Dijkstra算法求最短路径

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>

#pragma warning(disable:4996)

#define MAX_NAME 10
#define MAX_VERTEX_NUM 26

typedef char VertexType[MAX_NAME];
typedef unsigned int AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];//邻接距阵

struct MGraph//定义网
{
    VertexType vexs[MAX_VERTEX_NUM];
    AdjMatrix arcs;
    int vexnum, arcnum;
};

int LocateVex( MGraph& G, VertexType u ) //定位
{
    register int i;

    for ( i = 0; i < G.vexnum; ++ i )
    {
        if ( strcmp( u, G.vexs[i] ) == 0 )
        {
            return i;
        }
    }
    return -1;
}

void CreateDN( MGraph& G ) //建网
{
    int i, j, k, w;
    VertexType va, vb;

    printf( "请输入有向网G的顶点数和弧数(以空格作为间隔)
" );
    scanf( "%d %d", &G.vexnum, &G.arcnum );

    memset( G.vexs, 0, sizeof( G.vexs ) );
    printf( "请输入%d个顶点的值(<%d个字符):
", G.vexnum, MAX_NAME );
    for ( i = 0; i < G.vexnum; ++ i )
    {
        scanf( "%s", G.vexs[i] );
    }

    memset( G.arcs, 0xff, sizeof( G.arcs ) );
    printf( "请输入%d条弧的弧尾 弧头 权值(以空格作为间隔): 
", G.arcnum );
    for ( k = 0; k < G.arcnum; ++ k )
    {
        scanf( "%s%s%d%*c", va, vb, &w );
        i = LocateVex( G, va );
        j = LocateVex( G, vb );
        G.arcs[i][j] = w;
    }
}

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

void ShortestPath_DIJ( MGraph& G, int v0, PathMatrix P, ShortPathTable D )
{
    int v, w, i;
    unsigned int min;
    unsigned int final[MAX_VERTEX_NUM];

    for ( v = 0; v < G.vexnum; ++ v )
    {
        final[v] = 0;
        D[v] = G.arcs[v0][v];

        memset( P[v], 0, sizeof( int ) * G.vexnum );

        if ( D[v] < UINT_MAX )
        {
            P[v][v0] = P[v][v] = 1;
        }
    }

    D[v0] = 0;
    final[v0] = 1;
    for ( i = 1; i < G.vexnum; ++ i )
    {
        min = UINT_MAX;
        for ( w = 0; w < G.vexnum; ++ w )
        {
            if ( !final[w] && D[w] < min )
            {
                v = w;
                min = D[w];
            }
        }

        final[v] = 1;

        for ( w = 0; w < G.vexnum; ++ w )
        {
            if ( !final[w] && min < UINT_MAX && G.arcs[v][w] < UINT_MAX && ( min + G.arcs[v][w] < D[w] ) )
            {
                D[w] = min + G.arcs[v][w];
                memcpy( P[w], P[v], sizeof( int ) * G.vexnum );
                P[w][w] = 1;
            }
        }
    }
}

int main()
{
    int i, j;
    MGraph g;
    PathMatrix p;
    ShortPathTable d;

    CreateDN( g );

    ShortestPath_DIJ( g, 0, p, d ); //以g中位置为0的顶点为源点，球其到其余各顶点的最短距离。存于d中

    printf( "最短路径数组p[i][j]如下:
" );
    for ( i = 0; i < g.vexnum; ++ i )
    {
        for ( j = 0; j < g.vexnum; ++ j )
        {
            printf( "%2d", p[i][j] );
        }
        printf( "
" );
    }

    printf( "%s到各顶点的最短路径长度为：
", g.vexs[0] );
    for ( i = 1; i < g.vexnum; ++i )
    {
        if ( d[i] != UINT_MAX )
        {
            printf( "%s-%s:%d
", g.vexs[0], g.vexs[i], d[i] );
        }
        else
        {
            printf( "%s-%s:无路
", g.vexs[0], g.vexs[i] );
        }
    }

    system( "PAUSE" );
    return 0;
}

/*
请输入有向网G的顶点数和弧数(以空格作为间隔)
6 8
请输入6个顶点的值(<10个字符):
v1
v2
v3
v4
v5
v6
请输入8条弧的弧尾 弧头 权值(以空格作为间隔):
v1 v3 10
v1 v5 30
v1 v6 100
v2 v3 5
v3 v4 50
v4 v6 10
v5 v4 20
v5 v6 60
最短路径数组p[i][j]如下:
 0 0 0 0 0 0
 0 0 0 0 0 0
 1 0 1 0 0 0
 1 0 0 1 1 0
 1 0 0 0 1 0
 1 0 0 1 1 1
v1到各顶点的最短路径长度为：
v1-v2:无路
v1-v3:10
v1-v4:50
v1-v5:30
v1-v6:60
请按任意键继续. . .
*/