图——普里姆算法——构建最小生成树（采用邻接矩阵的方式存储）

include "stdafx.h"

#include
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#include
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#include
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#include 
#include
#include

using namespace std;

typedef struct
{
    vector vexs;//顶点表
    vector> arcs;//边表
    int vexnums, arcnums;
}AMGraph; //邻接矩阵表示一个图

class Solution {
public:
    void CreateGraph(AMGraph &G)
    {
        int num = 0;
        cout << "请输入顶点个数：";
        cin >> num;
        G.vexnums = num;
        cout << "请输入边的个数：";
        cin >> num;
        G.arcnums = num;
        //依次输入各个顶点
        cout << "依次输入各个顶点:" << endl;
        for (int i = 0; i < G.vexnums; ++i)
        {
            int ch;
            cin >> ch;
            G.vexs.push_back(ch);
        }
        for (int i = 0; i < G.vexnums; ++i)//初始化各个边
        {
            vector vec;
            vec.clear();
            for (int j = 0; j < G.vexnums; ++j)
            {
                vec.push_back(0);
            }
            G.arcs.push_back(vec);

        }
        cout << "依次输入两个关联的顶点：" << endl;
        for (int i = 0; i < G.arcnums; ++i)
        {
            int vex1;
            int vex2;
            cin >> vex1 >> vex2;
            G.arcs[vex1][vex2] = 1;
            G.arcs[vex2][vex1] = 1;//
            cout << "一条边构建成功！" << endl;
        }
        GetGraph(G);
    }

    //为了试验方便，我们自己创建一个固定的图
    void CreatAGraph(AMGraph &G)
    {
        //创建顶点
        G.vexnums = 6;
        G.arcnums = 6;
        for (int i = 0; i < G.vexnums; ++i)
        {
            G.vexs.push_back(i);
        }
        for (int i = 0; i < G.vexnums; ++i)//初始化各个边
        {
            vector vec;
            vec.clear();
            for (int j = 0; j < G.vexnums; ++j)
            {
                vec.push_back(0);
            }
            G.arcs.push_back(vec);
        }
        G.arcs[0][1] = 6;
        G.arcs[1][0] = 6;
        G.arcs[0][2] = 1;
        G.arcs[2][0] = 1;
        G.arcs[0][3] = 5;
        G.arcs[3][0] = 5;

        G.arcs[1][2] = 5;
        G.arcs[2][1] = 5;
        G.arcs[1][4] = 3;
        G.arcs[4][1] = 3;

        G.arcs[2][4] = 6;
        G.arcs[4][2] = 6;
        G.arcs[2][5] = 4;
        G.arcs[5][2] = 4;

        G.arcs[3][2] = 5;
        G.arcs[3][2] = 5;
        G.arcs[3][5] = 2;
        G.arcs[5][3] = 2;
        

        G.arcs[4][5] = 6;
        G.arcs[5][4] = 6;

        GetGraph(G);
    }


    vector visited;//用来标注对应的节点是否被访问，如果被访问，则访问下一个节点
    void DFSTraverse(AMGraph G)//深度优先遍历
    {
        visited.clear();
        //初始化，假设每个节点都没有被访问
        for (int i = 0; i < G.vexnums; ++i)
        {
            visited.push_back(0);//没访问的都设置为0，访问过的都设置为1
        }
        for (int v = 0; v < G.vexnums; ++v)
        {
            if (visited[v] == 0)//保证节点没有被访问
                DFS(G, v);
        }
        cout << endl;
    }
    void DFS(AMGraph G, int v) //对i节点进行深度优先遍历
    {
        cout << "v_" << v << "  ";
        visited[v] = 1;
        for (int i = 0; i < G.vexnums; ++i)
        {
            if (G.arcs[v][i] != 0 && visited[i] == 0)//存在边,且i节点没有访问过
                DFS(G, i);
        }
        return;
    }

    void  BFSTraverse(AMGraph G)//广度优先遍历
    {
        visited.clear();
        for (int i = 0; i < G.vexnums; ++i)
        {
            visited.push_back(0);//没访问的都设置为0，访问过的都设置为1
        }
        for (int v = 0; v < G.vexnums; ++v)
        {
            if (visited[v] == 0 )
            {
                cout << "v_" << v << "  ";//节点没有被访问
                visited[v] = 1;
            }
            for (int i = 0; i < G.vexnums; ++i)
            {
                if (visited[i] == 0 && G.arcs[v][i] != 0)
                {
                    cout << "v_" << i << "  ";//节点没有被访问
                    visited[i] = 1;
                }
            }
        }
        cout << endl;
    }
    void BFS(AMGraph G, int v)
    {
        if (visited[v] == 0)
        {
            cout << "v_" << v << "  ";//节点没有被访问
            visited[v] = 1;
        }

        for (int i = 0; i < G.vexnums; ++i)
        {
            if (visited[i] == 0)
            {
                cout << "v_" << v << "  ";//节点没有被访问
                visited[v] = 1;
            }
        }
    }

    void  GetGraph(AMGraph G)
    {
        cout << "顶点信息：" << endl;
        for (int i = 0; i < G.vexnums; ++i)
        {
            cout << G.vexs[i] << "  ";
        }
        cout << endl;
        cout << "边的信息：" << endl;
        for (int i = 0; i < G.vexnums; ++i)
        {
            for (int j = 0; j < G.vexnums; ++j)
            {
                cout << G.arcs[i][j] << "  ";
            }
            cout << endl;
        }
    }
    //用普利姆算法构建最小生成树，最小生成树存在返回T
    vectornodes;//存储已经存在在U集合里面的点，每次从剩下的节点选择离nodes集合里面距离最小的节点
vectorrenodes;//存储剩余的节点

    AMGraph  MinSpanTree_Prim(AMGraph G)
    {
        
        AMGraph T;
        T.vexnums = G.vexnums;
        //初始化顶点
        for (int i = 0; i < T.vexnums; ++i)
        {
            T.vexs.push_back(i);
        }
        //初始化边
        for (int i = 0; i < T.vexnums; ++i)
        {
            renodes.push_back(i);//向renodes中插入节点
            vector vec;
            
            for (int j = 0; j < T.vexnums; ++j)
            {
            //  T.arcs[i][j] = 0;   //初始化T
            
                vec.push_back(0);
            }
            T.arcs.push_back(vec);
        }
        
        //从v_0开始选边
        nodes.push_back(0);//第0个边给node节点
        renodes.erase(renodes.begin()+0);

    
        while (nodes.size()!=T.vexnums)
        {
            int minDistance = G.arcs[nodes[0]][renodes[0]];//记录最小距离
        
            int minNode1 = nodes[0];
            int minNode2 = renodes[0];//记录离最小距离的节点
            int flag = 0;//renodes中要删除的节点
            bool visist = false;
            int i = 0, j = 0;
            for ( i = 0; i < nodes.size(); ++i)//选择距离最小的边
            {
                for ( j = 0; j < renodes.size(); ++j)
                {
                    //找到最小距离，且最小距离和原来节点不形成回路
                    //if (visist == false && minDistance==0 && G.arcs[nodes[i]][renodes[j]] != 0 ) //距离不等于0 //只执行一次，找到最短距离
                    if ( minDistance == 0 && G.arcs[nodes[i]][renodes[j]] != 0) //距离不等于0 //只执行一次，找到最短距离
                    {
                        minDistance = G.arcs[nodes[i]][renodes[j]];
                        minNode1 = nodes[i];
                        minNode2 = renodes[j];
                        flag = j;
                    //  visist = true;  //visit保证这条语句只访问一次
                    //  cout << "flag:" << flag << endl;
                    }
                    if (G.arcs[nodes[i]][renodes[j]] != 0 && minDistance > G.arcs[nodes[i]][renodes[j]])
                    {
                        minDistance = G.arcs[nodes[i]][renodes[j]];
                    minNode1 = nodes[i];
                        minNode2 = renodes[j];
                        flag = j;
                    //  cout << "flag:" << flag << endl;
                    }
                    
                }
            //  cout << "最短距离是：" << minDistance << endl;
            }
            
            T.arcs[minNode1][minNode2] = minDistance;
            T.arcs[minNode2][minNode1] = minDistance;
            T.arcnums++;
            nodes.push_back(minNode2);
            //cout << "flag:" << flag << endl;
            cout << "nodes:" ;
            print(nodes);
            cout << endl;
            
            renodes.erase(renodes.begin()+flag);
            //cout << "renodes:";
            //print(renodes);
            //cout << endl;
            //cout << endl;
            //cout << "T.vexnums:" << T.vexnums;
            //cout << "nodes.size():" << nodes.size();
        }
        return T;
    }
    void print(vector vec)
    {
        for (int i = 0; i < vec.size(); ++i)
            cout << vec[i] << "  ";
    }
    //用克鲁斯算法构建最小生成树，最小生成树返回T
    /*AMGraph MinSpanTree_Kruskal(AMGraph G)
    {

    }*/
};
int main()
{


    Solution so;

    AMGraph G;
    //so.CreateGraph(G);
    so.CreatAGraph(G);
    cout << "G深度优先遍历：" << endl;
    so.DFSTraverse(G);

    cout << "G广度优先遍历：" << endl;
    so.BFSTraverse(G);
    //so.GetGraph(G);

    AMGraph T;
    T = so.MinSpanTree_Prim(G);
    cout << "T深度优先遍历：" << endl;
    so.DFSTraverse(T);
    cout << "T的信息：" << endl;
    so.GetGraph(T);

    return 0;
}

转载于:https://www.cnblogs.com/wdan2016/p/6183844.html