算法导论 ch23 最小生成树 Prim

最新推荐文章于 2023-02-20 08:20:41 发布

最新推荐文章于 2023-02-20 08:20:41 发布 · 82 阅读

本文介绍使用Prim算法计算无向加权图的最小生成树(MST)的过程。通过一个具体的例子展示了如何从指定的起始顶点逐步构建最小生成树，并计算其总权重。最后给出了运行结果，展示了每个被选中顶点的父节点及其距离。

/* * get the MST using Prim algorithm * sv : start vertex */ void AdjMatrixGraph::mst_prim(int sv){ // the min distance to the current MST int *d = new int[v]; // the parent in the MST int *p = new int[v]; // has the vertex been selected? bool *selected = new bool[v]; for(int i = 0; i < v; i++){ p[i] = -1; d[i] = std::numeric_limits<int>::max(); selected[i] = false; } d[sv] = 0; selected[sv] = true; int selectedV = sv; for(int i = 0; i < v; i++){ // update distance and parent for(int i = 0; i < v; i++){ if(!selected[i]){ if (d[i] > A[selectedV * v + i]){ d[i] = A[selectedV * v + i]; p[i] = selectedV; } } } int vToBeSelected; int distance = std::numeric_limits<int>::max(); // find the vertex which has not been selected with the min distance for(int i = 0; i < v; i++){ if(!selected[i]){ if (d[i] < distance){ distance = d[i]; vToBeSelected = i; } } } //cout << "now selecting vertex is " << vToBeSelected << ", and distance is " << distance << endl; selectedV = vToBeSelected; selected[vToBeSelected] = true; } int weight = 0; for(int i = 0; i < v; i++){ weight += d[i]; cout << "vertex " << i << " is selected with parent " << p[i] << ", and distance is " << d[i] << endl; } cout << "weight of MST is " << weight << endl; }

test program:

#include "../ch22/Edge.h" #include "../ch22/Graph.h" #include <iostream> #include <vector> #include <algorithm> using namespace std; int main() { Edge e[] = { { 1, 2, 4 }, { 1, 8, 8 }, { 2, 8, 11 }, { 2, 3, 8 }, { 3, 4, 7 }, { 3, 6, 4 }, { 3, 9, 2 }, { 4, 5, 9 }, { 4, 6, 14 }, { 5, 6, 10 }, { 6, 7, 2 }, { 7, 8, 1 }, { 7, 9, 6 }, { 8, 9, 7 } }; Edges* edges = Edges::getInstance(); for (unsigned int i = 0; i < sizeof(e)/sizeof(Edge); i++) { edges->insert(&(e[i])); } int numberOfVertexes = 9; AdjMatrixGraph *g1 = new AdjMatrixGraph(numberOfVertexes, edges, false, true); MatrixGraphBuilder* mgb = MatrixGraphBuilder::getInstance(); g1->build(mgb); //g1->display(); g1->mst_prim(0); }

run result:

vertex 0 is selected with parent -1, and distance is 0 vertex 1 is selected with parent 0, and distance is 4 vertex 2 is selected with parent 1, and distance is 8 vertex 3 is selected with parent 2, and distance is 7 vertex 4 is selected with parent 3, and distance is 9 vertex 5 is selected with parent 2, and distance is 4 vertex 6 is selected with parent 5, and distance is 2 vertex 7 is selected with parent 6, and distance is 1 vertex 8 is selected with parent 2, and distance is 2 weight of MST is 37