4-2 Shortest Path [4]

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 
#include 

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; VNv; V++ )
        printf("%d ", dist[V]);
    printf("\n");
    for ( V=0; VNv; 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 11
0 4 5
0 7 10
1 7 40
3 0 40
3 1 20
3 2 100
3 7 70
4 7 5
6 2 1
7 5 3
7 2 50
3

Sample Output:

40 20 100 0 45 53 -1 50 
3 3 3 -1 0 7 -1 0

result:

void ShortestDist( MGraph Graph, int dist[], int path[], Vertex S )
{
 
 Vertex know[MaxVertexNum];
 Vertex i,j;
 Vertex min;
 for(i=0;iNv;i++)
 {
  know[i]=0;
  dist[i]=INFINITY;
  path[i]=-1;
 }
    dist[S]=0;
while(1)
 {
  j=-1;
  min=INFINITY;
    for(i=0;iNv;i++)
    {
     if(know[i]==0&&dist[i]Nv;i++)
    {
     if(know[i]==0)
     {
        if(dist[j]+Graph->G[j][i]G[j][i];
      path[i]=j;
        }         
     }
    }
   }
      for(i=0;iNv;i++)
    {
     if(dist[i]==INFINITY)
     {
      dist[i]=-1;
     }
    }
    path[S]=-1;
    dist[S]=0;
}