最短路算法

根据大话数据结构整理

/***********************************输入：邻接矩阵vMatrix*输出：最短路径***********************************/#include <iostream>#include <vector>using namespace std;#define INF 65535/*********Dijkstra************/void Dijstra(vector<vector<int>>&Matrix, int v0){    vector<int> patharc(Matrix.size());    vector<int> shortPathTable(Matrix.size());    vector<bool> visit(Matrix.size());    for (unsigned i = 0; i < Matrix.size(); i++)        shortPathTable[i] = Matrix[v0][i];    visit[v0] = true;//v0点已访问    for (unsigned v = 1; v < Matrix.size(); v++)//只需要找到n-1个点组成路径    {        //找到所有未访问点最小权值        int min = INF;        int k;              for (unsigned w = 0; w < Matrix.size(); w++)        {            if (!visit[w] && shortPathTable[w] < min)            {                k = w;                min = shortPathTable[w];            }        }        visit[k] = true;        //更新权值        for (unsigned w = 0; w < Matrix.size(); w++)        {            if (!visit[w] && (min + Matrix[k][w] < shortPathTable[w]))            {                shortPathTable[w] = min + Matrix[k][w];                patharc[w] = k;//表示w的前驱点是k            }        }    }    //输出路径    cout << "（Dijstra）顶点" << v0 << "到各点的最短路径：" << endl;    vector<vector<int>> vvOut(Matrix.size());    for (unsigned i = 0; i < vvOut.size(); i++)    {        int end = i;        vvOut[i].push_back(i);        while (end != v0)        {            end = patharc[end];            vvOut[i].push_back(end);        }        if (i == v0)            vvOut[i].push_back(v0);    }    for (unsigned i = 0; i < vvOut.size(); i++)    {        auto iter = vvOut[i].rbegin();        cout << *iter++;        for (; iter != vvOut[i].rend(); iter++)            cout << "->" << *iter;        cout << endl;    }}/*********Floyd****************/void Floyd(vector<vector<int>>&Matrix){    //初始化    vector<vector<int>> pathMatrix(Matrix.size(), vector<int>(Matrix.size()));    vector<vector<int>> shortPathTable(Matrix);    for (unsigned v = 0; v < Matrix.size(); v++)        for (unsigned w = 0; w < Matrix.size(); w++)            pathMatrix[v][w] = w;    //3层循环    for (unsigned k = 0; k < Matrix.size(); k++)    {        for (unsigned v = 0; v < Matrix.size(); v++)        {            for (unsigned w = 0; w < Matrix.size(); w++)            {                if (shortPathTable[v][w] > shortPathTable[v][k] + shortPathTable[k][w])                {                    shortPathTable[v][w] = shortPathTable[v][k] + shortPathTable[k][w];                    pathMatrix[v][w] = pathMatrix[v][k];                }            }        }    }    for (unsigned v = 0; v < Matrix.size(); v++)    {        cout << "（Floyd）顶点" << v << "到各点的最短路径：" << endl;        for (unsigned w = 0; w < Matrix.size(); w++)        {                       cout << v;            int end = pathMatrix[v][w];            while (end != w)            {                cout << "->" << end;                end = pathMatrix[end][w];            }            cout << "->" << w << endl;        }    }}/*********主函数****************/int main(){       int nodeNum, N, data1, data2, data3;    cin >> nodeNum >> N;    /******建立邻接矩阵**********/    vector<vector<int>> vMatrix(nodeNum, vector<int>(nodeNum, INF));    for (int j = 0; j < nodeNum; j++)        vMatrix[j][j] = 0;    for (int i = 0; i < N; i++)    {        cin >> data1 >> data2 >> data3;        vMatrix[data1][data2] = data3;        vMatrix[data2][data1] = data3;    }    Dijstra(vMatrix, 0);    Floyd(vMatrix);    return 0;}/*case:顶点数n,边数m,m条边*//*9150 1 100 5 111 2 181 8 121 6 162 3 222 8 83 4 203 7 163 6 243 8 214 5 264 7 75 6 176 7 19*/