最短路径Dijkstra(邻接矩阵)

最新推荐文章于 2022-09-20 08:23:55 发布

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最新推荐文章于 2022-09-20 08:23:55 发布

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CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/venow/archive/2012/08/20/2644247.html

本文介绍了一个使用邻接矩阵实现的Dijkstra算法，用于寻找加权图中两点间的最短路径。通过读取文件构造图，并输出从指定起点到其它各点的最短路径长度。

#include "stdafx.h"
#include <iostream>
#include <fstream>
#include <Windows.h>

using namespace std;

#define INFINITY 65535
#define MAX_VERTEX_NUM 20  //顶点最多个数
#define LENGTH 5           //顶点字符长度

//*********************************邻接矩阵***********************************begin
//邻接矩阵
typedef struct _Graph
{
    int matrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
    char vexs[MAX_VERTEX_NUM][LENGTH];
    int vexnum;
    int arcs;
}Graph;

int LocateVex(const Graph & g, char name[LENGTH])
{
    for (int i = 0; i < g.vexnum; i++)
    {
        if (0 == strcmp(g.vexs[i], name))
        {
            return i;
        }
    }
    return -1;
}

//图的建造
void CreateGraph(Graph &g)
{
    ifstream fcin(_T("dijkstra.txt"));
    fcin>>g.vexnum;
    for (int i = 0; i < g.vexnum; i++)
    {
        for (int j = 0; j < g.vexnum; j++)
        {
            g.matrix[i][j] = INFINITY;
        }
    }
    for (int i = 0; i < g.vexnum; i++)
    {
        fcin>>g.vexs[i];
    }
    fcin>>g.arcs;
    char arcHead[LENGTH];
    char arcTail[LENGTH];
    int weight;
    for (int i = 0; i < g.arcs; i++)
    {
        memset(arcHead, 0, LENGTH);
        memset(arcTail, 0, LENGTH);
        fcin>>arcTail>>arcHead>>weight;
        int x = LocateVex(g, arcHead);
        int y = LocateVex(g, arcTail);
        //g.matrix[x][y] = weight;
        g.matrix[y][x] = weight;
    }
}

//************************************邻接矩阵**************************************end
//************************************最短路径************************************begin

typedef int PathMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
typedef int ShortPathTable[MAX_VERTEX_NUM];

void ShortestPath_DIJ(Graph g, int v0, PathMatrix &P, ShortPathTable &D)
{
    bool final[MAX_VERTEX_NUM];
    int v = 0;
    for (; v < g.vexnum; v++)
    {
        final[v] = false;
        D[v] = g.matrix[v0][v];
        for (int w = 0; w < g.vexnum; w++)
        {
            P[v][w] = false;
        }
        if (D[v] < INFINITY)
        {
            P[v][v0] = true;
            P[v][v] = true;
        }
    }
    D[v0] = 0;
    final[v0] = true;
    for (int i = 1; i < g.vexnum; i++)
    {
        int min = INFINITY;
        for (int w = 0; w < g.vexnum; w++)
        {
            if (!final[w])
            {
                if (D[w] < min)
                {
                    v = w;
                    min = D[w];
                }
            }
        }
        final[v] = true;
        for (int w = 0; w < g.vexnum; w++)
        {
            if (!final[w] && (min + g.matrix[v][w]) < D[w])
            {
                D[w] = min + g.matrix[v][w];
                for (int j = 0; j < g.vexnum; j++)
                {
                    P[w][j] = P[v][j];
                }
                
                P[w][w] = true;
            }
        }
    }
}

//************************************最短路径************************************end
//辅助函数，设置控制台的颜色
void SetConsoleTextColor(WORD dwColor)
{
    HANDLE handle = GetStdHandle(STD_OUTPUT_HANDLE);
    if (INVALID_HANDLE_VALUE == handle)
    {
        return;
    }
    SetConsoleTextAttribute(handle, dwColor);
}

int _tmain(int argc, _TCHAR* argv[])
{
    Graph graph;
    CreateGraph(graph);

    PathMatrix P;
    ShortPathTable D;
    SetConsoleTextColor(FOREGROUND_GREEN | FOREGROUND_INTENSITY);
    cout<<"************************最短路径**************************"<<endl<<endl;
    ShortestPath_DIJ(graph, 0, P, D);
    cout<<"最短路径数组p[i][j]如下:"<<endl;
    for(int i = 0; i < graph.vexnum; ++i)
    {
        for(int j=0;j<graph.vexnum;++j)
            cout<<P[i][j]<<"  ";
        cout<<endl;
    }
    cout<<"源点到各顶点的最短路径长度为:"<<endl;
    for(int i = 1;i < graph.vexnum; ++i)
    {
        if (INFINITY == D[i])
        {
            cout<<graph.vexs[0]<<"  "<<graph.vexs[i]<<"  无"<<endl; 
        }
        else
        {
            cout<<graph.vexs[0]<<"  "<<graph.vexs[i]<<"  "<<D[i]<<endl; 
        }
    }

    return 0;
}

界面运行如下：

建造图用到的dijkstra.txt如下：

6
V0 V1 V2 V3 V4 V5
8
V0 V2 10
V0 V4 30
V0 V5 100
V1 V2 5
V2 V3 50
V3 V5 10
V4 V3 20
V4 V5 60

转载于:https://www.cnblogs.com/venow/archive/2012/08/20/2644247.html