poj 2762 Going from u to v or from v to u?(强连通分量+缩点重构图+拓扑排序)

http://poj.org/problem?id=2762

Going from u to v or from v to u?

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 12733		Accepted: 3286

Description

In order to make their sons brave, Jiajia and Wind take them to a big cave. The cave has n rooms, and one-way corridors connecting some rooms. Each time, Wind choose two rooms x and y, and ask one of their little sons go from one to the other. The son can either go from x to y, or from y to x. Wind promised that her tasks are all possible, but she actually doesn't know how to decide if a task is possible. To make her life easier, Jiajia decided to choose a cave in which every pair of rooms is a possible task. Given a cave, can you tell Jiajia whether Wind can randomly choose two rooms without worrying about anything?

Input

The first line contains a single integer T, the number of test cases. And followed T cases. 
The first line for each case contains two integers n, m(0 < n < 1001,m < 6000), the number of rooms and corridors in the cave. The next m lines each contains two integers u and v, indicating that there is a corridor connecting room u and room v directly. 

Output

The output should contain T lines. Write 'Yes' if the cave has the property stated above, or 'No' otherwise.

Sample Input

1
3 3
1 2
2 3
3 1

Sample Output

Yes

Source

POJ Monthly--2006.02.26,zgl & twb

【题解】：

　　这题题目大概意思就是说 判断两个点之间是不是能够走通，u到v 或者 v到u 都行，这题开始题目意思都理解错了，一开始以为就是一个判断强连通的题；

　　先求强连通分量；

　　然后将强连通分量缩点，重构图；

　　强连通分量内部的点肯定是可以两两到的，所以可以不用管了；

　　缩点后的图，然后进行拓扑排序，如果有两个及以上的点的入度为0，那么他们之间肯定是不可达的，所以不符合

　　如图：

　　

【code】：

 /**
 Judge Status:Accepted     Memory:4896K
 Time:485MS        Language:G++
 Code Lenght:2940B   Author:cj
 */

 #include<iostream>
 #include<algorithm>
 #include<stdio.h>
 #include<string.h>
 #include<vector>
 #include<stack>

 using namespace std;
 #define N 1010
 #define M 6060

 struct Edge
 {
     int v;
     int next;
     int u;
 }edge[M];  //M  开始传的N  RE

 int head[N],edge_cnt;//这一行变量是构造边的

 int pre[N],lowlink[N],sccno[N],dfs_cnt,scc_cnt;  //这两行是Tarjan算法求强连通分量用的
 stack<int> stk;

 vector<int> G[N];  //缩点重构图用的邻接链表
 int in[N],mark[N][N];  //入度统计，以及重复边的标记

 void init()
 {
     memset(head,-,sizeof(head));
     edge_cnt = ;
 }

 void addEdge(int a,int b)
 {
     edge[edge_cnt].v = b;
     edge[edge_cnt].next = head[a];
     edge[edge_cnt].u = a;   //这里记录a,重构图用，方便遍历所有边
     head[a] = edge_cnt++;
 }

 void Tarjan(int u)  //强连通分量
 {
     stk.push(u);
     pre[u] = lowlink[u] = ++dfs_cnt;
     int i;
     for(i=head[u];i!=-;i=edge[i].next)
     {
         int v = edge[i].v;
         if(!pre[v])
         {
             Tarjan(v);
             lowlink[u] = min(lowlink[u],lowlink[v]);
         }
         else if(!sccno[v])
         {
             lowlink[u] = min(lowlink[u],pre[v]);
         }
     }
     if(pre[u]==lowlink[u])
     {
         scc_cnt++;
         int x;
         do
         {
             x = stk.top();
             stk.pop();
             sccno[x] = scc_cnt;  //sccno[x]表示下标为x的节点所在的第几个强连通分量
         }while(x!=u);
     }
 }

 void findscc(int n)
 {
     memset(pre,,sizeof(pre));
     memset(lowlink,,sizeof(lowlink));
     memset(sccno,,sizeof(sccno));
     dfs_cnt = scc_cnt = ;
     while(!stk.empty()) //初始化 以防万一
     {
         stk.pop();
     }
     int i;
     for(i=;i<=n;i++)   if(!pre[i]) Tarjan(i);
 }

 void getNewMap()  //重构缩点后的图，存入邻接链表G中
 {
     int i,j;
     for(i=;i<=scc_cnt;i++)
     {
         G[i].clear();
         in[i] = ;
     }
     memset(mark,,sizeof(mark));
     for(i=;i<edge_cnt;i++)
     {
         int v = edge[i].v;
         int u = edge[i].u;
         if(sccno[u]!=sccno[v])
         {
             if(!mark[u][v])  //重复边标记
             {
                 G[sccno[u]].push_back(sccno[v]);
                 in[sccno[v]]++;  //入度统计
             }
             mark[u][v] = ;
         }
     }
 }

 int cntInid()  //计算入度为0的位置，以及是不是一个
 {
     int i,cnt=,id=;
     for(i=;i<=scc_cnt;i++)
     {
         if(!in[i])
         {
             cnt++;
             id = i;
         }
     }
     if(cnt==)
         return id;
     return ;
 }

 int isOK()  //用拓扑排序判断是否可行
 {
     int id = cntInid();
     if(!id)  return ;
     int i;
     in[id] = -;
     for(i=;i<G[id].size();i++)
     {
         in[G[id][i]]--;
     }
     if(G[id].size()>)  return isOK();
     return ;
 }

 int main()
 {
     int t;
     scanf("%d",&t);
     while(t--)
     {
         int n,m;
         scanf("%d%d",&n,&m);
         int i;
         init();
         for(i=;i<m;i++)
         {
             int a,b;
             scanf("%d%d",&a,&b);
             addEdge(a,b);
         }
         findscc(n);  //求强连通分量
         if(scc_cnt==)  //如果只有一个那么肯定可行
         {
             puts("Yes");
             continue;
         }
         getNewMap();  //用强连通分量缩点，重构图
         if(isOK())  puts("Yes"); //拓扑排序判断
         else  puts("No");
     }
     return ;
 }