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

 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 <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 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; V<G->Nv; V++ )
printf("%d ", dist[V]);
printf("\n");
for ( V=0; V<G->Nv; 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 <Graph->Nv; i++)
if (dist[i] == INFINITY)
dist[i] = -1;
}