POJ 2762 Going from u to v or from v to u? （图论-tarjan）

Going from u to v or from v to u?

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 14469		Accepted: 3801

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

题目大意：


解题思路：


解题代码：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;

const int maxn=1100;
const int maxm=51000;

struct edge{
int u,v,next;
edge(int u0=0,int v0=0){
u=u0;v=v0;
}
}e[maxm];

int n,m,head[maxn],dfn[maxn],low[maxn],mark[maxn],w[maxn],color[maxn],dp[maxn],cnt,nc,index;
vector <int> vec;
vector <vector<int> > dfsmap;

void addedge(int u,int v){
e[cnt]=edge(u,v);e[cnt].next=head[u];head[u]=cnt++;
}

void input(){
cnt=nc=index=0;
scanf("%d%d",&n,&m);
vec.clear();
for(int i=0;i<=n;i++){
w[i]=dfn[i]=0;
mark[i]=false;
color[i]=dp[i]=head[i]=-1;
}
int u,v;
while(m-- >0){
scanf("%d%d",&u,&v);
addedge(u,v);
}
}

void tarjan(int s){
dfn[s]=low[s]=++index;
mark[s]=true;
vec.push_back(s);
for(int i=head[s];i!=-1;i=e[i].next){
int d=e[i].v;
if(!dfn[d]){
tarjan(d);
low[s]=min(low[d],low[s]);
}else if(mark[d]){
low[s]=min(low[s],dfn[d]);
}
}
if(dfn[s]==low[s]){
nc++;
int d;
do{
d=vec.back();
vec.pop_back();
color[d]=nc;
mark[d]=false;
w[nc]++;
}while(d!=s);
}
}

int DP(int s){
if(dp[s]!=-1) return dp[s];
int ans=w[s];
for(int i=0;i<dfsmap[s].size();i++){
int d=dfsmap[s][i];
if(DP(d)+w[s]>ans) ans=DP(d)+w[s];
}
return dp[s]=ans;
}

void solve(){
for(int i=1;i<=n;i++){
if(!dfn[i]) tarjan(i);
}
dfsmap.clear();
dfsmap.resize(nc+1);
for(int i=0;i<cnt;i++){
int x=color[e[i].u],y=color[e[i].v];
if(x!=y){
dfsmap[x].push_back(y);
//cout<<x<<"->"<<y<<endl;
}
}
int ans=0;
for(int i=1;i<=nc;i++){
if(DP(i)>ans) ans=DP(i);
//cout<<i<<" "<<ans<<endl;
}
if(ans>=n) printf("Yes\n");
else printf("No\n");
}

int main(){
int t;
scanf("%d",&t);
while(t-- >0){
input();
solve();
}
return 0;
}