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 
#include 
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*/
/*
9
15
0 1 10
0 5 11
1 2 18
1 8 12
1 6 16
2 3 22
2 8 8
3 4 20
3 7 16
3 6 24
3 8 21
4 5 26
4 7 7
5 6 17
6 7 19
*/