6-11 Shortest Path [1]（25 分）

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本文介绍了一种求解有向图中从任意顶点到指定源顶点的无权最短距离算法。通过使用队列实现广度优先搜索，算法能够有效地找到每个顶点到源顶点的距离。

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):

Sample Output:

-1 1 0 3 2 2 1

void ShortestDist(LGraph Graph, int dist[], Vertex S)
{
int Front = 0, Rear = 0;
Vertex* queue = (Vertex*)malloc(MaxVertexNum * sizeof(Vertex));
for (int i = 0; i < MaxVertexNum; i++)
queue[i] = dist[i] = -1;
queue[0] = S;
dist[S] = 0;
PtrToAdjVNode ptr;
while (Front <= Rear) {
ptr = Graph->G[queue[Front]].FirstEdge;
while (ptr != NULL) {
if (dist[ptr->AdjV] == -1) {
dist[ptr->AdjV] = dist[queue[Front]] + 1;
queue[++Rear] = ptr->AdjV;
}
ptr = ptr->Next;
}
Front++;
}
}