elektro

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}")

vorlesung/L08_graphen/graph.py

@@ -2,9 +2,12 @@ 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):
@@ -205,6 +208,68 @@ class Graph:
                 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."""
@@ -243,8 +308,6 @@ class AdjacencyListGraph(Graph):
         return result
 
 
-
-
 class AdjacencyMatrixGraph(Graph):
     """A graph implemented as an adjacency matrix."""
     def __init__(self):

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()