6-16 Topological Sort（25 point(s)）

6-16 Topological Sort（25 point(s)）

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[] whereTopOrder[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 caseTopSort 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 71 04 32 12 03 24 14 2

Sample Output 1:

4 3 2 1 0

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

5 80 31 04 32 12 03 24 14 2

Sample Output 2:

ERROR拓扑排序问题，具体讲解可以看点击打开链接 ，感觉讲的很清楚代码：
bool TopSort( LGraph Graph, Vertex TopOrder[] ){int indegree[MaxVertexNum];//用于保存每个点的入度 int q[MaxVertexNum];//队列，用于优化时间复杂度，每次找零度的点只需要从上次零度点相邻的里面找int i;int num = 0;//记录拓扑排序数组下标 int head=0,tail=0;PtrToAdjVNode t;for(i = 0; i < Graph->Nv; i++){indegree[i] = 0;}for(i = 0; i < Graph->Nv; i++){//遍历每一个点 t = Graph->G[i].FirstEdge; while(t){//遍历每一个点后面所连的点 indegree[t->AdjV]++;t = t->Next;}}//对入度进行初始化 for(i = 0; i < Graph->Nv; i++){if(indegree[i]==0){q[tail++] = i;//先找到入度为零的点，加入队列，然后对队列进行操作即可 }}if(head==tail)return false;//如果找了一圈没有入度为零的点，肯定不对，返回false//队列操作while(head<tail){t = Graph->G[q[head]].FirstEdge;//取出队首的元素while(t){//对队首元素相邻的点进行遍历，操作 if(indegree[t->AdjV]<0)return false;//如果这个点入度为负数，说明之前肯定已经放在拓扑排序数组里了，再出现说明有环 indegree[t->AdjV]--;//相邻元素入度减一 if(indegree[t->AdjV]==0){q[tail++] = t->AdjV;//减后为零入队 }t = t->Next;} indegree[q[head]] = -1;//表示这个点不能再出现了 TopOrder[num++] = q[head++]; }if(num!=Graph->Nv)return false;else return true; }