HDU 5222 ——Exploration——————【并查集+拓扑排序判有向环】
Exploration
Time Limit: 30000/15000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 194 Accepted Submission(s): 63
Problem Description
Miceren likes exploration and he found a huge labyrinth underground!
This labyrinth has N caves and some tunnels connecting some pairs of caves.
There are two types of tunnel, one type of them can be passed in only one direction and the other can be passed in two directions. Tunnels will collapse immediately after Miceren passing them.
Now, Miceren wants to choose a cave as his start point and visit at least one other cave, finally get back to start point.
As his friend, you must help him to determine whether a start point satisfing his request exists.
This labyrinth has N caves and some tunnels connecting some pairs of caves.
There are two types of tunnel, one type of them can be passed in only one direction and the other can be passed in two directions. Tunnels will collapse immediately after Miceren passing them.
Now, Miceren wants to choose a cave as his start point and visit at least one other cave, finally get back to start point.
As his friend, you must help him to determine whether a start point satisfing his request exists.
Input
The first line contains a single integer
T, indicating the number of test cases.
Each test case begins with three integers N, M1, M2, indicating the number of caves, the number of undirectional tunnels, the number of directional tunnels.
The next M1 lines contain the details of the undirectional tunnels. Each line contains two integers u, v meaning that there is a undirectional tunnel between u, v. (u ≠ v)
The next M2 lines contain the details of the directional tunnels. Each line contains integers u, v meaning that there is a directional tunnel from u to v. (u ≠ v)
T is about 100.
1 ≤ N,M1,M2 ≤ 1000000.
There may be some tunnels connect the same pair of caves.
The ratio of test cases with N > 1000 is less than 5%.
Each test case begins with three integers N, M1, M2, indicating the number of caves, the number of undirectional tunnels, the number of directional tunnels.
The next M1 lines contain the details of the undirectional tunnels. Each line contains two integers u, v meaning that there is a undirectional tunnel between u, v. (u ≠ v)
The next M2 lines contain the details of the directional tunnels. Each line contains integers u, v meaning that there is a directional tunnel from u to v. (u ≠ v)
T is about 100.
1 ≤ N,M1,M2 ≤ 1000000.
There may be some tunnels connect the same pair of caves.
The ratio of test cases with N > 1000 is less than 5%.
Output
For each test queries, print the answer. If Miceren can do that, output "YES", otherwise "NO".
Sample Input
2
5 2 1
1 2
1 2
4 5
4 2 2
1 2
2 3
4 3
4 1
Sample Output
YES
NO
Hint
If you need a larger stack size, please use #pragma comment(linker, "/STACK:102400000,102400000") and submit your solution using C++.
题目大意：给你n个山洞，m1条无向隧道，m2条有向隧道，要你从一个山洞出发，经过除出发点外至少一个山洞回到出发点，一条隧道经过后会坍塌，问是否存在满足要求的路径。
解题思路：
首先对于所有的无向边，我们使用并查集将两边的点并起来。
若一条边未合并之前，两端的点已经处于同一个集合了，那么说明必定存在可行的环（因为这两个点处于同一个并查集集合中，那么它们之间至少存在一条路径） 如果上一步没有判断出环，那么仅靠无向边是找不到环的 考虑到，处于同一个并查集集合中的点之间必定存在一条路径互达，因此将一个集合的点合并之后（利用缩点），原问题等价于在新生成的有向图中是否有环 我们知道，有向无环图必定存在拓扑序，因此只需使用拓扑排序判定即可 时间复杂度O(N+M1+M2)
#include<stdio.h>
#include<string.h>
#include<vector>
#include<iostream>
#include<queue>
#include<algorithm>
using namespace std;
int n,m1,m2;
const int maxn=1e6+666;
int fa[maxn]; //并查集的father数组
bool flag[maxn]; //标记缩点、不重复加入队列
int indeg[maxn]; //记录入度
vector<int>Mp[maxn];//存有向边
int Find(int x){
return fa[x]=fa[x]==x?x:Find(fa[x]);
}
bool Union(int x,int y){
int fx,fy;
fx=Find(x);
fy=Find(y);
if(fx<fy){
fa[fy]=fx;
}else if(fx>fy){
fa[fx]=fy;
}else{ //如果该无向边的两端同属一个集合，加入该边后，肯定形成环
return true;
}
return false;
}
bool u_f_set(){
for(int i=1;i<=n;i++) //初始化fa
fa[i]=i;
bool cir=0; //是否形成环
for(int i=0;i<m1;i++){
int u,v;
scanf("%d %d",&u,&v);
if(!cir&&Union(u,v)) //如果形成环，只需输入，不操作
cir=1;
}
return cir;
}
bool topo_sort(){
for(int i=0;i<=n;i++)
Mp[i].clear();
memset(indeg,0,sizeof(indeg));
memset(flag,0,sizeof(flag));
bool cir=0; //初始化
for(int i=0;i<m2;i++){
int u,v,fu,fv;
scanf("%d%d",&u,&v);
if(cir==1) //如果已经有环，只需输入
continue;
fu=Find(u);
fv=Find(v);
if(fu==fv){ //如果有向边两个端点在一个集合（缩点）中，必成环
cir=1;
}else{
Mp[fu].push_back(fv); //存有向边
indeg[fv]++; //该集合（缩点）入度加一
}
}
if(cir==1){
return 1;
}else{
queue<int>Q;
while(!Q.empty())
Q.pop();
int cnt_c=0;
for(int i=1;i<=n;i++){
int i_f=Find(i);
if(i_f==i){
cnt_c++; //记录所有集合（缩点）个数
}
if(indeg[i_f]==0&&flag[i_f]==0){ //该集合（缩点）入度为零，且未加入队列
Q.push(i_f);
flag[i_f]=1;
}
}
int cnt=0;
while(!Q.empty()){ //bfs_topo排序
int u=Q.front();
cnt++; //记录拓扑排序排了多少个集合（缩点）
Q.pop();
for(int i=0;i<Mp[u].size();i++){
int j=Mp[u][i];
indeg[j]--;
if(indeg[j]==0&&flag[j]==0){
Q.push(j);
flag[j]=1;
}
}
}
if(cnt_c==cnt){ //如果总的集合个数等于拓扑排序的集合个数，说明无环
return false;
}else{
return true;
}
}
}
int main(){
int t;
scanf("%d",&t);
while(t--){
scanf("%d%d%d",&n,&m1,&m2);
if(u_f_set()){
for(int i=0;i<m2;i++){
int u,v;
scanf("%d%d",&u,&v);
}printf("YES\n");
}
else{
if(topo_sort()) printf("YES\n");
else printf("NO\n");
}
}
}
/*
55
3 1 1
1 3
3 2
NO
4 2 2
1 2
2 3
4 3
4 1
NO
7 3 4
2 1
1 7
3 4
6 3
5 6
4 5
7 6
YES
4 1 3
4 1
3 2
4 3
4 1
YES
7 2 3
1 2
2 3
4 5
5 6
6 4
YES
9 4 4
1 2
1 7
3 4
8 9
7 6
5 6
4 5
6 3
YES
*/