6-3 Topological Sort (25分)

Write a program to find the topological order in a digraph.

Format of functions:

bool TopSort( LGraph Graph, Vertex TopOrder[] );

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 topological order is supposed to be stored in TopOrder[] where TopOrder[i] is the i-th vertex in the resulting sequence. The topological sort cannot be successful if there is a cycle in the graph – in that case TopSort must return false; otherwise return true.

Notice that the topological order might not be unique, but the judge’s input guarantees the uniqueness of the result.

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 */

bool TopSort( LGraph Graph, Vertex TopOrder[] );

int main()
{
    int i;
    Vertex TopOrder[MaxVertexNum];
    LGraph G = ReadG();

    if ( TopSort(G, TopOrder)==true )
        for ( i=0; i<G->Nv; i++ )
            printf("%d ", TopOrder[i]);
    else
        printf("ERROR");
    printf("\n");

    return 0;
}

/* Your function will be put here */

Sample Input 1 (for the graph shown in the figure):

5 7
1 0
4 3
2 1
2 0
3 2
4 1
4 2

Sample Output 1:

4 3 2 1 0 

Sample Input 2 (for the graph shown in the figure):

5 8
0 3
1 0
4 3
2 1
2 0
3 2
4 1
4 2

Sample Output 2:

ERROR

源码：

int Indegree[MaxVertexNum];
bool TopSort( LGraph Graph, Vertex TopOrder[] )
{
    int count=0;
    //初始化Indegree
    for(int i=0;i<Graph->Nv;i++)
    {
        Indegree[i]=0;
    }
    for(int i=0;i<Graph->Nv;i++)
    {
        PtrToAdjVNode p=Graph->G[i].FirstEdge;
        while(p)
        {
            Indegree[p->AdjV]++;
            p=p->Next;
        }
    }
    //初始化栈
    int stack[MaxVertexNum];
    int f=-1;
    for(int i=0;i<Graph->Nv;i++)
    {
        if(!Indegree[i])
            stack[++f]=i;
    }
    //top
    while(f!=-1)
    {
        int t=stack[f--];
        TopOrder[count++]=t;
        PtrToAdjVNode p=Graph->G[t].FirstEdge;
        while(p)
        {
            if(--Indegree[p->AdjV]==0)
                stack[++f]=p->AdjV;
            p=p->Next;
        }
    }
    if(count<Graph->Nv)
        return false;
    else
        return true;
}