elektro

data/aoc2212test.txt

@@ -0,0 +1,5 @@
+Sabqponm
+abcryxxl
+accszExk
+acctuvwj
+abdefghi

data/aoc2416test.txt

@@ -0,0 +1,15 @@
+###############
+#.......#....E#
+#.#.###.#.###.#
+#.....#.#...#.#
+#.###.#####.#.#
+#.#.#.......#.#
+#.#.#####.###.#
+#...........#.#
+###.#.#####.#.#
+#...#.....#.#.#
+#.#.#.###.#.#.#
+#.....#...#.#.#
+#.###.#.#.#.#.#
+#S..#.....#...#
+###############

data/elektro.txt

@@ -0,0 +1,8 @@
+"Höhleneingang";"Ost/West-Passage";5
+"Höhleneingang";"Nord/Süd-Passage";3
+"Nord/Süd-Passage";"Nebelraum";7
+"Steiniger Pfad";"Ost/West-Passage";2
+"Ost/West-Passage";"Schwefelgewölbe";4
+"Schwefelgewölbe";"Steiniger Pfad";1
+"Schatzkammer";"Nebelraum";2
+"Steiniger Pfad";"Schatzkammer";6

data/labyrinth.txt

@@ -0,0 +1,9 @@
+xxxxxxxxxxxxxxxxxxxxx
+x                   x
+x        S          x
+x                   x
+x      xxxxxxxx     x
+x                   x
+x                   x
+x            A      x
+xxxxxxxxxxxxxxxxxxxxx

data/labyrinth1.txt

@@ -0,0 +1,5 @@
+xxxxxAxxxxxxxxx
+x           xSx
+xxxxxxxxxx xx x
+x             x
+xxxxxxxxxxxxxxx

praktika/07_hashtable/praktikum.py

@@ -34,27 +34,9 @@ def fs(x: MemoryCell, i: Literal, m: Literal) -> Literal:
                 return position % m
 
 
-class TestHashTableOpenAddressing(unittest.TestCase):
-
-    def test_hash_function(self):
-        x = MemoryCell(22)
-        m = Literal(20)
-        self.assertEqual(11, h(x, m).value)
-
-    def test_probe_function(self):
-        x = MemoryCell(22)
-        i = Literal(0)
-        m = Literal(20)
-        self.assertEqual(11, f(x, i, m).value)
-        i = Literal(1)
-        self.assertEqual(17, f(x, i, m).value)
-        i = Literal(2)
-        self.assertEqual(13, f(x, i, m).value)
-
 
 
 if __name__ == "__main__":
-    #unittest.main()
 
     print("*** Aufgabe 3 ***")
     size =  Literal(20)

praktika/08_graph/schatz.py

@@ -0,0 +1,37 @@
+import re
+from utils.project_dir import get_path
+from vorlesung.L08_graphen.graph import Graph, AdjacencyListGraph, AdjacencyMatrixGraph
+
+
+def read_cave_into_graph(graph: Graph, filename: str):
+    """Read a cave description from a file and insert it into the given graph."""
+    filename = get_path(filename)
+    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)
+
+
+graph = AdjacencyListGraph()
+# graph = AdjacencyMatrixGraph()
+read_cave_into_graph(graph, "data/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)
+graph.graph("Höhle")
+
+

praktika/09_aoc/rendeer.py

@@ -0,0 +1,59 @@
+from utils.project_dir import get_path
+from vorlesung.L08_graphen.graph import AdjacencyListGraph
+
+DIRECTIONS = [(1,0), (0, 1), (-1, 0), (0, -1)]
+
+class D16Solution:
+
+    def __init__(self):
+        with open(get_path("data/aoc2416.txt"), "r") as file:
+            self.puzzle = [line.strip() for line in file]
+        self.cells = set()
+        self.start = None
+        self.end = None
+
+    def get_cells_start_end(self):
+        for row in range(len(self.puzzle)):
+            for col in range(len(self.puzzle[row])):
+                if self.puzzle[row][col] != '#':
+                    self.cells.add((col, row))
+                if self.puzzle[row][col] == 'S':
+                    self.start = (col, row)
+                if self.puzzle[row][col] == 'E':
+                    self.end = (col, row)
+
+    def get_label(self, cell, direction):
+        """Generate a label for a cell based on its coordinates and direction."""
+        return f"{cell[0]},{cell[1]}_{direction}"
+
+    def create_graph(self):
+        graph = AdjacencyListGraph()
+        for cell in self.cells:
+            for direction in DIRECTIONS:
+                label = self.get_label(cell, direction)
+                graph.insert_vertex(label)
+        for cell in self.cells:
+            for d, direction in enumerate(DIRECTIONS):
+                label = self.get_label(cell, direction)
+                dx, dy = direction
+                neighbor = (cell[0] + dx, cell[1] + dy)
+                if neighbor in self.cells:
+                    graph.connect(label, self.get_label(neighbor, direction))
+                direction_left = DIRECTIONS[(d - 1) % 4]
+                direction_right = DIRECTIONS[(d + 1) % 4]
+                graph.connect(label, self.get_label(cell, direction_left), 1000)
+                graph.connect(label, self.get_label(cell, direction_right), 1000)
+        return graph
+
+if __name__ == "__main__":
+    solution = D16Solution()
+    solution.get_cells_start_end()
+    graph = solution.create_graph()
+    start = solution.get_label(solution.start, DIRECTIONS[0])
+    print(f"Start: {start}")
+    distance_map, predecessor_map = graph.dijkstra(start)
+    end_labels = [solution.get_label(solution.end, direction) for direction in DIRECTIONS]
+    end_vertices = [graph.get_vertex(label) for label in end_labels]
+    min_weight = min([distance_map[vertex] for vertex in end_vertices])
+    print(f"Minimum distance to End {solution.end}: {min_weight}")
+

praktika/10_electro/electro.py

@@ -0,0 +1,32 @@
+from vorlesung.L08_graphen.graph import Graph, AdjacencyMatrixGraph
+from utils.project_dir import get_path
+import re
+
+def read_elektro_into_graph(graph: Graph, filename: str):
+    pattern = re.compile(r'"([^"]+)";"([^"]+)";(\d+)')
+    with (open(filename, "r") as file):
+        for line in file:
+            m = pattern.match(line)
+            if m:
+                start_name = m.group(1)
+                end_name = m.group(2)
+                cost = int(m.group(3))
+                graph.insert_vertex(start_name)
+                graph.insert_vertex(end_name)
+                graph.connect(start_name, end_name, cost)
+                graph.connect(end_name, start_name, cost)
+
+if __name__ == "__main__":
+    graph = AdjacencyMatrixGraph()
+    read_elektro_into_graph(graph, get_path("data/elektro.txt"))
+
+    parents, cost = graph.mst_prim()
+    print(f"Kosten nach Prim: {cost}")
+    for node, parent in parents.items():
+        if parent is not None:
+            print(f"{node} - {parent}")
+
+    edges, cost = graph.mst_kruskal()
+    print(f"Kosten nach Kruskal: {cost}")
+    for start_name, end_name, _ in edges:
+        print(f"{start_name} - {end_name}")

utils/priority_queue.py

@@ -0,0 +1,40 @@
+import heapq
+
+class PriorityQueue:
+    def __init__(self):
+        self.heap = []
+        self.entry_finder = {}  # map: item -> [priority, item]
+        self.REMOVED = '<removed>'
+        self.counter = 0  # unique sequence count to break ties
+
+    def add_or_update(self, item, priority):
+        if item in self.entry_finder:
+            self.remove(item)
+        count = self.counter
+        entry = [priority, count, item]
+        self.entry_finder[item] = entry
+        heapq.heappush(self.heap, entry)
+        self.counter += 1
+
+    def remove(self, item):
+        entry = self.entry_finder.pop(item)
+        entry[-1] = self.REMOVED  # mark as removed
+
+    def pop(self):
+        while self.heap:
+            priority, count, item = heapq.heappop(self.heap)
+            if item != self.REMOVED:
+                del self.entry_finder[item]
+                return item, priority
+        return None
+
+if __name__ == "__main__":
+    pq = PriorityQueue()
+    pq.add_or_update('task1', 1)
+    pq.add_or_update('task2', float('inf'))
+    pq.add_or_update('task3', float('inf'))
+
+    print(pq.pop())  # Should print ('task1', 1)
+    pq.add_or_update('task2', 0)  # Update priority of 'task1'
+    print(pq.pop())  # Should print ('task2', 0)
+    print(pq.pop())  # Should print ('task3', 3)

vorlesung/L05_binaere_baeume/bin_tree.py

@@ -1,6 +1,4 @@
 from vorlesung.L05_binaere_baeume.bin_tree_node import BinaryTreeNode
-from utils.memory_manager import MemoryManager
-from utils.memory_array import MemoryArray
 from utils.project_dir import get_path
 from datetime import datetime
 import graphviz

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()