6-11 Shortest Path [1] (25分)

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 );

 

where LGraph is 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 


代码：

#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 */
    int a,b;
    LGraph g = (LGraph)malloc(sizeof(struct GNode));
    scanf("%d%d",&g -> Nv,&g -> Ne);
    for(int i = 0;i < g -> Nv;i ++) {
        g -> G[i].FirstEdge = NULL;
    }
    for(int i = 0;i < g -> Ne;i ++) {
        scanf("%d%d",&a,&b);
        PtrToAdjVNode p = (PtrToAdjVNode)malloc(sizeof(struct AdjVNode));
        p -> AdjV = b;
        p -> Next = g -> G[a].FirstEdge;
        g -> G[a].FirstEdge = p;
    }
    return g;
}

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 */
void ShortestDist( LGraph Graph, int dist[], Vertex S ) {
    for(int i = 0;i < Graph -> Nv;i ++) {
        dist[i] = -1;
    }
    int vis[MaxVertexNum] = {0};
    dist[S] = 0;
    while(1) {
        int m = MaxVertexNum,t = -1;
        for(int i = 0;i < Graph -> Nv;i ++) {
            if(!vis[i] && dist[i] != -1 && dist[i] < m) {
                m = dist[i];
                t = i;
            }
        }
        if(t == -1) break;
        vis[t] = 1;
        PtrToAdjVNode p = Graph -> G[t].FirstEdge;
        while(p) {
            if(!vis[p -> AdjV]) {
                if(dist[p -> AdjV] == -1 || dist[p -> AdjV] > dist[t] + 1) dist[p -> AdjV] = dist[t] + 1;
            }
            p = p -> Next;
        }
    }
}