Data Structure-graph (updating)

I. minimum Spanning Tree: returns a tree T in a given undirected graph G, giving the tree edge in graph G and minimizing the sum of edge weights of the entire tree.

Core Idea of algorithms: greedy

1. kru.pdf algorithm (greedy side)

(1) Sort all edges in ascending order by edge weight;

(2) test all edges from small to large by edge weight. If the two vertices connected to the current test edge are not in the same connected block, add the test edge to the current minimal spanning tree. Otherwise, the edge is discarded;

(3) execute Step 2 until the number of edges in the Minimum Spanning Tree is equal to the sum of vertices minus 1 or ends after all edges are tested.

If the number of edges of the Minimum Spanning Tree is smaller than the total number of vertices minus 1, the graph is not connected.

 

Data Structure-graph (updating)