[codeforces741C] Arpa’s overnight party and Mehrdad’s silent entering_arpa鈥檚 overnight party and mehrdad鈥檚 silent enteri-优快云博客

本文链接：https://blog.youkuaiyun.com/dxyinme/article/details/90033800

本文探讨了在给定情侣关系下，如何为参与者分配两种不同颜色，确保情侣颜色不同且连续三人颜色不完全相同的问题。通过构建图并进行染色，提供了一种有效的解决方案。

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time limit per test : 1 second
memory limit per test : 256 megabytes

Note that girls in Arpa’s land are really attractive.

Arpa loves overnight parties. In the middle of one of these parties Mehrdad suddenly appeared. He saw $n$ pairs of friends sitting around a table. $i$ -th pair consisted of a boy, sitting on the $a_i$ -th chair, and his girlfriend, sitting on the $b_i$ -th chair. The chairs were numbered $1$ through $2 n$ in clockwise direction. There was exactly one person sitting on each chair.

There were two types of food: Kooft and Zahre-mar. Now Mehrdad wonders, was there any way to serve food for the guests such that:

Each person had exactly one type of food,
No boy had the same type of food as his girlfriend,
Among any three guests sitting on consecutive chairs, there was two of them who had different type of food. Note that chairs $2 n$ and $1$ are considered consecutive.

Find the answer for the Mehrdad question. If it was possible, find some arrangement of food types that satisfies the conditions.
Input

The first line contains an integer $n (1 ≤ n ≤ 10^5)$ — the number of pairs of guests.

The $i$ -th of the next n lines contains a pair of integers $a_i$ and $b_i (1 ≤ a_i, b_i ≤ 2n)$ — the number of chair on which the boy in the $i$ -th pair was sitting and the number of chair on which his girlfriend was sitting. It’s guaranteed that there was exactly one person sitting on each chair.
Output

If there is no solution, print $- 1$ .

Otherwise print $n$ lines, the $i$ -th of them should contain two integers which represent the type of food for the $i$ -th pair. The first integer in the line is the type of food the boy had, and the second integer is the type of food the girl had. If someone had Kooft, print $1$ , otherwise print $2$ .

If there are multiple solutions, print any of them.

Example

Input

Output

1 2
2 1
1 2

题意：
给定n个关系(ai,bi)，表示(ai,bi)之间是情侣关系，情侣的颜色不能相同，相邻的三个人的颜色不能相同，1和2*n是相邻的。你要将所有人染色（一共两种颜色），求一组染色方案。

题解:
首先，如果按照12121212…这样染色的话，在没有情侣关系的情况下肯定是可以的。然后如果两个点之间有情侣关系，则他们之间连一条边。然后将所有的 $2 * i$ 和 $2 * i + 1$ 连边，然后跑一次图染色就行。

#include<bits/stdc++.h>
#define LiangJiaJun main
using namespace std;
int ne,h[200004],cl[200004];
int u[200004],v[200004],n;
struct edge{
    int to,nt;
}e[400004];
void add(int u,int v){
     e[++ne].to=v;e[ne].nt=h[u];
     h[u]=ne;
}
int dfs(int x,int c){
    cl[x]=c;
    for(int i=h[x];i;i=e[i].nt){
        if(!cl[e[i].to]){
            bool t=dfs(e[i].to,3-c);
            if(!t)return 0;
        }
        else if(cl[e[i].to]==cl[x]){
            return 0;
        }
    }
    return 1;
}
int LiangJiaJun(){
    ne=0;
    memset(cl,0,sizeof(cl));
    memset(h,0,sizeof(h));
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
        scanf("%d%d",&u[i],&v[i]);
        add(u[i],v[i]);
        add(v[i],u[i]);
    }
    for(int i=1;i<=n;i++){
        add(i*2,i*2-1);
        add(i*2-1,i*2);
    }
    for(int i=1;i<=2*n;i++){
        if(!cl[i]){
            if(!dfs(i,1))return puts("-1"),0;
        }
    }
    for(int i=1;i<=n;i++){
        printf("%d %d\n",cl[u[i]],cl[v[i]]);
    }
    return 0;
}