技術標籤：PTA演算法

6-11Shortest Path [1](25point(s))

Write a program to find the unweighted shortest distances from any vertex to a given source vertex in a digraph.

Format of functions:

void ShortestDist( LGraph Graph, int dist[], Vertex S );

whereLGraphis defined as the following:

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;
 

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 MaxVertexNum 10  /* maximum number of vertices */
typedef int Vertex;      /* vertices are numbered from 0 to MaxVertexNum-1 */

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

LGraph ReadG(); /* details omitted */

void ShortestDist( LGraph Graph, int dist[], Vertex S );

int main()
{
    int dist[MaxVertexNum];
    Vertex S, V;
    LGraph 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
0 5
0 6
5 3
2 1
2 6
6 4
4 5
6 5
2

Sample Output:

-1 1 0 3 2 2 1 

Example:

void ShortestDist( LGraph Graph, int dist[], Vertex S )
{
    bool visited[MaxVertexNum];
    for(int i = 0; i < Graph->Nv; i++) {
        dist[i] = -1;
        visited[i] = false;
    }
    dist[S] = 0;
    for(int i = 0; i < Graph->Nv; i++) {
        PtrToAdjVNode node;
        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;
        node = Graph->G[min].FirstEdge;
        while(node) {
            if(!visited[node->AdjV] && dist[node->AdjV] == -1) {
                dist[node->AdjV] = dist[min] + 1;
            }
            node = node->Next;
        }
    }
}
 

思路：

1. 使用迪傑斯特拉演算法，對鄰近未訪問的節點dist+1；2. 使用廣度優先搜尋，dist+1.