Codeforces Round #396 (Div. 2) D. Mahmoud and a Dictionary （并查集）

淩亂°似流年 2022-07-10 15:29 131阅读 0赞

D. Mahmoud and a Dictionary

time limit per test

4 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Mahmoud wants to write a new dictionary that contains *n* words and relations between them. There are two types of relations: synonymy (i. e. the two words mean the same) and antonymy (i. e. the two words mean the opposite). From time to time he discovers a new relation between two words.

He know that if two words have a relation between them, then each of them has relations with the words that has relations with the other. For example, if like means love and love is the opposite of hate, then like is also the opposite of hate. One more example: iflove is the opposite of hate and hate is the opposite of like, then love means like, and so on.

Sometimes Mahmoud discovers a wrong relation. A wrong relation is a relation that makes two words equal and opposite at the same time. For example if he knows that love means like and like is the opposite of hate, and then he figures out that hate meanslike, the last relation is absolutely wrong because it makes hate and like opposite and have the same meaning at the same time.

After Mahmoud figured out many relations, he was worried that some of them were wrong so that they will make other relations also wrong, so he decided to tell every relation he figured out to his coder friend Ehab and for every relation he wanted to know is it correct or wrong, basing on the previously discovered relations. If it is wrong he ignores it, and doesn't check with following relations.

After adding all relations, Mahmoud asked Ehab about relations between some words based on the information he had given to him. Ehab is busy making a Codeforces round so he asked you for help.

Input

The first line of input contains three integers *n*, *m* and *q* (2 ≤ *n* ≤ 105, 1 ≤ *m*, *q* ≤ 105) where *n* is the number of words in the dictionary,*m* is the number of relations Mahmoud figured out and *q* is the number of questions Mahmoud asked after telling all relations.

The second line contains *n* distinct words *a*1, *a*2, ..., *a**n* consisting of small English letters with length not exceeding 20, which are the words in the dictionary.

Then *m* lines follow, each of them contains an integer *t* (1 ≤ *t* ≤ 2) followed by two different words *x**i* and *y**i* which has appeared in the dictionary words. If *t* = 1, that means *x**i* has a synonymy relation with *y**i*, otherwise *x**i* has an antonymy relation with *y**i*.

Then *q* lines follow, each of them contains two different words which has appeared in the dictionary. That are the pairs of words Mahmoud wants to know the relation between basing on the relations he had discovered.

All words in input contain only lowercase English letters and their lengths don't exceed 20 characters. In all relations and in all questions the two words are different.

Output

First, print *m* lines, one per each relation. If some relation is wrong (makes two words opposite and have the same meaning at the same time) you should print "NO" (without quotes) and ignore it, otherwise print "YES" (without quotes).

After that print *q* lines, one per each question. If the two words have the same meaning, output 1. If they are opposites, output 2. If there is no relation between them, output 3.

See the samples for better understanding.

Examples

input

3 3 4
    hate love like
    1 love like
    2 love hate
    1 hate like
    love like
    love hate
    like hate
    hate like

output

YES
    YES
    NO
    1
    2
    2
    2

input

8 6 5
    hi welcome hello ihateyou goaway dog cat rat
    1 hi welcome
    1 ihateyou goaway
    2 hello ihateyou
    2 hi goaway
    2 hi hello
    1 hi hello
    dog cat
    dog hi
    hi hello
    ihateyou goaway
    welcome ihateyou

output

YES
    YES
    YES
    YES
    NO
    YES
    3
    3
    1
    1
    2

题解：看到那些找相邻关系，上下关系的，不难想到并查集（dsu）.

这题的并查集的father数组开两倍空间。

那么就形成了两个一样大小的集合 \{1， 2 …… n\}， \{n+1, ……， n+n\} 。

那么对于两个词 x, y来说：

如果关系是近义词，那么就在同一个集合内建树，也就是fa\[find(x)\] = find(y)，fa\[find(x+n)\] = find(y+n)。  
如果是相反词，那么就在两个集合交叉建树，也就是 fa\[find(x)\] = find(y + n) ，fa\[find(y+n)\] = find(x)。

从而可以判断x和y的关系。

AC代码：

#include<bits/stdc++.h>
    using namespace std;
    const int mod=1e9+7;
    const int maxn=2e5+7; 
    map<string,int>mp;
    int fa[2*maxn];
    int n;
    void init()
    {
    	for(int i=0;i<=n;i++){
    		fa[i]=i; fa[i+n]=i+n;
    	}
    }
    int find(int x)
    {
    	return fa[x]==x ? fa[x] : fa[x] = find(fa[x]);
    }
    int main()
    {
    	int m,q;
    	string s;
    	cin>>n>>m>>q;
    	init();
    	mp.clear();
    	for(int i=1;i<=n;i++){
    		cin>>s;
    		mp[s] = i;
    	}
    	int op;
    	string a,b;
    	for(int i=1;i<=m;i++){
    		cin>>op>>a>>b;
    		int x=mp[a];
    		int y=mp[b];
    		if(op==1){ //同义词 
    			if(find(x) == find(y + n)){
    				puts("NO");
    			}
    			else{
    				puts("YES");
    				fa[find(y)] = find(x);
    				fa[find(y + n)] = find(x + n);
    			}
    		}
    		else if(op==2){ //反义词 
    			if(find(x) == find(y)){
    				puts("NO");
    			}
    			else{
    				puts("YES"); 
    				fa[find(y)] = find(x + n);
    				fa[find(y + n)] =find(x);
    			}
    		}
    	}
    	
    	for(int i=1;i<=q;i++){
    		cin>>a>>b;
    		int x=mp[a];
    		int y=mp[b];
    		int fa=find(x);
    		int fb=find(y);
    		if(fa==fb){  //同义词 
    			puts("1");
    		} 
    		else if(find(x+n)==find(y)){ //反义词 
    			puts("2");
    		}
    		else puts("3");
    	}
    	return 0;
    }