技術標籤：PTA演算法

6-12Shortest Path [2](25point(s))

Write a program to find the weighted shortest distances 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[], Vertex S );

whereMGraph

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.

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[], Vertex S );

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

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

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

    return 0;
}

/* Your function will be put here */
 

Sample Input (for the graph shown in the figure):

7 9
0 1 1
0 5 1
0 6 1
5 3 1
2 1 2
2 6 3
6 4 4
4 5 5
6 5 12
2

Sample Output:

-1 2 0 13 7 12 3 

Example:

void ShortestDist( MGraph Graph, int dist[], Vertex S )
{
    bool visited[MaxVertexNum];
    for(int i = 0; i < Graph->Nv; i++) {
        visited[i] = false;
        dist[i] = -1;
    }
    dist[S] = 0;
    for(int i = 0; i < Graph->Nv; i++) {
        int min = -1;
        for(int j = 0; j < Graph->Nv; j++) {
            if(!visited[j] && dist[j] != -1) {
                if(min == -1 || dist[min] > dist[j]) {
                    min = j;
                }
            }
        }
        if(min == -1) break;
        visited[min] = true;
        for(int j = 0; j < Graph->Nv; j++) {
            if(j != min && Graph->G[min][j] < INFINITY) {
                if(dist[j] == -1 || (dist[j] > dist[min] + Graph->G[min][j])) {
                    dist[j] = dist[min] + Graph->G[min][j];
                }
            }
        }
    }
}

思路：

使用迪傑斯特拉演算法，計算最短距離