Lecture 6

SoSe24/lec04_trees/avl_tree.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence
+from SoSe24.lec04_trees.bin_tree import BinTree, BinTreeNode
+from time import perf_counter as pfc
+
+class AVLTreeNode(BinTreeNode):
+    def __init__(self, value: AlgoDatValue):
+        super().__init__(value)
+        self.parent = None
+        self.balance = 0
+
+    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) -> BinTreeNode:
+        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 == 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) -> BinTreeNode:
+        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 == 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) -> BinTreeNode:
+        self.right = self.right.right_rotate()
+        return self.left_rotate()
+
+    def left_right_rotate(self) -> BinTreeNode:
+        self.left = self.left.left_rotate()
+        return self.right_rotate()
+
+class AVLTree(BinTree):
+
+    def new_node(self, value: AlgoDatValue):
+        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: AlgoDatValue):
+        node, parent = super().insert(value)
+        node.parent = parent
+        if parent:
+            self.balance(parent)
+        return node, parent
+
+    def delete(self, value: AlgoDatValue):
+        node, parent = super().delete(value)
+        if node:
+            node.parent = parent
+        if parent:
+            self.balance(parent)
+
+
+
+if __name__ == "__main__":
+    z = read_int_sequence("../../seq0.txt")
+    print(z, len(z))
+    start = pfc()
+    tree = AVLTree()
+    for i in z:
+        tree.insert(i)
+    tree.walk()
+    tree.tree_walk()
+    tree.levelwalk()
+    tree.graph_walk()
+    tree.delete(AlgoDatValue(46))
+    tree.delete(AlgoDatValue(48))
+    #tree.graph_walk()
+    print(f"Dauer: {pfc() - start:.4f}s")
+    AlgoDatValue.summary()

SoSe24/lec04_trees/avl_tree_plot.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence, read_int_sequence_limited
+import matplotlib
+matplotlib.use('TkAgg')
+import matplotlib.pyplot as plt
+import avl_tree as avl
+
+if __name__ == "__main__":
+    filename = "../../seq3_sorted.txt"
+    #filename = "../../seq3.txt"
+    dummy = read_int_sequence(filename)
+    n = len(dummy)
+    step = n // 100
+
+    memory_values = []
+    compare_values = []
+
+    for right_end in range(1, n, step):
+        AlgoDatValue.reset()
+        z = read_int_sequence_limited(filename, right_end)
+        tree = avl.AVLTree()
+        for i in z:
+            tree.insert(i)
+        memory_values.append(AlgoDatValue.memory)
+        compare_values.append(AlgoDatValue.compare)
+
+    plt.plot(range(1, n, step), memory_values, 'b', label='Memory')
+    plt.plot(range(1, n, step), compare_values, 'r', label='Compare')
+    plt.legend()
+    plt.show()

SoSe24/lec04_trees/b_tree.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence
+from time import perf_counter as pfc
+
+
+class BTreeNode:
+    def __init__(self, m: int):
+        self.n = 0
+        self.leaf = True
+        self.keys = AlgoDatArray(2 * m - 1)
+        self.children = [None] * (2 * m)
+
+    def __str__(self):
+        return "(" + " ".join([str(self.keys[i]) for i in range(self.n)]) + ")"
+
+class BTree:
+    def __init__(self, m: int):
+        self.m = m
+        self.root = BTreeNode(m)
+
+    def search(self, key: AlgoDatValue, start: BTreeNode = None) -> BTreeNode:
+        if not start:
+            start = self.root
+        i = 0
+        while i < start.n and key > start.keys[i]:
+            i += 1
+        if i < start.n and key == start.keys[i]:
+            return start
+        if start.leaf:
+            return None
+        return self.search(key, start.children[i])
+
+    def split_child(self, parent: BTreeNode, i: int):
+        child = parent.children[i]
+        h = BTreeNode(self.m)
+        h.leaf = child.leaf
+        h.n = self.m - 1
+        for j in range(self.m - 1):
+            h.keys[j] = child.keys[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
+        for j in range(parent.n, i, -1):
+            parent.children[j + 1] = parent.children[j]
+            parent.keys[j] = parent.keys[j - 1]
+        parent.children[i + 1] = h
+        parent.keys[i] = child.keys[self.m - 1]
+        parent.n += 1
+
+    def insert(self, k: AlgoDatValue):
+        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, k)
+        else:
+            self.insert_in_node(r, k)
+
+    def insert_in_node(self, start: BTreeNode, k: AlgoDatValue):
+        i = start.n
+        if start.leaf:
+            while i >= 1 and k < start.keys[i-1]:
+                start.keys[i] = start.keys[i-1]
+                i -= 1
+            start.keys[i] = k
+            start.n += 1
+        else:
+            j = 0
+            while j < start.n and k > start.keys[j]:
+                j += 1
+            if start.children[j].n == 2 * self.m - 1:
+                self.split_child(start, j)
+                if k > start.keys[j]:
+                    j += 1
+            self.insert_in_node(start.children[j], k)
+
+    def walk(self, start: BTreeNode = None):
+        if not start:
+            start = self.root
+        i = 0
+        while i < start.n:
+            if not start.leaf:
+                self.walk(start.children[i])
+            print(start.keys[i], end=" ")
+            i += 1
+        if not start.leaf:
+            self.walk(start.children[i])
+
+    def height(self, start: BTreeNode = None):
+        if not start:
+            start = self.root
+        if start.leaf:
+            return 0
+        return 1 + self.height(start.children[0])
+
+    def graph_walk(self):
+        queue = [ self.root ]
+        with open("../../btree.gv", "w") as file:
+            file.write("digraph BTree {\n")
+            file.write("    node [fontname=\"Arial\"];\n")
+            while queue:
+                current = queue.pop(0)
+                p = str(current)
+                file.write(f'"{p}"; \n')
+                i = 0
+                while i <= current.n:
+                    if not current.leaf:
+                        queue.append(current.children[i])
+                        c = str(current.children[i])
+                        file.write(f'"{p}" -> "{c}";\n')
+                    i += 1
+            file.write("}")
+
+
+if __name__ == "__main__":
+    z = read_int_sequence("../../seq2.txt")
+    start = pfc()
+    tree = BTree(3)
+    for i in z:
+        tree.insert(i)
+    print(f"Height: {tree.height()}")
+    tree.walk()
+    tree.graph_walk()
+    s = tree.search(AlgoDatValue(0))
+    print(f"\nKnoten mit 0: {str(s)}")
+    print(f"Dauer: {pfc() - start:.4f}s")
+    AlgoDatValue.summary()

SoSe24/lec04_trees/bin_tree.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence
+from time import perf_counter as pfc
+
+class BinTreeNode:
+    def __init__(self, value: AlgoDatValue):
+        self.value = value
+        self.left = None
+        self.right = None
+
+    def __str__(self):
+        return f"{self.value}"
+
+    def height(self) -> int:
+        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)
+
+
+
+class BinTree:
+    def __init__(self):
+        self.root = None
+
+    def new_node(self, value: AlgoDatValue) -> BinTreeNode:
+        return BinTreeNode(value)
+
+    def insert(self, value: AlgoDatValue) -> (BinTreeNode, BinTreeNode):
+        if not self.root:
+            self.root = self.new_node(value)
+            return self.root, None
+
+        current = self.root
+        while True:
+            if value < current.value:
+                if current.left:
+                    current = current.left
+                else:
+                    current.left = self.new_node(value)
+                    return current.left, current
+            elif value >= current.value:
+                if current.right:
+                    current = current.right
+                else:
+                    current.right = self.new_node(value)
+                    return current.right, current
+            else:
+                return None, None
+
+    def search(self, value: AlgoDatValue) -> BinTreeNode:
+        current = self.root
+        while current:
+            if value < current.value:
+                current = current.left
+            elif value > current.value:
+                current = current.right
+            else:
+                return current
+        return None
+
+    def delete(self, value: AlgoDatValue):
+        parent = None
+        current = self.root
+        while current:
+            if value < current.value:
+                parent = current
+                current = current.left
+            elif value >= current.value:
+                parent = current
+                current = current.right
+            else:
+                break
+        else:
+            return
+
+        if current.left and current.right:
+            parent = current
+            successor = current.right
+            while successor.left:
+                parent = successor
+                successor = successor.left
+            current.value.value = successor.value.value
+            current = successor
+
+        if current.left:
+            child = current.left
+        else:
+            child = current.right
+
+        if not parent:
+            self.root = child
+            return child, None
+        elif parent.left == current:
+            parent.left = child
+            return child, parent
+        else:
+            parent.right = child
+            return child, parent
+
+    def walk(self): # in-order
+        print("[ ", end="")
+        self.walk_recursive(self.root, 0, 0)
+        print(" ]")
+
+
+    def graph_walk(self):
+        self.leaf_counter = 0
+        with open("../../graph.gv", "w") as file:
+            file.write("digraph BST {\n")
+            file.write("    node [fontname=\"Arial\"];\n")
+            self.graph_walk_recursive(self.root, file)
+            file.write("}")
+
+    def graph_walk_recursive(self, current, file):
+        if current is not None:
+            if current.left:
+                file.write(f"{current.value} -> {current.left.value}; \n")
+                self.graph_walk_recursive(current.left, file)
+            else:
+                file.write(f"left{self.leaf_counter} [shape=point]; \n")
+                file.write(f"{current.value} -> left{self.leaf_counter}; \n")
+                self.leaf_counter += 1
+            if current.right:
+                file.write(f"{current.value} -> {current.right.value}; \n")
+                self.graph_walk_recursive(current.right, file)
+            else:
+                file.write(f"right{self.leaf_counter} [shape=point]; \n")
+                file.write(f"{current.value} -> right{self.leaf_counter}; \n")
+                self.leaf_counter += 1
+
+
+    def tree_walk(self):
+        self.walk_recursive(self.root, 0, 1)
+
+    def walk_recursive(self, node: BinTreeNode, level = 0, increase = 1):
+        if node:
+            if increase >= 1:
+                end = "\n"
+            else:
+                end = " "
+            self.walk_recursive(node.left, level+increase, increase)
+            print(" "*level*3 + str(node.value), end=end)
+            self.walk_recursive(node.right, level+increase, increase)
+
+    def levelwalk(self):
+        if self.root is None:
+            return
+        queue = [self.root]
+        while queue:
+            current = queue.pop(0)
+            print(current.value, end=" ")
+            if current.left:
+                queue.append(current.left)
+            if current.right:
+                queue.append(current.right)
+        print()
+
+
+if __name__ == "__main__":
+    z = read_int_sequence("../../seq0.txt")
+    print(z, len(z))
+    start = pfc()
+    tree = BinTree()
+    for i in z:
+        tree.insert(i)
+    tree.walk()
+    tree.tree_walk()
+    tree.levelwalk()
+    tree.delete(AlgoDatValue(46))
+    tree.graph_walk()
+    print(f"Dauer: {pfc() - start:.4f}s")
+    AlgoDatValue.summary()

SoSe24/lec04_trees/bin_tree_plot.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence, read_int_sequence_limited
+import matplotlib
+matplotlib.use('TkAgg')
+import matplotlib.pyplot as plt
+import bin_tree as bt
+
+if __name__ == "__main__":
+    filename = "../../seq3_sorted.txt"
+    #filename = "../../seq3.txt"
+    dummy = read_int_sequence(filename)
+    n = len(dummy)
+    step = n // 100
+
+    memory_values = []
+    compare_values = []
+
+    for right_end in range(1, n, step):
+        AlgoDatValue.reset()
+        z = read_int_sequence_limited(filename, right_end)
+        tree = bt.BinTree()
+        for i in z:
+            tree.insert(i)
+        memory_values.append(AlgoDatValue.memory)
+        compare_values.append(AlgoDatValue.compare)
+        print(right_end, AlgoDatValue.compare)
+
+    plt.plot(range(1, n, step), memory_values, 'b', label='Memory')
+    plt.plot(range(1, n, step), compare_values, 'r', label='Compare')
+    plt.legend()
+    plt.show()

SoSe24/lec05_hash/hash_table.py

+from SoSe24.algodat.foundation import AlgoDatArray, AlgoDatValue, read_int_sequence, MinusInf
+from time import perf_counter as pfc
+
+#Goldener Schnitt
+import math
+a = (math.sqrt(5) - 1) / 2
+
+def h(x, m):
+    return int(x*a - int(x*a) * m)
+
+def f(x, i, m):
+    return (h(x, m) + i + 14*i*i) % m
+
+def f1(x, i, m):
+    if i % 2 == 0:
+        return (h(x, m) + i*i) % m
+    return ((h(x, m) - i*i) % m + m) % m
+
+class HashTable:
+    def __init__(self, m, h, f=None):
+        self.m = m
+        self.h = h
+        self.f = f
+        self.table = AlgoDatArray(m)
+
+    def insert(self, x):
+        i = 0
+        while i < self.m:
+            j = self.f(x.value, i, self.m)
+            if self.is_free(j):
+                self.table[j].value = x.value
+                return True
+            i += 1
+        return False
+
+    def search(self, x):
+        i = 0
+        while i < self.m:
+            j = f(x, i, self.m)
+            if self.table[j] == x:
+                return True
+            if self.table[j] == None:
+                return False
+            i += 1
+        return False
+
+    def delete(self, x):
+        i = 0
+        while i < self.m:
+            j = f(x, i, self.m)
+            if self.table[j].value == x:
+                self.table[j].value = "DELETED"
+                return True
+            if self.table[j].value is None:
+                return False
+            i += 1
+        return False
+
+    def __str__(self):
+        return str(self.table)
+
+    def alpha(self):
+        i=0
+        used = 0
+        while i < self.m:
+            used += 0 if self.is_free(i) else 1
+            i += 1
+        return used / self.m
+
+    def is_free(self, i):
+        if self.table[i] == None:
+            return True
+        if  self.table[i] == "DELETED":
+            return True
+        return False
+
+if __name__ == "__main__":
+    z = read_int_sequence("../../seq1.txt")
+    start = pfc()
+    hash = HashTable(31, h, f)
+    for i in z:
+        hash.insert(i)
+    print(hash)
+    print(f"Alpha: {hash.alpha()}")
+    hash.delete(34)
+    hash.search(47)
+    hash.search(243)
+    print(hash)
+    print(f"Alpha: {hash.alpha()}")
+    print(f"Dauer: {pfc() - start:.4f}s")
+    AlgoDatValue.summary()

SoSe24/lec06_graph/bfs.py

+from collections import deque
+from typing import List
+import re
+from enum import Enum
+
+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
+
+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):
+        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 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 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
+
+
+
+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):
+        adjacency_list = self.adjacency_map[name1]
+        dest = self.vertex_map[name2]
+        adjacency_list.append(dest)
+
+    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 self.adjacency_map[name]
+
+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(0)
+            self.adjacency_matrix.append([0] * len(self.vertex_list)) # add a new row
+
+    def connect(self, name1: str, name2: str):
+        index1 = self.index_map[name1]
+        index2 = self.index_map[name2]
+        self.adjacency_matrix[index1][index2] = 1
+
+    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] == 1:
+                name = self.vertex_list[i].value
+                result.append(self.get_vertex(name))
+        return result
+
+def read_cave_into_graph(graph: Graph, filename: str):
+    """Read a cave description from a file and insert it into the given graph."""
+    with open(filename, "r") as file:
+        lines = file.readlines()
+        for line in lines:
+            # match a line with two node names and an optional direction
+            m = re.match(r"(^\s*\"(.*)\"\s*([<>]*)\s*\"(.*)\"\s*)", line)
+            if m:
+                startnode = m.group(2)
+                endnode = m.group(4)
+                opcode = m.group(3)
+                graph.insert_vertex(startnode)
+                graph.insert_vertex(endnode)
+                if '>' in opcode:
+                    graph.connect(startnode, endnode)
+                if '<' in opcode:
+                    graph.connect(endnode, startnode)
+
+
+if __name__ == "__main__":
+    graph = AdjacencyListGraph()
+    #graph = AdjacencyMatrixGraph()
+    read_cave_into_graph(graph, "../../hoehle.txt")
+    _, predecessor_map = graph.bfs('Höhleneingang')
+    path = graph.path('Schatzkammer', predecessor_map)
+    print(path)
+    _, predecessor_map = graph.bfs('Schatzkammer')
+    path = graph.path('Höhleneingang', predecessor_map)
+    print(path)