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)\n" );
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):\n", 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): \n", 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:\n" );
for ( i = 0; i < g.vexnum; ++ i )
{
for ( j = 0; j < g.vexnum; ++ j )
{
printf( "%2d", p[i][j] );
}
printf( "\n" );
}

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