Init

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.")

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()
+

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)

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()
+

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)

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()
+

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)

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()
+

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)

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()
+

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)

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)

vorlesung/L05_binaere_baeume/__init__.py

@@ -0,0 +1 @@
+from vorlesung.L05_binaere_baeume.bin_tree import BinaryTree

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)

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)

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)

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()
+

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()
+

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)

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)
+
+

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()
+

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}!")

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)

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)}")

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)]) + ")"

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)

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)

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))

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
+
+
+

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()