4-2 Shortest Path [4]

4-2 Shortest Path [4]   (10分)

Write a program to find the weighted shortest distances from any vertex to a given source vertex in a digraph. If there is more than one minimum path from v to w, a path with the fewest number of edges is chosen. It is guaranteed that all the weights are positive and such a path is unique for any vertex.

Format of functions:

void ShortestDist( MGraph Graph, int dist[], int path[], Vertex S );

where MGraph is defined as the following:

typedef struct GNode *PtrToGNode;struct GNode{    int Nv;    int Ne;    WeightType G[MaxVertexNum][MaxVertexNum];};typedef PtrToGNode MGraph;

The shortest distance from V to the source S is supposed to be stored in dist[V]. If V cannot be reached from S, store -1 instead. If W is the vertex being visited right before V along the shortest path from S to V, then path[V]=W. If V cannot be reached from S, path[V]=-1, and we have path[S]=-1.

Sample program of judge:

#include <stdio.h>#include <stdlib.h>typedef enum {false, true} bool;#define INFINITY 1000000#define MaxVertexNum 10  /* maximum number of vertices */typedef int Vertex;      /* vertices are numbered from 0 to MaxVertexNum-1 */typedef int WeightType;typedef struct GNode *PtrToGNode;struct GNode{    int Nv;    int Ne;    WeightType G[MaxVertexNum][MaxVertexNum];};typedef PtrToGNode MGraph;MGraph ReadG(); /* details omitted */void ShortestDist( MGraph Graph, int dist[], int path[], Vertex S );int main(){    int dist[MaxVertexNum], path[MaxVertexNum];    Vertex S, V;    MGraph G = ReadG();    scanf("%d", &S);    ShortestDist( G, dist, path, S );    for ( V=0; V<G->Nv; V++ )        printf("%d ", dist[V]);    printf("\n");    for ( V=0; V<G->Nv; V++ )        printf("%d ", path[V]);    printf("\n");    return 0;}/* Your function will be put here */

Sample Input (for the graph shown in the figure):

8 110 4 50 7 101 7 403 0 403 1 203 2 1003 7 704 7 56 2 17 5 37 2 503

Sample Output:

40 20 100 0 45 53 -1 50 
3 3 3 -1 0 7 -1 0
void ShortestDist( MGraph Graph, int dist[], int path[], Vertex S )  {      int visit[MaxVertexNum];      int i;       /*初始化*/      for(int i=0; i<Graph->Nv; i++) {          dist[i]=Graph->G[S][i];          path[i]=S;          visit[i]=0;      }      //原点的初始化    visit[S]=1;    dist[S]=0;      path[S]=-1;    /*书上的dijikstra算法的实现*/          while(1) {          int min=INFINITY;        int v=-1;         for(i=0; i<Graph->Nv; i++)  {              if(!visit[i]&&dist[i]<min)  {                     min=dist[i];                v=i;              }          }          /*找不到最小的dist，跳出循环*/        if(v==-1)        break;          visit[v]=1;          for(i=0; i<Graph->Nv; i++){  //遍历v的所有邻接点，如果经过v到其邻接点i的距离比原来到i更短，更新            if(!visit[i]&&dist[v]+Graph->G[v][i]<dist[i]){                  dist[i]=dist[v]+Graph->G[v][i];                  path[i]=v;    //并且计i前为v            }             }       }      for(i=0; i<Graph->Nv; i++)  {  //按题目要求把到不了的点初始化        if(dist[i]==INFINITY)  {              dist[i]=-1;              path[i]=-1;          }      }  }