400))
+        random.seed()
+        l =list(range(1, 101))
+        random.shuffle(l)
+        self.z = MemoryArray(l)
+        self.finished = False
+        self.sort_generator = insert_sort_stepwise(self.z)
+
+    def update_game(self):
+        if not self.finished:
+            try:
+                next(self.sort_generator)
+            except StopIteration:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        for i, cell in enumerate(self.z):
+            x = 50 + i*3
+            y = 350 - cell.value * 3
+            pygame.draw.rect(self.screen, BLUE, (x, y, 3, 3))
+        super().draw_game()
+
+
+if __name__ == "__main__":
+    b = InsertGame()
+    b.run()
+
--- a/vorlesung/L02_elementares_sortieren/insert_sorting.py
+++ b/vorlesung/L02_elementares_sortieren/insert_sorting.py
@ -0,0 +1,61 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+def insert_sort_stepwise(z: MemoryArray):
+    n = z.length()
+    j = MemoryCell()
+    elem = MemoryCell()
+    for i in mrange(n):
+        elem.set(z[i])
+        j.set(i)
+        while j > Literal(0) and z[j.pred()] > elem:
+            z[j].set(z[j.pred()])
+            j -= Literal(1)
+            yield z
+        z[j].set(elem)
+        yield z
+
+
+def insert_sort(z: MemoryArray):
+    sort_generator = insert_sort_stepwise(z)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+def sort_file(filename, sort_func):
+    z = MemoryArray.create_array_from_file(filename)
+    sort_func(z)
+    return z
+
+
+def analyze_complexity(sort_func, sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sort_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size)
+        else:
+            random_array = MemoryArray.create_random_array(size, -100, 100)
+        sort_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+if __name__ == '__main__':
+        analyze_complexity(insert_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+        #analyze_complexity(insert_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], True)
--- a/vorlesung/L02_elementares_sortieren/select_game.py
+++ b/vorlesung/L02_elementares_sortieren/select_game.py
@ -0,0 +1,41 @@
+import random
+import pygame
+from utils.game import Game
+from utils.memory_array import MemoryArray
+from select_sorting import select_sort_stepwise
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+
+class SelectGame(Game):
+
+    def __init__(self):
+        super().__init__("Select Game", fps=60, size=(400, 400))
+        random.seed()
+        l =list(range(1, 101))
+        random.shuffle(l)
+        self.z = MemoryArray(l)
+        self.finished = False
+        self.sort_generator = select_sort_stepwise(self.z)
+
+    def update_game(self):
+        if not self.finished:
+            try:
+                next(self.sort_generator)
+            except StopIteration:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        for i, cell in enumerate(self.z):
+            x = 50 + i*3
+            y = 350 - cell.value * 3
+            pygame.draw.rect(self.screen, BLUE, (x, y, 3, 3))
+        super().draw_game()
+
+
+if __name__ == "__main__":
+    b = SelectGame()
+    b.run()
+
--- a/vorlesung/L02_elementares_sortieren/select_sorting.py
+++ b/vorlesung/L02_elementares_sortieren/select_sorting.py
@ -0,0 +1,58 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+def select_sort_stepwise(z: MemoryArray):
+    n = z.length()
+    cur_min = MemoryCell()
+    for i in mrange(n):
+        cur_min.set(i)
+        for j in mrange(i.succ(), n):
+            if z[j] < z[cur_min]:
+                cur_min.set(j)
+        swap(z, i, int(cur_min))
+        yield z
+
+
+def select_sort(z: MemoryArray):
+    sort_generator = select_sort_stepwise(z)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+def sort_file(filename, sort_func):
+    z = MemoryArray.create_array_from_file(filename)
+    sort_func(z)
+    return z
+
+
+def analyze_complexity(sort_func, sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sort_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size)
+        else:
+            random_array = MemoryArray.create_random_array(size, -100, 100)
+        sort_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+if __name__ == '__main__':
+        analyze_complexity(select_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+#        analyze_complexity(select_sort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100], True)
--- a/vorlesung/L03_fortgeschrittenes_sortieren/heap_game.py
+++ b/vorlesung/L03_fortgeschrittenes_sortieren/heap_game.py
@ -0,0 +1,42 @@
+import random
+import pygame
+from utils.game import Game
+from utils.memory_array import MemoryArray
+from utils.literal import Literal
+from heap_sorting import heap_sort_stepwise
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+
+class HeapGame(Game):
+
+    def __init__(self):
+        super().__init__("Heap Game", fps=20, size=(400, 400))
+        random.seed()
+        l =list(range(1, 101))
+        random.shuffle(l)
+        self.z = MemoryArray(l)
+        self.finished = False
+        self.sort_generator = heap_sort_stepwise(self.z)
+
+    def update_game(self):
+        if not self.finished:
+            try:
+                next(self.sort_generator)
+            except StopIteration:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        for i, cell in enumerate(self.z):
+            x = 50 + i*3
+            y = 350 - cell.value * 3
+            pygame.draw.rect(self.screen, BLUE, (x, y, 3, 3))
+        super().draw_game()
+
+
+if __name__ == "__main__":
+    sort_game = HeapGame()
+    sort_game.run()
+
--- a/vorlesung/L03_fortgeschrittenes_sortieren/heap_sorting.py
+++ b/vorlesung/L03_fortgeschrittenes_sortieren/heap_sorting.py
@ -0,0 +1,93 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+def heap_sort_stepwise(z: MemoryArray):
+    n = z.length()
+    yield from make_max_heap(z)
+    with MemoryCell(n) as heapsize:
+        for i in mrange(n, 1, -1):
+            swap(z, 0, i.pred())
+            yield z
+            heapsize.set(heapsize.pred())
+            yield from max_heapyfy(z, Literal(1), heapsize)
+
+
+def heap_sort(z: MemoryArray):
+    sort_generator = heap_sort_stepwise(z)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+
+def left_child(i: Literal):
+    return Literal(2 * int(i))
+
+
+def right_child(i: Literal):
+    return Literal(2 * int(i) + 1)
+
+
+def adjust_index(i: Literal):
+    return i.pred()
+
+
+def make_max_heap(z: MemoryArray):
+    n = z.length()
+    for i in mrange(int(n) // 2, 0, -1):
+        yield from max_heapyfy(z, i, n)
+
+
+def max_heapyfy(z: MemoryArray, i: Literal, heapsize: Literal):
+    l = left_child(i)
+    r = right_child(i)
+    with MemoryCell(i) as max_value:
+        if l <= heapsize and z[adjust_index(l)] > z[adjust_index(i)]:
+            max_value.set(l)
+        if r <= heapsize and z[adjust_index(r)] > z[adjust_index(max_value)]:
+            max_value.set(r)
+        if max_value != i:
+            swap(z, int(i)-1, int(max_value)-1)
+            yield z
+            yield from max_heapyfy(z, max_value, heapsize)
+
+
+def sort_file(filename, sort_func):
+    z = MemoryArray.create_array_from_file(filename)
+    sort_func(z)
+    return z
+
+
+def analyze_complexity(sort_func, sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sort_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size)
+        else:
+            random_array = MemoryArray.create_random_array(size, -100, 100)
+        sort_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+
+if __name__ == '__main__':
+    sizes = range(10, 101, 10)
+    analyze_complexity(heap_sort, sizes)
+    # analyze_complexity(quick_sort, sizes, True)
--- a/vorlesung/L03_fortgeschrittenes_sortieren/quick_game.py
+++ b/vorlesung/L03_fortgeschrittenes_sortieren/quick_game.py
@ -0,0 +1,42 @@
+import random
+import pygame
+from utils.game import Game
+from utils.memory_array import MemoryArray
+from utils.literal import Literal
+from quick_sorting import quick_sort_stepwise
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+
+class QuickGame(Game):
+
+    def __init__(self):
+        super().__init__("Quick Game", fps=10, size=(400, 400))
+        random.seed()
+        l =list(range(1, 101))
+        random.shuffle(l)
+        self.z = MemoryArray(l)
+        self.finished = False
+        self.sort_generator = quick_sort_stepwise(self.z, Literal(0), Literal(self.z.length().pred()))
+
+    def update_game(self):
+        if not self.finished:
+            try:
+                next(self.sort_generator)
+            except StopIteration:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        for i, cell in enumerate(self.z):
+            x = 50 + i*3
+            y = 350 - cell.value * 3
+            pygame.draw.rect(self.screen, BLUE, (x, y, 3, 3))
+        super().draw_game()
+
+
+if __name__ == "__main__":
+    sort_game = QuickGame()
+    sort_game.run()
+
--- a/vorlesung/L03_fortgeschrittenes_sortieren/quick_sorting.py
+++ b/vorlesung/L03_fortgeschrittenes_sortieren/quick_sorting.py
@ -0,0 +1,81 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+def quick_sort_stepwise(z: MemoryArray, l: Literal, r: Literal):
+    if l < r:
+        q = partition(z, l, r)
+        yield z
+        yield from quick_sort_stepwise(z, l, q.pred())
+        yield from quick_sort_stepwise(z, q.succ(), r)
+        yield z
+
+
+def partition(z: MemoryArray, l: Literal, r: Literal):
+    with MemoryCell(z[r]) as pivot, MemoryCell(l) as i, MemoryCell(r.pred()) as j:
+            while i < j:
+                while z[i] < pivot:
+                    i.set(i.succ())
+                while j > l and z[j] >= pivot:
+                    j.set(j.pred())
+                if i < j:
+                    swap(z, int(i), int(j))
+                    i.set(i.succ())
+                    j.set(j.pred())
+            if i == j and z[i] < pivot:
+                i.set(i.succ())
+            if z[i] != pivot:
+                swap(z, int(i), int(r))
+            return Literal(i)
+
+
+def quick_sort(z: MemoryArray, l: Literal = None, r: Literal = None):
+    if l is None:
+        l = Literal(0)
+    if r is None:
+        r = z.length().pred()
+    sort_generator = quick_sort_stepwise(z, l, r)
+    while True:
+        try:
+            next(sort_generator)
+        except StopIteration:
+            break
+
+
+def sort_file(filename, sort_func):
+    z = MemoryArray.create_array_from_file(filename)
+    sort_func(z)
+    return z
+
+
+def analyze_complexity(sort_func, sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sort_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size)
+        else:
+            random_array = MemoryArray.create_random_array(size, -100, 100)
+        sort_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+
+if __name__ == '__main__':
+    sizes = range(10, 101, 5)
+    #analyze_complexity(quick_sort, sizes)
+    analyze_complexity(quick_sort, sizes, True)
--- a/vorlesung/L04_besondere_sortierverfahren/count_sorting.py
+++ b/vorlesung/L04_besondere_sortierverfahren/count_sorting.py
@ -0,0 +1,60 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+
+
+def count_sort(a: MemoryArray, b: MemoryArray, k: int):
+    c = MemoryArray(Literal(k + 1))
+    for i in mrange(Literal(k + 1)):
+        c[i].set(Literal(0))
+
+    for j in mrange(a.length()):
+        c[a[j]].set(c[a[j]].succ())
+
+    for i in mrange(Literal(1), Literal(k + 1)):
+        c[i].set(int(c[i]) + int(c[i.pred()]))
+
+    for j in mrange(a.length().pred(), Literal(-1), Literal(-1)):
+        b[c[a[j]].pred()].set(a[j])
+        c[a[j]].set(c[a[j]].pred())
+
+
+
+def analyze_complexity(sizes, presorted=False):
+    """
+    Analysiert die Komplexität einer Sortierfunktion.
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        if presorted:
+            random_array = MemoryArray.create_sorted_array(size, 0, 100)
+        else:
+            random_array = MemoryArray.create_random_array(size, 0, 100)
+        dest_array = MemoryArray(Literal(size))
+        count_sort(random_array, dest_array, 100)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "writes"])
+
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+
+if __name__ == '__main__':
+
+    # Test the count_sort function
+    a = MemoryArray([2, 5, 3, 0, 2, 3, 0, 3])
+    b = MemoryArray(Literal(len(a)))
+    count_sort(a, b, 5)
+
+    sizes = range(10, 101, 10)
+    analyze_complexity(sizes)
+    # analyze_complexity(sizes, True)
--- a/vorlesung/L05_binaere_baeume/init.py
+++ b/vorlesung/L05_binaere_baeume/init.py
@ -0,0 +1 @@
+from vorlesung.L05_binaere_baeume.bin_tree import BinaryTree
--- a/vorlesung/L05_binaere_baeume/analyze_avl_tree.py
+++ b/vorlesung/L05_binaere_baeume/analyze_avl_tree.py
@ -0,0 +1,26 @@
+from utils.memory_manager import MemoryManager
+from utils.memory_array import MemoryArray
+from utils.literal import Literal
+from vorlesung.L05_binaere_baeume.avl_tree import AVLTree
+
+def analyze_complexity(sizes):
+    """
+    Analysiert die Komplexität
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        tree = AVLTree()
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        for i in range(size-1):
+            tree.insert(int(random_array[Literal(i)]))
+        MemoryManager.reset()
+        tree.insert(int(random_array[Literal(size-1)]))
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares"])
+
+if __name__ == "__main__":
+    sizes = range(1, 1001, 2)
+    analyze_complexity(sizes)
--- a/vorlesung/L05_binaere_baeume/analyze_binary_tree.py
+++ b/vorlesung/L05_binaere_baeume/analyze_binary_tree.py
@ -0,0 +1,26 @@
+from utils.memory_manager import MemoryManager
+from utils.memory_array import MemoryArray
+from utils.literal import Literal
+from vorlesung.L05_binaere_baeume.bin_tree import BinaryTree
+
+def analyze_complexity(sizes):
+    """
+    Analysiert die Komplexität
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        tree = BinaryTree()
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        for i in range(size-1):
+            tree.insert(int(random_array[Literal(i)]))
+        MemoryManager.reset()
+        tree.insert(int(random_array[Literal(size-1)]))
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares"])
+
+if __name__ == "__main__":
+    sizes = range(1, 1001, 2)
+    analyze_complexity(sizes)
--- a/vorlesung/L05_binaere_baeume/avl_tree.py
+++ b/vorlesung/L05_binaere_baeume/avl_tree.py
@ -0,0 +1,94 @@
+from utils.memory_array import MemoryArray
+from vorlesung.L05_binaere_baeume.avl_tree_node import AVLTreeNode
+from vorlesung.L05_binaere_baeume.bin_tree import BinaryTree
+import logging
+
+class AVLTree(BinaryTree):
+
+    def __init__(self):
+        super().__init__()
+
+    def new_node(self, value):
+        return AVLTreeNode(value)
+
+
+    def balance(self, node: AVLTreeNode):
+        node.update_balance()
+        if node.balance == -2:
+            if node.left.balance <= 0:
+                node = node.right_rotate()
+            else:
+                node = node.left_right_rotate()
+        elif node.balance == 2:
+            if node.right.balance >= 0:
+                node = node.left_rotate()
+            else:
+                node = node.right_left_rotate()
+        if node.parent:
+            self.balance(node.parent)
+        else:
+            self.root = node
+
+    def insert(self, value):
+        insert_generator = self.insert_stepwise(value)
+        node, parent = None, None
+        while True:
+            try:
+                node, parent = next(insert_generator)
+            except StopIteration:
+                break
+        return node, parent
+
+    def insert_stepwise(self, value):
+        node, parent = super().insert(value)
+        yield None, None
+        node.parent = parent
+        if parent:
+            self.balance(parent)
+        return node, parent
+
+
+    def delete(self, value):
+        node, parent = super().delete(value)
+        if node:
+            node.parent = parent
+        if parent:
+            self.balance(parent)
+
+    def graph_filename(self):
+        return "AVLTree"
+
+if __name__ == "__main__":
+
+    def print_node(node, indent=0, level=0):
+        print((indent * 3) * " ", node.value)
+
+    tree = AVLTree()
+    #values = [5, 3, 7, 2, 4, 6, 5, 8]
+    values = MemoryArray.create_array_from_file("data/seq2.txt")
+
+    for value in values:
+        tree.insert(value)
+
+
+    print("In-order traversal:")
+    tree.in_order_traversal(print_node)
+    print("\nLevel-order traversal:")
+    tree.level_order_traversal(print_node)
+    print("\nTree structure traversal:")
+    tree.tree_structure_traversal(print_node)
+    print("\nGraph traversal:")
+    tree.graph_traversal()
+
+    tree.insert(9)
+    tree.graph_traversal()
+
+    print("\nDeleting 5:")
+    tree.delete(5)
+
+    print("In-order traversal after deletion:")
+    tree.in_order_traversal(print_node)
+    print("\nLevel-order traversal after deletion:")
+    tree.level_order_traversal(print_node)
+    print("\nTree structure traversal after deletion:")
+    tree.tree_structure_traversal(print_node)
--- a/vorlesung/L05_binaere_baeume/avl_tree_game.py
+++ b/vorlesung/L05_binaere_baeume/avl_tree_game.py
@ -0,0 +1,59 @@
+import random
+import pygame
+from utils.game import Game
+from avl_tree import AVLTree
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+BLACK = (0, 0, 0)
+WIDTH = 800
+HEIGHT = 400
+MARGIN = 20
+
+class AVLTreeGame(Game):
+
+    def __init__(self):
+        super().__init__("AVLTree Game", fps=10, size=(WIDTH, HEIGHT))
+        random.seed()
+        self.z = list(range(1, 501))
+        random.shuffle(self.z)
+        self.finished = False
+        self.tree = AVLTree()
+        self.tree.get_height = lambda node: 0 if node is None else 1 + max(self.tree.get_height(node.left), self.tree.get_height(node.right))
+        self.height = self.tree.get_height(self.tree.root)
+        self.generator = None
+
+    def update_game(self):
+        if not self.finished:
+            if self.generator is None:
+                self.generator = self.tree.insert_stepwise(self.z.pop())
+            try:
+                next(self.generator)
+            except StopIteration:
+                self.generator = None
+            if self.generator is None and len(self.z) == 0:
+                self.finished = True
+            self.height = self.tree.get_height(self.tree.root)
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        if self.height > 0:
+            self.draw_tree(self.tree.root, WIDTH // 2, MARGIN, WIDTH // 4 - MARGIN)
+        super().draw_game()
+
+    def draw_tree(self, node, x, y, x_offset):
+        y_offset = (HEIGHT - (2 * MARGIN)) / self.height
+        if node is not None:
+            pygame.draw.circle(self.screen, BLUE, (x, y), 2)
+            if node.left is not None:
+                pygame.draw.line(self.screen, BLACK, (x, y), (x - x_offset, y + y_offset))
+                self.draw_tree(node.left, x - x_offset, y + y_offset, x_offset // 2)
+            if node.right is not None:
+                pygame.draw.line(self.screen, BLACK, (x, y), (x + x_offset, y + y_offset))
+                self.draw_tree(node.right, x + x_offset, y + y_offset, x_offset // 2)
+
+if __name__ == "__main__":
+    tree_game = AVLTreeGame()
+    tree_game.run()
+
--- a/vorlesung/L05_binaere_baeume/avl_tree_node.py
+++ b/vorlesung/L05_binaere_baeume/avl_tree_node.py
@ -0,0 +1,61 @@
+from vorlesung.L05_binaere_baeume.bin_tree_node import BinaryTreeNode
+
+class AVLTreeNode(BinaryTreeNode):
+    def __init__(self, value):
+        super().__init__(value)
+        self.parent = None
+        self.balance = 0
+
+    def __repr__(self):
+        return f"TreeNode(id={id(self)} value={self.value}, left={self.left}, right={self.right})"
+
+    def graphviz_rep(self, row, col, dot):
+        dot.node(str(id(self)), label=str(self.value), pos=f"{col},{-row}!", xlabel=str(self.balance))
+
+    def update_balance(self):
+        left_height = self.left.height() if self.left else 0
+        right_height = self.right.height() if self.right else 0
+        self.balance = right_height - left_height
+
+    def right_rotate(self):
+        new_root = self.left
+        new_root.parent = self.parent
+        self.left = new_root.right
+        if self.left:
+            self.left.parent = self
+        new_root.right = self
+        self.parent = new_root
+        if new_root.parent:
+            if new_root.parent.left is self:
+                new_root.parent.left = new_root
+            else:
+                new_root.parent.right = new_root
+        self.update_balance()
+        new_root.update_balance()
+        return new_root
+
+    def left_rotate(self):
+        new_root = self.right
+        new_root.parent = self.parent
+        self.right = new_root.left
+        if self.right:
+            self.right.parent = self
+        new_root.left = self
+        self.parent = new_root
+        if new_root.parent:
+            if new_root.parent.left is self:
+                new_root.parent.left = new_root
+            else:
+                new_root.parent.right = new_root
+        self.update_balance()
+        new_root.update_balance()
+        return new_root
+
+    def right_left_rotate(self):
+        self.right = self.right.right_rotate()
+        return self.left_rotate()
+
+    def left_right_rotate(self):
+        self.left = self.left.left_rotate()
+        return self.right_rotate()
+
--- a/vorlesung/L05_binaere_baeume/bin_search.py
+++ b/vorlesung/L05_binaere_baeume/bin_search.py
@ -0,0 +1,61 @@
+import random
+
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+from utils.literal import Literal
+
+
+def binary_search(z: MemoryArray, s: MemoryCell, l: Literal = None, r: Literal = None):
+    """
+    Perform a binary search on the sorted array z for the value x.
+    """
+    if l is None:
+        l = Literal(0)
+    if r is None:
+        r = Literal(z.length().pred())
+    if l > r:
+        return None
+    with MemoryCell(l) as m:
+        m += r
+        m //= Literal(2)
+        if s < z[m]:
+            return binary_search(z, s, l, m.pred())
+        elif s > z[m]:
+            return binary_search(z, s, m.succ(), r)
+        else:
+            return m
+
+
+def analyze_complexity(sizes):
+    """
+    Analysiert die Komplexität
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        random_array = MemoryArray.create_sorted_array(size)
+        search_value = random.randint(-100, 100)
+        binary_search(random_array, MemoryCell(search_value))
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "adds"])
+
+
+
+
+if __name__ == "__main__":
+    # Example usage
+    arr = MemoryArray([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
+    search_value = MemoryCell(8)
+    result = binary_search(arr, search_value)
+    if result is not None:
+        print(f"Value {search_value} found at index {result}.")
+    else:
+        print(f"Value {search_value} not found in the array.")
+
+
+    sizes = range(1, 1001, 2)
+    analyze_complexity(sizes)
--- a/vorlesung/L05_binaere_baeume/bin_tree.py
+++ b/vorlesung/L05_binaere_baeume/bin_tree.py
@ -0,0 +1,206 @@
+from vorlesung.L05_binaere_baeume.bin_tree_node import BinaryTreeNode
+from utils.project_dir import get_path
+from datetime import datetime
+import graphviz
+
+
+class BinaryTree:
+
+    def __init__(self):
+        self.root = None
+        self.size = 0
+
+    def new_node(self, value):
+        return BinaryTreeNode(value)
+
+    def insert(self, value):
+        self.size += 1
+        value = self.new_node(value)
+        if self.root is None:
+            self.root = value
+            return self.root, None
+        else:
+            current = self.root
+            while True:
+                if value < current:
+                    if current.left:
+                        current = current.left
+                    else:
+                        current.left = value
+                        return current.left, current
+                elif value >= current:
+                    if current.right:
+                        current = current.right
+                    else:
+                        current.right = value
+                        return current.right, current
+                else:
+                    return None, None
+
+    def search(self, value):
+        current = self.root
+        value = self.new_node(value)
+        while current:
+            if value < current:
+                current = current.left
+            elif value > current:
+                current = current.right
+            else:
+                return current
+        return None
+
+    def delete(self, value):
+        # Der Wert wird im Baum gesucht und der erste Treffer gelöscht
+        # Rückgabe falls der Wert gefunden wird:
+        # der Knoten, der den zu löschenden Knoten ersetzt und der Elternknoten des gelöschten Knotens
+        parent = None
+        current = self.root
+        value = self.new_node(value)
+        while current:
+            if value < current:
+                parent = current
+                current = current.left
+            elif value > current:
+                parent = current
+                current = current.right
+            else:
+                # Knoten gefunden
+                break
+        else:
+            # Wert nicht gefunden
+            return None, None
+        return self.delete_node(current, parent)
+
+    def delete_node(self, current, parent):
+        # Der übergebene Knoten wird
+        # Rückgabe ist ein Tupel:
+        # der Knoten, der den zu löschenden Knoten ersetzt und der Elternknoten des gelöschten Knotens
+        self.size -= 1
+        # Fall 3: Es gibt zwei Kinder: wir suchen den Nachfolger
+        if current.left and current.right:
+            parent = current
+            successor = current.right
+            while successor.left:
+                parent = successor
+                successor = successor.left
+            # Wert des Nachfolgers wird in den Knoten geschrieben, der gelöscht werden soll
+            current.value = successor.value
+            # Ab jetzt muss successor gelöscht werden; parent ist bereits richtig gesetzt
+            current = successor
+
+        # Ermitteln des einen Kindes (falls es eines gibt), sonst None
+        # Das eine Kind ist der Ersatz für den Knoten, der gelöscht werden soll
+        if current.left:
+            child = current.left
+        else:
+            child = current.right
+
+        # Falls es keinen Elternknoten gibt, ist der Ersatzknoten die Wurzel
+        if not parent:
+            self.root = child
+            return child, None
+        elif parent.left is current:
+            parent.left = child
+            return child, parent
+        else:
+            parent.right = child
+            return child, parent
+
+
+    def in_order_traversal(self, callback):
+
+        def in_order_traversal_recursive(callback, current):
+            if current is not None:
+                in_order_traversal_recursive(callback, current.left)
+                callback(current)
+                in_order_traversal_recursive(callback, current.right)
+
+        in_order_traversal_recursive(callback, self.root)
+
+
+    def level_order_traversal(self, callback):
+        if self.root is None:
+            return
+        queue = [(self.root, 0)]
+        while queue:
+            current, level = queue.pop(0)
+            callback(current, level)
+            if current.left is not None:
+                queue.append((current.left, level + 1))
+            if current.right is not None:
+                queue.append((current.right, level + 1))
+
+    def tree_structure_traversal(self, callback):
+
+        def tree_structure_traversal_recursive(callback, current, level):
+            nonlocal line
+            if current:
+                tree_structure_traversal_recursive(callback, current.left, level + 1)
+                callback(current, level, line)
+                line += 1
+                tree_structure_traversal_recursive(callback, current.right, level + 1)
+
+        line = 0
+        tree_structure_traversal_recursive(callback, self.root, 0)
+
+    def graph_filename(self):
+        return "BinaryTree"
+
+    def graph_traversal(self):
+        def define_node(node, level, line):
+            nonlocal dot
+            if node is not None:
+                node.graphviz_rep(level, line, dot)
+
+        def graph_traversal_recursive(current):
+            nonlocal dot
+            if current is not None:
+                if current.left:
+                    dot.edge(str(id(current)), str(id(current.left)))
+                    graph_traversal_recursive(current.left)
+                if current.right:
+                    dot.edge(str(id(current)), str(id(current.right)))
+                    graph_traversal_recursive(current.right)
+
+        dot = graphviz.Digraph( name="BinaryTree",
+                                engine="neato",
+                                node_attr={"shape": "circle", "fontname": "Arial"},
+                                format="pdf" )
+        self.tree_structure_traversal(define_node)
+        graph_traversal_recursive(self.root)
+        timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
+        filename = f"{self.graph_filename()}_{timestamp}.gv"
+        filename = get_path(filename)
+        dot.render(filename)
+
+if __name__ == "__main__":
+    tree = BinaryTree()
+    values = [5, 3, 7, 2, 4, 6, 5, 8]
+
+    for value in values:
+        tree.insert(value)
+
+    def print_node(node, indent=0, line=None):
+        print((indent * 3) * " ", node.value)
+
+
+    print("In-order traversal:")
+    tree.in_order_traversal(print_node)
+    print("\nLevel-order traversal:")
+    tree.level_order_traversal(print_node)
+    print("\nTree structure traversal:")
+    tree.tree_structure_traversal(print_node)
+    print("\nGraph traversal:")
+    tree.graph_traversal()
+
+    print("\nDeleting 5:")
+    tree.delete(5)
+
+    print("In-order traversal after deletion:")
+    tree.in_order_traversal(print_node)
+    print("\nLevel-order traversal after deletion:")
+    tree.level_order_traversal(print_node)
+    print("\nTree structure traversal after deletion:")
+    tree.tree_structure_traversal(print_node)
+
+
--- a/vorlesung/L05_binaere_baeume/bin_tree_game.py
+++ b/vorlesung/L05_binaere_baeume/bin_tree_game.py
@ -0,0 +1,54 @@
+import random
+import pygame
+from utils.game import Game
+from bin_tree import BinaryTree
+
+WHITE = (255, 255, 255)
+BLUE = (0, 0, 255)
+BLACK = (0, 0, 0)
+WIDTH = 800
+HEIGHT = 400
+MARGIN = 20
+
+class BinTreeGame(Game):
+
+    def __init__(self):
+        super().__init__("BinTree Game", fps=10, size=(WIDTH, HEIGHT))
+        random.seed()
+        self.z = list(range(1, 101))
+        random.shuffle(self.z)
+        self.finished = False
+        self.tree = BinaryTree()
+        self.tree.get_height = lambda node: 0 if node is None else 1 + max(self.tree.get_height(node.left), self.tree.get_height(node.right))
+        self.height = self.tree.get_height(self.tree.root)
+
+    def update_game(self):
+        if not self.finished:
+            i = self.z.pop()
+            self.tree.insert(i)
+            self.height = self.tree.get_height(self.tree.root)
+            if len(self.z) == 0:
+                self.finished = True
+        return True
+
+    def draw_game(self):
+        self.screen.fill(WHITE)
+        if self.height > 0:
+            self.draw_tree(self.tree.root, WIDTH // 2, MARGIN, WIDTH // 4 - MARGIN)
+        super().draw_game()
+
+    def draw_tree(self, node, x, y, x_offset):
+        y_offset = (HEIGHT - (2 * MARGIN)) / self.height
+        if node is not None:
+            pygame.draw.circle(self.screen, BLUE, (x, y), 2)
+            if node.left is not None:
+                pygame.draw.line(self.screen, BLACK, (x, y), (x - x_offset, y + y_offset))
+                self.draw_tree(node.left, x - x_offset, y + y_offset, x_offset // 2)
+            if node.right is not None:
+                pygame.draw.line(self.screen, BLACK, (x, y), (x + x_offset, y + y_offset))
+                self.draw_tree(node.right, x + x_offset, y + y_offset, x_offset // 2)
+
+if __name__ == "__main__":
+    tree_game = BinTreeGame()
+    tree_game.run()
+
--- a/vorlesung/L05_binaere_baeume/bin_tree_node.py
+++ b/vorlesung/L05_binaere_baeume/bin_tree_node.py
@ -0,0 +1,22 @@
+from utils.memory_cell import MemoryCell
+
+class BinaryTreeNode(MemoryCell):
+
+    def __init__(self, value):
+        super().__init__(value)
+        self.left = None
+        self.right = None
+
+    def height(self):
+        left_height = self.left.height() if self.left else 0
+        right_height = self.right.height() if self.right else 0
+        return 1 + max(left_height, right_height)
+
+    def __repr__(self):
+        return f"TreeNode(value={self.value}, left={self.left}, right={self.right})"
+
+    def __str__(self):
+        return str(self.value)
+
+    def graphviz_rep(self, row, col, dot):
+        dot.node(str(id(self)), label=str(self.value), pos=f"{col},{-row}!")
--- a/vorlesung/L06_b_baeume/analyze_b_tree.py
+++ b/vorlesung/L06_b_baeume/analyze_b_tree.py
@ -0,0 +1,58 @@
+from utils.memory_manager import MemoryManager
+from utils.memory_array import MemoryArray
+from utils.literal import Literal
+from b_tree import BTree
+from b_tree_node import BTreeNode
+
+class MemoryManagerBTree(MemoryManager):
+    """
+    Diese Klasse erweitert den MemoryManager, um spezifische Statistiken für B-Bäume zu speichern.
+    """
+
+    @staticmethod
+    def count_loads():
+        return sum([cell.loaded_count for cell in MemoryManager().cells if isinstance(cell, BTreeNode)])
+
+    @staticmethod
+    def count_saves():
+        return sum([cell.saved_count for cell in MemoryManager().cells if isinstance(cell, BTreeNode)])
+
+    @staticmethod
+    def save_stats(count):
+        data = {    "cells": MemoryManager.count_cells(),
+                    "reads": MemoryManager.count_reads(),
+                    "writes": MemoryManager.count_writes(),
+                    "compares": MemoryManager.count_compares(),
+                    "adds": MemoryManager.count_adds(),
+                    "subs": MemoryManager.count_subs(),
+                    "muls": MemoryManager.count_muls(),
+                    "divs": MemoryManager.count_divs(),
+                    "bitops": MemoryManager.count_bitops(),
+                    "loads": MemoryManagerBTree.count_loads(),
+                    "saves": MemoryManagerBTree.count_saves()  }
+        MemoryManager.stats[count] = data
+
+
+
+
+def analyze_complexity(sizes):
+    """
+    Analysiert die Komplexität
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        tree = BTree(5)
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        for i in range(size-1):
+            tree.insert(int(random_array[Literal(i)]))
+        MemoryManager.reset()
+        tree.insert(int(random_array[Literal(size-1)]))
+        MemoryManagerBTree.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares", "loads", "saves"])
+
+if __name__ == "__main__":
+    sizes = range(1, 1001, 2)
+    analyze_complexity(sizes)
--- a/vorlesung/L06_b_baeume/b_tree.py
+++ b/vorlesung/L06_b_baeume/b_tree.py
@ -0,0 +1,120 @@
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_array import MemoryArray
+from b_tree_node import BTreeNode
+
+class BTree:
+    def __init__(self, m: int):
+        self.m = m
+        self.root = BTreeNode(m)
+
+    def search(self, value, start: BTreeNode = None) -> BTreeNode | None:
+        if not start:
+            start = self.root
+        start.load()
+        i = 0
+        if not isinstance(value, MemoryCell):
+            value = MemoryCell(value)
+        while i < start.n and value > start.value[Literal(i)]:
+            i += 1
+        if i < start.n and value == start.value[Literal(i)]:
+            return start
+        if start.leaf:
+            return None
+        return self.search(value, start.children[i])
+
+    def split_child(self, parent: BTreeNode, i: int):
+        child = parent.children[i]
+        child.load()
+        h = BTreeNode(self.m)
+        h.leaf = child.leaf
+        h.n = self.m - 1
+        for j in range(self.m - 1):
+            h.value[Literal(j)] = child.value[Literal(j + self.m)]
+        if not h.leaf:
+            for j in range(self.m):
+                h.children[j] = child.children[j + self.m]
+            for j in range(self.m, child.n + 1):
+                child.children[j] = None
+        child.n = self.m - 1
+        child.save()
+        h.save()
+        for j in range(parent.n, i, -1):
+            parent.children[j + 1] = parent.children[j]
+            parent.value[Literal(j)] = parent.value[Literal(j - 1)]
+        parent.children[i + 1] = h
+        parent.value[Literal(i)] = child.value[Literal(self.m - 1)]
+        parent.n += 1
+        parent.save()
+
+    def insert(self, value):
+        if not isinstance(value, MemoryCell):
+            value = MemoryCell(value)
+        r = self.root
+        if r.n == 2 * self.m - 1:
+            h = BTreeNode(self.m)
+            self.root = h
+            h.leaf = False
+            h.n = 0
+            h.children[0] = r
+            self.split_child(h, 0)
+            self.insert_in_node(h, value)
+        else:
+            self.insert_in_node(r, value)
+
+    def insert_in_node(self, start: BTreeNode, value):
+        start.load()
+        i = start.n
+        if start.leaf:
+            while i >= 1 and value < start.value[Literal(i-1)]:
+                start.value[Literal(i)] = start.value[Literal(i-1)]
+                i -= 1
+            start.value[Literal(i)].set(value)
+            start.n += 1
+            start.save()
+        else:
+            j = 0
+            while j < start.n and value > start.value[Literal(j)]:
+                j += 1
+            if start.children[j].n == 2 * self.m - 1:
+                self.split_child(start, j)
+                if value > start.value[Literal(j)]:
+                    j += 1
+            self.insert_in_node(start.children[j], value)
+
+    def traversal(self, callback):
+        def traversal_recursive(node, callback):
+            i = 0
+            while i < node.n:
+                if not node.leaf:
+                    traversal_recursive(node.children[i], callback)
+                callback(node.value[Literal(i)])
+                i += 1
+            if not node.leaf:
+                traversal_recursive(node.children[i], callback)
+
+        traversal_recursive(self.root, callback)
+
+    def walk(self):
+        def print_key(key):
+            print(key, end=" ")
+
+        self.traversal(print_key)
+
+    def height(self, start: BTreeNode = None):
+        if not start:
+            start = self.root
+        if start.leaf:
+            return 0
+        return 1 + self.height(start.children[0])
+
+
+if __name__ == "__main__":
+    a = MemoryArray.create_array_from_file("data/seq3.txt")
+    tree = BTree(3)
+    for cell in a:
+        tree.insert(cell)
+    print(f"Height: {tree.height()}")
+    tree.walk()
+    s = tree.search(0)
+    print(f"\nKnoten mit 0: {str(s)}")
--- a/vorlesung/L06_b_baeume/b_tree_node.py
+++ b/vorlesung/L06_b_baeume/b_tree_node.py
@ -0,0 +1,29 @@
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_array import MemoryArray
+
+class BTreeNode(MemoryCell):
+
+    def __init__(self, m: int):
+        super().__init__()
+        self.m = m
+        self.n = 0
+        self.leaf = True
+        self.value = MemoryArray(Literal(2 * m - 1))
+        self.children = [None] * (2 * m)
+        self.loaded_count = 0
+        self.saved_count = 0
+
+    def reset_counters(self):
+        super().reset_counters()
+        self.loaded_count = 0
+        self.saved_count = 0
+
+    def load(self):
+        self.loaded_count += 1
+
+    def save(self):
+        self.saved_count += 1
+
+    def __str__(self):
+        return "(" + " ".join([str(self.value[Literal(i)]) for i in range(self.n)]) + ")"
--- a/vorlesung/L07_hashtable/init.py
+++ b/vorlesung/L07_hashtable/init.py
--- a/vorlesung/L07_hashtable/analyze_hashtable.py
+++ b/vorlesung/L07_hashtable/analyze_hashtable.py
@ -0,0 +1,60 @@
+import math
+import random
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_array import MemoryArray
+from utils.memory_manager import MemoryManager
+from vorlesung.L07_hashtable.hashtable import HashTableOpenAddressing
+
+#Goldener Schnitt
+a = Literal((math.sqrt(5) - 1) / 2)
+
+# Hashfunktion nach multiplikativer Methode
+def h(x: MemoryCell, m: Literal) -> Literal:
+    with MemoryCell(int(x * a)) as integer_part, MemoryCell(x * a) as full_product:
+        with MemoryCell(full_product - integer_part) as fractional_part:
+            return Literal(abs(int(fractional_part * m)))
+
+# Quadratische Sondierung
+def f(x: MemoryCell, i: Literal, m: Literal) -> Literal:
+    c1 = 1
+    c2 = 5
+    with MemoryCell(h(x, m)) as initial_hash, MemoryCell(c2 * int(i) * int(i)) as quadratic_offset:
+        with MemoryCell(initial_hash + quadratic_offset) as probe_position:
+            probe_position += Literal(c1 * int(i)) # Linear component
+            return probe_position % m
+
+# Symmetrische quadratische Sondierung
+def fs(x: MemoryCell, i: Literal, m: Literal) -> Literal:
+    with MemoryCell(h(x, m)) as base_hash, MemoryCell(int(i) * int(i)) as square:
+        if int(i) % 2 == 0:  # gerades i: Vorwärtssondierung
+            with MemoryCell(base_hash + square) as position:
+                return position % m
+        else:  # ungerades i: Rückwärtssondierung
+            with MemoryCell(base_hash - square) as position:
+                return position % m
+
+
+def analyze_complexity(sizes):
+    """
+    Analysiert die Komplexität
+
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        ht = HashTableOpenAddressing(size, f)
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        for cell in random_array:
+            ht.insert(cell)
+        MemoryManager.reset()
+        cell = random.choice(random_array.cells)
+        ht.search(cell)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "compares"])
+
+
+if __name__ == "__main__":
+    sizes = range(1, 1001, 10)
+    analyze_complexity(sizes)
--- a/vorlesung/L07_hashtable/hashtable.py
+++ b/vorlesung/L07_hashtable/hashtable.py
@ -0,0 +1,76 @@
+from collections.abc import Callable
+from utils.literal import Literal
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.memory_range import mrange
+
+
+UNUSED_MARK = "UNUSED"
+DELETED_MARK = "DELETED"
+
+class HashTableOpenAddressing:
+    def __init__(self, m: Literal, f: Callable[[MemoryCell, Literal, Literal], Literal]):
+        if not isinstance(m, Literal):
+            m = Literal(m)
+        self.m = m
+        self.f = f
+        self.table = MemoryArray(m)
+        for i in mrange(m):
+            self.table[i].value = UNUSED_MARK
+
+    def insert(self, x: MemoryCell):
+        with MemoryCell(0) as i:
+            while i < self.m:
+                j = self.f(x, i, self.m)
+                if self.is_free(j):
+                    self.table[j].set(x)
+                    return True
+                i.set(i.succ())
+        return False
+
+    def search(self, x: MemoryCell):
+        with MemoryCell(0) as i:
+            while i < self.m:
+                j = self.f(x, i, self.m)
+                if self.is_unused(j):
+                    return False
+                if self.table[j] == x:
+                    return True
+                i.set(i.succ())
+        return False
+
+    def delete(self, x: MemoryCell):
+        with MemoryCell(0) as i:
+            while i < self.m:
+                j = self.f(x, i, self.m)
+                if self.is_unused(j):
+                    return False
+                if self.table[j] == x:
+                    self.table[j].value = DELETED_MARK
+                    return True
+                i.set(i.succ())
+        return False
+
+    def __str__(self):
+        return str(self.table)
+
+    def alpha(self):
+        with MemoryCell(0) as i:
+            used = 0
+            while i < self.m:
+                used += 0 if self.is_free(i) else 1
+                i.set(i.succ())
+        return used / int(self.m)
+
+    def is_unused(self, i: Literal):
+        if self.table[i].value == UNUSED_MARK:
+            return True
+        return False
+
+    def is_deleted(self, i: Literal):
+        if self.table[i].value == DELETED_MARK:
+            return True
+        return False
+
+    def is_free(self, i: Literal):
+        return self.is_unused(i) or self.is_deleted(i)
--- a/vorlesung/L08_graphen/init.py
+++ b/vorlesung/L08_graphen/init.py
--- a/vorlesung/L08_graphen/aoc2212.py
+++ b/vorlesung/L08_graphen/aoc2212.py
@ -0,0 +1,45 @@
+from vorlesung.L08_graphen.graph import Graph, AdjacencyMatrixGraph
+from utils.project_dir import get_path
+
+graph = AdjacencyMatrixGraph()
+start = ""
+end = ""
+
+def read_file(filename: str = "data/aoc2212.txt"):
+    """Read a file and return the content as a string."""
+
+    def adjust_char(char):
+        """Adjust character for comparison."""
+        if char == 'S':
+            return 'a'
+        elif char == 'E':
+            return 'z'
+        return char
+
+    global start, end
+    with open(get_path(filename), "r") as file:
+        quest = file.read().strip().splitlines()
+    for row, line in enumerate(quest):
+        for col, char in enumerate(line):
+            label = f"{row},{col}"
+            graph.insert_vertex(label)
+            if char == "S":
+                start = label
+            if char == "E":
+                end = label
+    for row, line in enumerate(quest):
+        for col, char in enumerate(line):
+            for neighbor in [(row - 1, col), (row, col - 1), (row + 1, col), (row, col + 1)]:
+                if 0 <= neighbor[0] < len(quest) and 0 <= neighbor[1] < len(line):
+                    if ord(adjust_char(quest[neighbor[0]][neighbor[1]])) <= ord(adjust_char(char)) + 1:
+                        label1 = f"{row},{col}"
+                        label2 = f"{neighbor[0]},{neighbor[1]}"
+                        graph.connect(label1, label2)
+
+
+# Lösung des Adventskalenders 2022, Tag 12
+read_file("data/aoc2212test.txt")
+graph.graph()
+distance_map, predecessor_map = graph.bfs(start)
+print(distance_map[graph.get_vertex(end)])
+print(graph.path(end, predecessor_map))
--- a/vorlesung/L08_graphen/graph.py
+++ b/vorlesung/L08_graphen/graph.py
@ -0,0 +1,366 @@
+from collections import deque
+from typing import List
+from enum import Enum
+import graphviz
+import math
+import heapq
+from datetime import datetime
+from utils.project_dir import get_path
+from utils.priority_queue import PriorityQueue
+from vorlesung.L09_mst.disjoint import DisjointValue
+
+
+class NodeColor(Enum):
+    """Enumeration for node colors in a graph traversal."""
+    WHITE = 1       # WHITE: not visited
+    GRAY = 2        # GRAY: visited but not all neighbors visited
+    BLACK = 3       # BLACK: visited and all neighbors visited
+
+
+class Vertex:
+    """A vertex in a graph."""
+    def __init__(self, value):
+        self.value = value
+
+    def __str__(self):
+        return str(self.value)
+
+    def __repr__(self):
+        return f"Vertex({self.value})"
+
+
+
+class Graph:
+    """A graph."""
+    def insert_vertex(self, name: str):
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def connect(self, name1: str, name2: str, weight: float = 1):
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def all_vertices(self) -> List[Vertex]:
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def get_vertex(self, name: str) -> Vertex:
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def get_adjacent_vertices(self, name: str) -> List[Vertex]:
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def get_adjacent_vertices_with_weight(self, name: str) -> List[tuple[Vertex, float]]:
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def all_edges(self) -> List[tuple[str, str, float]]:
+        raise NotImplementedError("Please implement this method in subclass")
+
+    def bfs(self, start_name: str):
+        """
+        Perform a breadth-first search starting at the given vertex.
+        :param start_name: the name of the vertex to start at
+        :return: a tuple of two dictionaries, the first mapping vertices to distances from the start vertex,
+                 the second mapping vertices to their predecessors in the traversal tree
+        """
+
+        color_map = {}                  # maps vertices to their color
+        distance_map = {}               # maps vertices to their distance from the start vertex
+        predecessor_map = {}            # maps vertices to their predecessor in the traversal tree
+
+        # Initialize the maps
+        for vertex in self.all_vertices():
+            color_map[vertex] = NodeColor.WHITE
+            distance_map[vertex] = None
+            predecessor_map[vertex] = None
+
+        # Start at the given vertex
+        start_node = self.get_vertex(start_name)
+        color_map[start_node] = NodeColor.GRAY
+        distance_map[start_node] = 0
+
+        # Initialize the queue with the start vertex
+        queue = deque()
+        queue.append(start_node)
+
+        # Process the queue
+        while len(queue) > 0:
+            vertex = queue.popleft()
+            for dest in self.get_adjacent_vertices(vertex.value):
+                if color_map[dest] == NodeColor.WHITE:
+                    color_map[dest] = NodeColor.GRAY
+                    distance_map[dest] = distance_map[vertex] + 1
+                    predecessor_map[dest] = vertex
+                    queue.append(dest)
+            color_map[vertex] = NodeColor.BLACK
+
+        # Return the distance and predecessor maps
+        return distance_map, predecessor_map
+
+    def dfs(self):
+        """
+        Perform a depth-first search starting at the first vertex.
+        :return: a tuple of two dictionaries, the first mapping vertices to distances from the start vertex,
+                 the second mapping vertices to their predecessors in the traversal tree
+        """
+        color_map : dict[Vertex, NodeColor]= {}
+        enter_map : dict[Vertex, int] = {}
+        leave_map : dict[Vertex, int] = {}
+        predecessor_map : dict[Vertex, Vertex | None] = {}
+        white_vertices = set(self.all_vertices())
+        time_counter = 0
+
+        def dfs_visit(vertex):
+            nonlocal time_counter
+            color_map[vertex] = NodeColor.GRAY
+            white_vertices.remove(vertex)
+            time_counter += 1
+            enter_map[vertex] = time_counter
+            for dest in self.get_adjacent_vertices(vertex.value):
+                if color_map[dest] == NodeColor.WHITE:
+                    predecessor_map[dest] = vertex
+                    dfs_visit(dest)
+            color_map[vertex] = NodeColor.BLACK
+            time_counter += 1
+            leave_map[vertex] = time_counter
+
+        # Initialize the maps
+        for vertex in self.all_vertices():
+            color_map[vertex] = NodeColor.WHITE
+            predecessor_map[vertex] = None
+
+        while white_vertices:
+            v = white_vertices.pop()
+            dfs_visit(v)
+
+        return enter_map, leave_map, predecessor_map
+
+
+    def path(self, destination, map):
+        """
+        Compute the path from the start vertex to the given destination vertex.
+        The map parameter is the predecessor map
+        """
+        path = []
+        destination_node = self.get_vertex(destination)
+        while destination_node is not None:
+            path.insert(0, destination_node.value)
+            destination_node = map[destination_node]
+        return path
+
+    def graph(self, filename: str = "Graph"):
+        dot = graphviz.Digraph( name=filename,
+                                node_attr={"fontname": "Arial"},
+                                format="pdf" )
+        for vertex in self.all_vertices():
+            dot.node(str(id(vertex)), label=str(vertex.value))
+        for edge in self.all_edges():
+            dot.edge(str(id(self.get_vertex(edge[0]))), str(id(self.get_vertex(edge[1]))), label=str(edge[2]))
+        timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
+        filename = f"{filename}_{timestamp}.gv"
+        filename = get_path(filename)
+        dot.render(filename)
+
+    def dijkstra(self, start_name: str) -> tuple[dict[Vertex, float], dict[Vertex, Vertex | None]]:
+        """
+        Führt den Dijkstra-Algorithmus für kürzeste Pfade durch, implementiert mit Knotenfarben.
+
+        Args:
+            start_name: Name des Startknotens
+
+        Returns:
+            Ein Tupel aus zwei Dictionaries:
+            - distance_map: Abbildung von Knoten auf ihre kürzeste Distanz vom Startknoten
+            - predecessor_map: Abbildung von Knoten auf ihre Vorgänger im kürzesten Pfad
+        """
+
+        def relax(vertex, dest, weight):
+            """
+            Entspannt die Kante zwischen vertex und dest.
+            Aktualisiert die Distanz und den Vorgänger, wenn ein kürzerer Pfad gefunden wird.
+            """
+            if distance_map[vertex] + weight < distance_map[dest]:
+                distance_map[dest] = distance_map[vertex] + weight
+                predecessor_map[dest] = vertex
+                queue.add_or_update(dest, distance_map[dest])
+
+        # Initialisierung der Maps
+        distance_map = {}  # Speichert kürzeste Distanzen
+        predecessor_map = {}  # Speichert Vorgänger
+
+        # Initialisiere alle Knoten
+        queue = PriorityQueue()
+        for vertex in self.all_vertices():
+            distance_map[vertex] = float('inf')  # Initiale Distanz unendlich
+            predecessor_map[vertex] = None  # Initialer Vorgänger None
+            queue.add_or_update(vertex, distance_map[vertex])  # Füge Knoten zur Prioritätswarteschlange hinzu
+
+
+
+        # Setze Startknoten
+        start_node = self.get_vertex(start_name)
+        distance_map[start_node] = 0
+        queue.add_or_update(start_node, distance_map[start_node])
+
+        while True:
+            entry = queue.pop()
+            if entry is None:
+                break
+            vertex = entry[0]
+            for dest, weight in self.get_adjacent_vertices_with_weight(vertex.value):
+                relax(vertex, dest, weight)
+        return distance_map, predecessor_map
+
+    def mst_prim(self, start_name: str = None):
+        """ Compute the minimum spanning tree of the graph using Prim's algorithm. """
+
+        distance_map = {}   # maps vertices to their current distance from the spanning tree
+        parent_map = {}     # maps vertices to their predecessor in the spanning tree
+
+        Vertex.__lt__ = lambda self, other: distance_map[self] < distance_map[other]
+
+        queue = []
+
+        if start_name is None:
+            start_name = self.all_vertices()[0].value
+
+        # Initialize the maps
+        for vertex in self.all_vertices():
+            distance_map[vertex] = 0 if vertex.value == start_name else math.inf
+            parent_map[vertex] = None
+            queue.append(vertex)
+
+        heapq.heapify(queue)    # Convert the list into a heap
+
+        # Process the queue
+        cost = 0 # The cost of the minimum spanning tree
+        while len(queue) > 0:
+            vertex = heapq.heappop(queue)
+            cost += distance_map[vertex] # Add the cost of the edge to the minimum spanning tree
+            for (dest, w) in self.get_adjacent_vertices_with_weight(vertex.value):
+                if dest in queue and distance_map[dest] > w:
+                    # Update the distance and parent maps
+                    queue.remove(dest)
+                    distance_map[dest] = w
+                    parent_map[dest] = vertex
+                    queue.append(dest)      # Add the vertex back to the queue
+                    heapq.heapify(queue)    # Re-heapify the queue
+
+        # Return the distance and predecessor maps
+        return parent_map, cost
+
+    def mst_kruskal(self, start_name: str = None):
+        """ Compute the minimum spanning tree of the graph using Kruskal's algorithm. """
+
+        cost = 0
+        result = []
+        edges = self.all_edges()
+
+        # Create a disjoint set for each vertex
+        vertex_map = {v.value: DisjointValue(v) for v in self.all_vertices()}
+
+        # Sort the edges by weight
+        edges.sort(key=lambda edge: edge[2])
+
+        # Process the edges
+        for edge in edges:
+            start_name, end_name, weight = edge
+            # Check if the edge creates a cycle
+            if not vertex_map[start_name].same_set(vertex_map[end_name]):
+                result.append(edge)
+                vertex_map[start_name].union(vertex_map[end_name])
+                cost += weight
+
+        return result, cost
+
+
+class AdjacencyListGraph(Graph):
+    """A graph implemented as an adjacency list."""
+    def __init__(self):
+        self.adjacency_map = {}     # maps vertex names to lists of adjacent vertices
+        self.vertex_map = {}        # maps vertex names to vertices
+
+    def insert_vertex(self, name: str):
+        if name not in self.vertex_map:
+            self.vertex_map[name] = Vertex(name)
+        if name not in self.adjacency_map:
+            self.adjacency_map[name] = []
+
+    def connect(self, name1: str, name2: str, weight: float = 1):
+        adjacency_list = self.adjacency_map[name1]
+        dest = self.vertex_map[name2]
+        adjacency_list.append((dest, weight))
+
+    def all_vertices(self) -> List[Vertex]:
+        return list(self.vertex_map.values())
+
+    def get_vertex(self, name: str) -> Vertex:
+        return self.vertex_map[name]
+
+    def get_adjacent_vertices(self, name: str) -> List[Vertex]:
+        return list(map(lambda x: x[0], self.adjacency_map[name]))
+
+    def get_adjacent_vertices_with_weight(self, name: str) -> List[tuple[Vertex, float]]:
+        return self.adjacency_map[name]
+
+    def all_edges(self) -> List[tuple[str, str, float]]:
+        result = []
+        for name in self.adjacency_map:
+            for (dest, weight) in self.adjacency_map[name]:
+                result.append((name, dest.value, weight))
+        return result
+
+
+class AdjacencyMatrixGraph(Graph):
+    """A graph implemented as an adjacency matrix."""
+    def __init__(self):
+        self.index_map = {}         # maps vertex names to indices
+        self.vertex_list = []       # list of vertices
+        self.adjacency_matrix = []  # adjacency matrix
+
+    def insert_vertex(self, name: str):
+        if name not in self.index_map:
+            self.index_map[name] = len(self.vertex_list)
+            self.vertex_list.append(Vertex(name))
+            for row in self.adjacency_matrix:   # add a new column to each row
+                row.append(None)
+            self.adjacency_matrix.append([None] * len(self.vertex_list)) # add a new row
+
+    def connect(self, name1: str, name2: str, weight: float = 1):
+        index1 = self.index_map[name1]
+        index2 = self.index_map[name2]
+        self.adjacency_matrix[index1][index2] = weight
+
+
+    def all_vertices(self) -> List[Vertex]:
+        return self.vertex_list
+
+    def get_vertex(self, name: str) -> Vertex:
+        index = self.index_map[name]
+        return self.vertex_list[index]
+
+    def get_adjacent_vertices(self, name: str) -> List[Vertex]:
+        index = self.index_map[name]
+        result = []
+        for i in range(len(self.vertex_list)):
+            if self.adjacency_matrix[index][i] is not None:
+                name = self.vertex_list[i].value
+                result.append(self.get_vertex(name))
+        return result
+
+    def get_adjacent_vertices_with_weight(self, name: str) -> List[tuple[Vertex, float]]:
+        index = self.index_map[name]
+        result = []
+        for i in range(len(self.vertex_list)):
+            if self.adjacency_matrix[index][i] is not None:
+                name = self.vertex_list[i].value
+                result.append((self.get_vertex(name), self.adjacency_matrix[index][i]))
+        return result
+
+    def all_edges(self) -> List[tuple[str, str, float]]:
+        result = []
+        for i in range(len(self.vertex_list)):
+            for j in range(len(self.vertex_list)):
+                if self.adjacency_matrix[i][j] is not None:
+                    result.append((self.vertex_list[i].value, self.vertex_list[j].value, self.adjacency_matrix[i][j]))
+        return result
+
+
+
--- a/vorlesung/L09_mst/init.py
+++ b/vorlesung/L09_mst/init.py
--- a/vorlesung/L09_mst/disjoint.py
+++ b/vorlesung/L09_mst/disjoint.py
@ -0,0 +1,18 @@
+
+
+class DisjointValue():
+
+    def __init__(self, value):
+        self.value = value
+        self.parent = None
+
+    def canonical(self):
+        if self.parent:
+            return self.parent.canonical()
+        return self
+
+    def same_set(self, other):
+        return self.canonical() == other.canonical()
+
+    def union(self, other):
+        self.canonical().parent = other.canonical()
--- a/vorlesung/init.py
+++ b/vorlesung/init.py
				`@ -0,0 +1 @@`
				`from vorlesung.L05_binaere_baeume.bin_tree import BinaryTree`