Going from u to v or from v to u? 【判定弱连通】=【tarjan求scc+ 缩点+topo】

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
题意 给一个有向图，问是否对于任意的两个点，都可以相互到达。
是不是和强连通很像，其实我少说了一个很重要的条件，就是这个任意的两个点：没有规定那个是起始点，那个是终点，都可以当起点或者终点。所以和强连通还是很不一样。 其实这样的图叫做弱连通图；
对于一个DAG（有向图求scc+缩点后的新图（有向无环图））图来说，其实这样题意的图（弱连通图），就是只要有一个起点，它可以走过所有的点，并到达终点。 这样的图符合题意（弱连通图）；

链接
代码
没加输入挂，334ms 加了输入挂64ms 。。 再一次感叹输入挂的强大。其实仔细想一下这道题的输入量 ，m*t*2==2*6000*t ;也就至少到了1e5级了。一般到1e5级的输入量，用输入挂，效果就很显著。

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<stack>
#include<queue>
#include<iostream>
#include<vector>
using namespace std;
const int MAXN= 1001+10;
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch>'9'||ch<'0'){ if(ch=='-') f=-1; ch=getchar();}
    while(ch>='0'&&ch<='9') { x=x*10+ch-'0';ch=getchar();}
    return x*f;
}  //  输入挂
/*------------------------------------*/
struct Edge {
    int from,to,next;
}edge[6000+10];
int head[MAXN],top;
int n,m;
void init(){
    memset(head,-1,sizeof(head));
    top=0;
}
void addedge(int a,int b){
    Edge e={a,b,head[a]};
    edge[top]=e;head[a]=top++;
}
void getmap(){
    int a,b;
  while(m--){
    a=read();b=read();
    addedge(a,b);
  }
}
int low[MAXN],dfn[MAXN];
int scc_cnt,sccno[MAXN];
stack<int>S;int Instack[MAXN];
vector<int>G[MAXN];
int dfs_clock;
void tarjan(int now,int par){
    low[now]=dfn[now]=++dfs_clock;
    S.push(now);Instack[now]=1;
    for(int i=head[now];i!=-1;i=edge[i].next){
        Edge e=edge[i];
        if(!dfn[e.to]){
            tarjan(e.to,now);
            low[now]=min(low[now],low[e.to]);
        }else if(Instack[e.to])
        low[now]=min(low[now],dfn[e.to]);
    }
    if(low[now]==dfn[now]) {
        scc_cnt++;
        for(;;){
            int nexts=S.top();S.pop();Instack[nexts]=0;
            sccno[nexts]=scc_cnt;
            if(nexts==now) break;
        }
    }
}
void find_cut(int le,int ri){
    memset(low,0,sizeof(low));
    memset(dfn,0,sizeof(dfn));
    memset(Instack,0,sizeof(Instack));
    memset(sccno,0,sizeof(sccno));
    dfs_clock=scc_cnt=0;
    for(int i=le;i<=ri;i++){
        if(!dfn[i]) tarjan(i,-1);
    }
}

int in[MAXN];
void suodian(){
    for(int i=1;i<=scc_cnt;i++) {
            in[i]=0;G[i].clear();
    }
    for(int i=0;i<top;i++){
        Edge e=edge[i];
        int now=sccno[e.from];
        int nexts=sccno[e.to];
        if(now!=nexts){
            G[now].push_back(nexts);
            in[nexts]++;
        }
    }
}
queue<int>Q;
bool topo(){
    while(!Q.empty()) Q.pop();
    int num=0;
    for(int i=1;i<=scc_cnt;i++){
        if(!in[i]) {
            Q.push(i);
            num++;
            if(num>1) return false;
        }
    }
    int k=0;
    while(!Q.empty()){
        int now=Q.front();Q.pop();num=0;k++;
        for(int i=0;i<G[now].size();i++){
            int v=G[now][i];
            if(--in[v]==0){
                Q.push(v);
                num++;
                if(num>1) return false;
            }
        }
    }
    return  k==scc_cnt;
}
void solve(){
    find_cut(1,n);
    suodian();
    if(scc_cnt==1) puts("Yes");
    else
    puts(topo()?"Yes":"No");
}
int main(){
    int t;t=read();while(t--){
        n=read();m=read();
        init();
        getmap();
        solve();
    }
    return 0;
}