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  • 最小生成树——prim

    prim:逐“点”生成最小生成树

    与Dijkstra不同的是:加入点到生成树中,不要考虑与源点的距离,而是考虑与生成树的距离

    #include <iostream>
    #include <cstring> 
    using namespace std;
    
    const int VERTEX_NUM = 20;
    const int INFINITY = 0x7fffffff;
    
    bool vis[VERTEX_NUM];
    int dist[VERTEX_NUM]; 
    int pre[VERTEX_NUM];
    
    class Graph {
    public:
    	int vexNum;
    	int edgeNum;
    	int vex[VERTEX_NUM];
    	int arc[VERTEX_NUM][VERTEX_NUM]; 
    };
    
    void createGraph(Graph &G)
    {
    	cout << "please input vexNum and edgeNum: ";
    	cin >> G.vexNum >> G.edgeNum;
    	for (int i = 0; i != G.vexNum; ++i) {
    		cout << "please input no" << i+1 << " vertex: ";
    		cin >>  G.vex[i];					// 自定义顶点序号 
    	}
    	for (int i = 0; i != G.vexNum; ++i) {
    		for (int j = 0; j != G.vexNum; ++j) {
    			G.arc[i][j] = INFINITY;
    		}
    	}
    	for (int k = 0; k != G.edgeNum; ++k) {
    		cout << "please input the vertex of edge(vi, vj) and weight: ";
    		int i, j, w;
    		cin >> i >> j >> w;
    		G.arc[i][j] = w;
    		G.arc[j][i] = G.arc[i][j];			
    	}
    }
    
    void prim(Graph &G, int src)
    {
    	memset(dist, INFINITY, VERTEX_NUM);
    	memset(vis, false, true);
    	for (int i = 0; i != G.vexNum; ++i) {
    		pre[i] = src;
    		dist[i] = G.arc[src][i];
    	}
    	vis[src] = true;
    	int lowcost;
    	int lowcostIndex;
    	for (int cnt = 1; cnt != G.vexNum; ++cnt) {
    		lowcost = INFINITY;
    		for (int i = 0; i != G.vexNum; ++i) {
    			if (dist[i] < lowcost && !vis[i]) {
    				lowcost = dist[i];		// 没意义,最小生成树考虑的是到生成树而不是源点 
    				lowcostIndex = i;
    			}
    		}
    		vis[lowcostIndex] = true;
    		for (int i = 0; i != G.vexNum; ++i) {
    			if (G.arc[lowcostIndex][i] != INFINITY && G.arc[lowcostIndex][i] < dist[i] && !vis[i])
    				dist[i] = G.arc[lowcostIndex][i];
    				pre[i] = lowcostIndex;
    		}
    	}
    }
    
    
    int main()
    {
    	Graph G;
    	createGraph(G);
    	int src = 0;
    	prim(G, src);
    	int sum = 0;
    	for (int i = 0; i != G.vexNum; ++i) {
    		if (src == i) continue;
    		sum += dist[i];
    	}
    	cout << sum << endl;
    } 
    

      

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  • 原文地址:https://www.cnblogs.com/xzxl/p/8652293.html
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