c编写 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 
#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

#include 
#include 




#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;
}


MGraph ReadG()
{
	MGraph P;
	int i,j,k;
	P=(MGraph)malloc(sizeof(struct GNode));
	scanf("%d%d",&P->Nv,&P->Ne);
	for( j=0;j		for( k=0;k			P->G[j][k]=-1;
		}
	}
	for( i=0;iNe;i++){
		int m,n;
		scanf("%d%d",&m,&n);
		scanf("%d",&P->G[m][n]);
	}
	
	return P;
}




/* Your function will be put here */
void ShortestDist( MGraph Graph, int dist[], int path[],Vertex S)
{
	int findmin(MGraph graph,int d[],int know[]);
	int i;
	Vertex known[MaxVertexNum];
	Vertex V,W;
	for(i=0;iNv;i++){
		dist[i]=INFINITY;
		path[i]=-1;
		known[i]=-1;
	}
	dist[S]=0;
	for(;;){
		V=findmin(Graph,dist,known);
		if(V==-1)
			break;
		known[V]=1;
		for(W=0;WNv;W++){
			if(Graph->G[V][W]>0){
					if(dist[V]+Graph->G[V][W]						dist[W]=dist[V]+Graph->G[V][W];
						path[W]=V;
					}


			}
		}
	}
	for(i=0;iNv;i++){
		if(dist[i]==INFINITY){
			dist[i]=-1;
			}
	}
}
int findmin(MGraph graph,int d[],int know[])
{
	int i;
	int count=0;
	int min;
	for(min=0;minNv;min++){
		if(know[min]==-1)
			break;
	}
	for(i=0;iNv;i++){
		if(d[min]>d[i]&&know[i]==-1)
			min=i;
		if(know[i]==1)
			count++;
	}
	if(count!=graph->Nv)
		return min;
	else return -1;
}