Minimum Spanning Tree in a Weighted Graph

December 24, 2023

Problem # Given a weighted undirected graph, find a minimum spanning tree that connects all nodes while minimizing the total weight of the edges Solution # Below is the complete Python code that finds a minimum spanning tree (MST) for a given weighted undirected graph using a variant of Prim’s algorithm: import heapq def minimum_spanning_tree(graph): # Assuming the graph is represented as an adjacency list where each entry is # a tuple of (node, weight), and graph is a dictionary # Initialize variables start_node = next(iter(graph)) # Starting from the first node in the graph mst = set() # To store the edges of the Minimum Spanning Tree visited = set([start_node]) edges = [(weight, start_node, to) for to, weight in graph[start_node]] heapq. ...