codeforces #547D Mike and Fish （二分图欧拉回路）

最新推荐文章于 2020-01-22 17:53:49 发布

w4149

最新推荐文章于 2020-01-22 17:53:49 发布

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分类专栏： CF —————妙题————— 二分图欧拉路文章标签：二分图欧拉回路 CF

本文链接：https://blog.youkuaiyun.com/w4149/article/details/78206980

博客介绍了如何帮助Mike在平面上的n个点放置红蓝鱼，使得每行每列的鱼颜色差不超过1。通过将坐标转化为二分图，并寻找欧拉回路进行交替染色，确保条件满足。解决方案包括调整奇度数节点，形成偶数度数的二分图，然后求解欧拉回路进行染色。

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Mike and Fish CodeForces - 547D

As everyone knows, bears love fish. But Mike is a strange bear; He hates fish! The even more strange thing about him is he has an infinite number of blue and red fish.

He has marked n distinct points in the plane. i-th point is point (xi, yi). He wants to put exactly one fish in each of these points such that the difference between the number of red fish and the blue fish on each horizontal or vertical line is at most 1.

He can’t find a way to perform that! Please help him.

Input
The first line of input contains integer n (1 ≤ n ≤ 2 × 105).

The next n lines contain the information about the points, i-th line contains two integers xi and yi (1 ≤ xi, yi ≤ 2 × 105), the i-th point coordinates.

It is guaranteed that there is at least one valid answer.

Output
Print the answer as a sequence of n characters ‘r’ (for red) or ‘b’ (for blue) where i-th character denotes the color of the fish in the i-th point.

Example
Input

4
1 1
1 2
2 1
2 2

Output

brrb

Input

3
1 1
1 2
2 1

Output

brr

思路：
摘自 < %popoqq >
补充一点
题目大意：给定平面上的n个点，要求将每个点染成红色/蓝色，使得每行/每列的红色点数和蓝色点数之差≤1。

坐标系中的问题，考虑把x坐标和y坐标分成两个集合，将每一个横坐标/纵坐标看做一个点，每个点看做一条连接两个坐标的边。
现在