图的拓扑排序—递归—迭代

#include <iostream>#include <ctime>#include <vector>using namespace std;typedef struct Link_graphic{//邻接表int value;Link_graphic *next;}Link_graphic,*pLink_graphic;typedef struct Queue{//队列Link_graphic *front,*tail;//头尾结点指针}Queue;void init(Queue *&queue)//队列初始化{queue->front=NULL;queue->tail=NULL;}void enqueue(Queue *& queue,int value)//入队列操作{if(queue->front==NULL && queue->tail==NULL){//当队列中还没有元素的时候pLink_graphic ls=new Link_graphic;ls->value=value;ls->next=NULL;queue->front=ls;queue->tail=ls;}else{pLink_graphic ls=new Link_graphic;ls->value=value;ls->next=NULL;queue->tail->next=ls;queue->tail=ls;}}void dequeue(Queue *&queue)//出队列操作{if(queue->front){pLink_graphic pt=queue->front;queue->front=queue->front->next;delete pt;}}void add_vertex(pLink_graphic &plg,pLink_graphic plgtmp)//添加结点{pLink_graphic tmp=plg->next;plg->next=plgtmp;plgtmp->next=tmp;}void delete_redundance(pLink_graphic *&plg,int n)//删除冗余边和自循环边{bool *visited=new bool[n];pLink_graphic plgtmp;pLink_graphic plgpre;for(int i=0;i<n;++i){for(int j=0;j<n;++j){visited[j]=false;}visited[i]=true;plgtmp=plg[i]->next;plgpre=plg[i];while(plgtmp){if(visited[plgtmp->value]){//如果该元素已经存在,plgpre->next=plgtmp->next;delete plgtmp;plgtmp=plgpre->next;}else{visited[plgtmp->value]=true;plgpre=plgtmp;plgtmp=plgtmp->next;}}}delete [] visited;}void dfs_visit(pLink_graphic *&plg,int value,int *visited)//深度优先遍历{visited[value]=1;//将当前结点标记为正在访问pLink_graphic plgtmp=plg[value]->next;while(plgtmp){if(visited[plgtmp->value]==0){//该结点尚未被访问dfs_visit(plg,plgtmp->value,visited);plgtmp=plgtmp->next;}else if(visited[plgtmp->value]==1){//当前是一条后向边,应该删除该条边pLink_graphic plt=plg[value]->next;pLink_graphic pltpre=plg[value];while(plt->value!=plgtmp->value){pltpre=plt;plt=plt->next;}pltpre->next=plt->next;plgtmp=plt->next;//指向下一个结点delete plt;//删除该结点}else{//该结点已经被访问，前向边plgtmp=plgtmp->next;}}visited[value]=2;//将当前边标记为已经访问结束}void directed_acyclic_graphs(pLink_graphic *&plg,int n)//有向无环图{int *visited=new int[n];//标记数组for(int i=0;i<n;++i){for(int j=0;j<n;++j){visited[j]=0;//将所有结点标记为尚未访问}dfs_visit(plg,i,visited);//深度优先遍历}}void topologic_dfs_visit(pLink_graphic *&plg,int value,bool *visited,int *dist,int &depth)//深度优先遍历{visited[value]=true;depth=depth+1;pLink_graphic plgtmp=plg[value]->next;while(plgtmp){if(visited[plgtmp->value]==false){topologic_dfs_visit(plg,plgtmp->value,visited,dist,depth);}plgtmp=plgtmp->next;}depth=depth+1;dist[value]=depth;//更新距离值}void topologic_depth_first_search(pLink_graphic *&plg,int *dist,int n)//深度优先搜索,并返回距离最大的结点的下标索引值{bool *visited=new bool[n];for(int i=0;i<n;++i){visited[i]=false;//标记为假}pLink_graphic plgtmp;int depth=0;//初始的深度值为0for(int i=0;i<n;++i){//对每个点都需要进行深度遍历plgtmp=plg[i];if(visited[plgtmp->value]==false){topologic_dfs_visit(plg,i,visited,dist,depth);//深度优先遍历}}}void topological_sort(pLink_graphic *& plg,int n)//拓扑排序{int *dist=new int[n];//记录拓扑长度for(int i=0;i<n;++i){dist[i]=0;}topologic_depth_first_search(plg,dist,n);//深度优先遍历for(int i=0;i<n;++i){cout<<dist[i]<<" ";}cout<<endl;delete [] dist;}int in_degree(pLink_graphic *&plg,int value,int n)//入度{pLink_graphic plgtmp;int count=0;for(int i=0;i<n;++i){if(i!=value){plgtmp=plg[i]->next;while(plgtmp){if(plgtmp->value==value){count++;}plgtmp=plgtmp->next;}}}return count;}int out_degree(pLink_graphic *&plg,int value,int n)//出度{pLink_graphic plgtmp=plg[value]->next;int count=0;while(plgtmp){++count;plgtmp=plgtmp->next;}return count;}bool vertify_isolated(pLink_graphic *&plg,int value,int n)//检查是否有孤立的点{int count_out=out_degree(plg,value,n);int count_in=in_degree(plg,value,n);if(count_out+count_in==0)//孤立的点return true;return false;}void break_isolated(pLink_graphic *&plg,int n)//打破孤立的点{int tmp1;//随机点pLink_graphic plgtmp;for (int i=0;i<n;++i){if(vertify_isolated(plg,i,n)){//检测是否有孤立的点while((tmp1=rand()%n)==i);//产生一个随机的点//增加出度if(rand()%2){plgtmp=new Link_graphic;plgtmp->value=tmp1;plgtmp->next=NULL;add_vertex(plg[i],plgtmp);}else{//添加入度plgtmp=new Link_graphic;plgtmp->value=i;plgtmp->next=NULL;add_vertex(plg[tmp1],plgtmp);}}}}void topologic_sort_iterator(pLink_graphic *&plg,int n)//另一种，迭代方式的拓扑排序{int *indegree=new int[n];//in_degree数组Queue *queue=new Queue;init(queue);for(int i=0;i<n;++i){indegree[i]=in_degree(plg,i,n);//计算每个点的入度if(indegree[i]==0){enqueue(queue,i);//如果该点的入度为0，则将其加入队列}}while(queue->front){//队列非空,将front元素出队列，并将与其想连的元素的入度减少1pLink_graphic plt=plg[queue->front->value]->next;while (plt){//与queue->front想连的元素的入度值都要减少1indegree[plt->value]--;if(indegree[plt->value]==0){enqueue(queue,plt->value);}plt=plt->next;}cout<<queue->front->value<<" ";dequeue(queue);// 弹出队列首元素}for(int i=0;i<n;++i){if(indegree[i]!=0){cout<<"there is a cycle..."<<endl;return;}}delete []indegree;delete queue;}int main(){srand((unsigned)time(NULL));int n=5;pLink_graphic *plg=new pLink_graphic[n];pLink_graphic plgtmp;//临时存放for(int i=0;i<n;++i){plg[i]=new Link_graphic;plg[i]->value=i;plg[i]->next=NULL;for(int j=0;j<rand()%n;++j){plgtmp=new Link_graphic;plgtmp->value=rand()%n;plgtmp->next=NULL;add_vertex(plg[i],plgtmp);//添加结点}}cout<<"initial values"<<endl;for(int i=0;i<n;++i){plgtmp=plg[i];while(plgtmp){cout<<plgtmp->value<<" ";plgtmp=plgtmp->next;}cout<<endl;}delete_redundance(plg,n);cout<<"after delete redundant"<<endl;cout<<endl<<endl;for(int i=0;i<n;++i){plgtmp=plg[i];while(plgtmp){cout<<plgtmp->value<<" ";plgtmp=plgtmp->next;}cout<<endl;}cout<<endl<<endl;break_isolated(plg,n);//检查是否有孤立点cout<<"after break isolated"<<endl;for(int i=0;i<n;++i){plgtmp=plg[i];while(plgtmp){cout<<plgtmp->value<<" ";plgtmp=plgtmp->next;}cout<<endl;}directed_acyclic_graphs(plg,n);cout<<endl;cout<<"directed acyclic graphs"<<endl;for(int i=0;i<n;++i){plgtmp=plg[i];while(plgtmp){cout<<plgtmp->value<<" ";plgtmp=plgtmp->next;}cout<<endl;}cout<<"after recursive topological sort"<<endl;topological_sort(plg,n);cout<<endl;cout<<"after iterator topological sort"<<endl;topologic_sort_iterator(plg,n);cout<<endl;for(int i=0;i<n;++i){delete[]plg[i];}delete[]plg;;}