6-17 Shortest Path [4]（25 分）

6-17 Shortest Path [4]（25 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 toV, 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

作者: DS课程组

单位: 浙江大学

时间限制: 400ms

内存限制: 64MB

代码长度限制: 16KB

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 path[], 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;
path[i] = -1;
}
Sure[V] = 1;
dist[V] = 0;
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];
path[i] = V;
}
}
else {
dist[i] = dist[V] + Graph->G[V][i];
path[i] = V;
}
}
}
V = FindMin(dist, Sure, Graph->Nv);
if (V != -1)
Sure[V] = 1;
}
for (Vertex i = 0; i Nv; i++)
if (dist[i] == INFINITY)
dist[i] = -1;
}