【Poj1703】Find them, Catch them（关系并查集）

桃扇骨 2022-07-16 01:44 99阅读 0赞

Find them, Catch them

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;1000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;10000K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;42064</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;12936</td> 
  </tr> 
 </tbody> 
</table>

Description

The police office in Tadu City decides to say ends to the chaos, as launch actions to root up the TWO gangs in the city, Gang Dragon and Gang Snake. However, the police first needs to identify which gang a criminal belongs to. The present question is, given two criminals; do they belong to a same clan? You must give your judgment based on incomplete information. (Since the gangsters are always acting secretly.)  
  
Assume N (N <= 10^5) criminals are currently in Tadu City, numbered from 1 to N. And of course, at least one of them belongs to Gang Dragon, and the same for Gang Snake. You will be given M (M <= 10^5) messages in sequence, which are in the following two kinds:  
  
1. D \[a\] \[b\]  
where \[a\] and \[b\] are the numbers of two criminals, and they belong to different gangs.  
  
2. A \[a\] \[b\]  
where \[a\] and \[b\] are the numbers of two criminals. This requires you to decide whether a and b belong to a same gang.

Input

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Each test case begins with a line with two integers N and M, followed by M lines each containing one message as described above.

Output

For each message "A \[a\] \[b\]" in each case, your program should give the judgment based on the information got before. The answers might be one of "In the same gang.", "In different gangs." and "Not sure yet."

Sample Input

1
    5 5
    A 1 2
    D 1 2
    A 1 2
    D 2 4
    A 1 4

Sample Output

Not sure yet.
    In different gangs.
    In the same gang.

Source

[POJ Monthly--2004.07.18][]

关系并查集

#include<cstdio>
    #include<iostream>
    #include<cstring>
    #include<cmath>
    #include<algorithm>
    using namespace std;
    const int N = 100000+10;
    int f[N],rank[N];
    int n,m;
    void init() {
    	for(int i=1; i<=n; i++) {
    		f[i]=i;
    		rank[i]=0;
    	}
    }
    int find(int x) {
    	if(x==f[x]) return f[x];
    	int fa=f[x];
    	f[x] = find(f[x]);  //路径压缩
    	rank[x] = (rank[x]+rank[fa])&1;
    	return f[x];
    }
    
    void Union(int x,int y) {
    	int a=find(x), b=find(y);
    	if(a==b) return ;
    	f[b] = a;
    	rank[b] = (rank[x]-rank[y]+1)&1;
    }
    int main() {
    	int T;
    	scanf("%d",&T);
    	while(T--) {
    		scanf("%d%d",&n,&m);
    		init();
    		char ch;
    		int a,b;
    		while(m--) {
    			getchar();
    			scanf("%c%d%d",&ch,&a,&b);
    			if(ch=='D') {
    				Union(a,b);
    			} else {
    				int fa=find(a),fb=find(b);
    				if(fa==fb) {
    					if(rank[a]==rank[b])
    						printf("In the same gang.\n");
    					else
    						printf("In different gangs.\n");
    				} else
    					printf("Not sure yet.\n");
    			}
    		}
    	}
    	return 0;
    }

[POJ Monthly--2004.07.18]: http://poj.org/searchproblem?field=source&key=POJ+Monthly--2004.07.18