Shortest Path [3]

3748 단어 데이터 구조
Write a program to not only find the weighted shortest distances, but also count the number of different minimum paths from any vertex to a given source vertex in a digraph. It is guaranteed that all the weights are positive.
Format of functions:
void ShortestDist( MGraph Graph, int dist[], int count[], 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. The number of different minimum paths from V to the source S is supposed to be stored in count[V] and count[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 count[], Vertex S );

int main()
{
    int dist[MaxVertexNum], count[MaxVertexNum];
    Vertex S, V;
    MGraph G = ReadG();

    scanf("%d", &S);
    ShortestDist( G, dist, count, S );

    for ( V=0; VNv; V++ )
        printf("%d ", dist[V]);
    printf("
"); for ( V=0; VNv; V++ ) printf("%d ", count[V]); printf("
"); 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 30
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 
1 1 4 1 1 3 0 3
Result:
void ShortestDist( MGraph Graph, int dist[], int count[], Vertex S )
{
 Vertex know[MaxVertexNum];
 Vertex i,j;
 Vertex min;
 Vertex dist2[MaxVertexNum];
 for(i=0;iNv;i++)
 {
  know[i]=0;
  dist[i]=INFINITY;
  dist2[i]=INFINITY;
  count[i]=0;
 }
    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];
        }         
     }
    }
   }
   
      for(i=0;iNv;i++)
   {
    know[i]=0;
   }
   dist2[S]=0;
   count[S]=1;
   while(1)
 {
  j=-1;
  min=INFINITY;
    for(i=0;iNv;i++)
    {
     if(know[i]==0&&dist2[i]Nv;i++)
    {
     if(know[i]==0)
     {
        if(dist2[j]+Graph->G[j][i]G[j][i];
      count[i]=count[j];
        }
     else if(dist[i]!=INFINITY&&dist2[j]+Graph->G[j][i]==dist[i])
      count[i]=count[j]+count[i];
     }
    }
   }
      for(i=0;iNv;i++)
    {
     if(dist[i]==INFINITY)
     {
      dist[i]=-1;
     }
    }
}

좋은 웹페이지 즐겨찾기