6-16 Shortest Path [3]（25 分）

6-16 Shortest Path [3]（25 分）

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 <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 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; V<G->Nv; V++ )
printf("%d ", dist[V]);
printf("\n");
for ( V=0; V<G->Nv; V++ )
printf("%d ", count[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 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

Vertex FindMin(int dist[], int Sure[], int N)
{
int i = 0, j = 0;
while (Sure[i] == 1 || dist[i] == INFINITY)
i++;
j = i + 1;
while (j < N) {
if (dist[i] > dist[j] && Sure[j] != 1) {
i = j;
return i;
}
else
j++;
}
if (i >= N)
return -1;
else
return i;
}

void ShortestDist(MGraph Graph, int dist[],int count[], Vertex S)
{
Vertex V = S;
int* Sure = (int*)malloc(Graph->Nv * sizeof(int));
memset(Sure, 0, Graph->Nv * sizeof(int));
for (int i = 0; i < MaxVertexNum; i++) {
dist[i] = INFINITY;
count[i] = 0;
}
Sure[V] = 1;
dist[V] = 0;
count[V] = 1;
while (V != -1) {
for (Vertex i = 0; i < Graph->Nv; i++) {
if (Graph->G[V][i] != INFINITY && V != i) {
if (dist[i] != INFINITY) {
if (dist[i] > dist[V] + Graph->G[V][i])
dist[i] = dist[V] + Graph->G[V][i];
else if (dist[i] == dist[V] + Graph->G[V][i])
count[i] = count[i] + count[V];
}
else {
dist[i] = dist[V] + Graph->G[V][i];
count[i] = count[V];
}
}
}
V = FindMin(dist, Sure, Graph->Nv);
if (V != -1) 
Sure[V] = 1;
}
for (Vertex i = 0; i <Graph->Nv; i++)
if (dist[i] == INFINITY)
dist[i] = -1;
}