Codeforces Round #403---C题(DFS,树)
C. Andryusha and Colored Balloons
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Andryusha goes through a park each day. The squares and paths between them look boring to Andryusha, so he decided to decorate them.
The park consists of n squares connected with (n - 1) bidirectional paths in such a way that any square is reachable from any other using these paths. Andryusha decided to hang a colored balloon at each of the squares. The baloons' colors are described by positive integers, starting from 1. In order to make the park varicolored, Andryusha wants to choose the colors in a special way. More precisely, he wants to use such colors that if a, b and c are distinct squares that a and b have a direct path between them, and b and c have a direct path between them, then balloon colors on these three squares are distinct.
Andryusha wants to use as little different colors as possible. Help him to choose the colors!
Input
The first line contains single integer n (3 ≤ n ≤ 2·105) — the number of squares in the park.
Each of the next (n - 1) lines contains two integers x and y (1 ≤ x, y ≤ n) — the indices of two squares directly connected by a path.
It is guaranteed that any square is reachable from any other using the paths.
Output
In the first line print single integer k — the minimum number of colors Andryusha has to use.
In the second line print n integers, the i-th of them should be equal to the balloon color on the i-th square. Each of these numbers should be within range from 1 to k.
Examples
Input
3
2 3
1 3
Output
3
1 3 2
Input
5
2 3
5 3
4 3
1 3
Output
5
1 3 2 5 4
Input
5
2 1
3 2
4 3
5 4
Output
3
1 2 3 1 2
Note
In the first sample the park consists of three squares: 1 → 3 → 2. Thus, the balloon colors have to be distinct.
Illustration for the first sample.
In the second example there are following triples of consequently connected squares:
- 1 → 3 → 2
- 1 → 3 → 4
- 1 → 3 → 5
- 2 → 3 → 4
- 2 → 3 → 5
- 4 → 3 → 5
We can see that each pair of squares is encountered in some triple, so all colors have to be distinct.
Illustration for the second sample.
In the third example there are following triples:
- 1 → 2 → 3
- 2 → 3 → 4
- 3 → 4 → 5
We can see that one or two colors is not enough, but there is an answer that uses three colors only.
Illustration for the third sample.
题意:
给你一个图,给所有节点染上颜色,要求是相邻的三个节点的颜色不能相同,求需要的最少的颜色数
思路:
为了方便叙述,我们给颜色编号,从1开始,不一样的序号代表不一样的颜色,序号最大者即为需要的颜色种数
首先,由题目上的条件,这个图一定是一棵树,因为是一颗树,我们可以从任一节点开始,DFS遍历完所有节点。
结合图为树的条件,经过分析得到,要使每相邻三个节点的颜色不同,
只需满足两个条件:
1.使这个节点和他的兄弟节点颜色不同
2.使这个节点和它的的父亲节点及爷爷节点颜色不同
为了满足这两个条件,并使得颜色数最少,我们在DFS到一个节点时,遍历他所有的子节点,都染上颜色,颜色序号在满足以上条件时要尽可能的小
Codeforces Round #403---C题(DFS,树)的更多相关文章
- Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals)
Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals) 说一点东西: 昨天晚上$9:05$开始太不好了,我在学校学校$9:40$放 ...
- 树的性质和dfs的性质 Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals) E
http://codeforces.com/contest/782/problem/E 题目大意: 有n个节点,m条边,k个人,k个人中每个人都可以从任意起点开始走(2*n)/k步,且这个步数是向上取 ...
- Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals)A模拟 B三分 C dfs D map
A. Andryusha and Socks time limit per test 2 seconds memory limit per test 256 megabytes input stand ...
- Codeforces Round #403 (Div. 2) B 三分 C dfs
B. The Meeting Place Cannot Be Changed time limit per test 5 seconds memory limit per test 256 megab ...
- 【贪心】【DFS】Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals) C. Andryusha and Colored Balloons
从任意点出发,贪心染色即可. #include<cstdio> #include<algorithm> using namespace std; int v[200010< ...
- Codeforces 842C--Ilya And The Tree(dfs+树)
原题链接:http://codeforces.com/contest/842/problem/C 题意:一个以1为根节点的树,每个节点有一个值ai,定义美丽度:从根节点到这个节点的路径上所有ai的gc ...
- Codeforces Round #403 (Div. 1, based on Technocup 2017 Finals)
Div1单场我从来就没上过分,这场又剧毒,半天才打出B,C挂了好几次最后还FST了,回紫了. AC:AB Rank:340 Rating:2204-71->2133 Div2.B.The Mee ...
- Codeforces Round#403 (Div. 1)
唉,昨天晚上迷迷糊糊地去打cf,结果fst两题,掉回蓝了... A.Andryusha and Colored Balloons 题意:给定一棵树,任意两个距离小等于二的点不能染相同的颜色,求最小颜色 ...
- Codeforces Round #456 B题
一.题意 给你一个n和一个k,让你从[1, n]区间内选k个数,这k个数异或和最大. 二.思路 我一开始看到这种题,不自觉地就想到,莫非又要搞很复杂的线段树.主席树?貌似还有些难搞啊.然而事实是:Co ...
- 2-sat Codeforces Round #403 (Div. 2, based on Technocup 2017 Finals) D
http://codeforces.com/contest/782/problem/D 题意: 每个队有两种队名,问有没有满足以下两个条件的命名方法: ①任意两个队的名字不相同. ②若某个队 A 选用 ...
随机推荐
- you_are_the_one(区间dp)
You Are the One Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)T ...
- GITFLOW流程
GITFLOW流程规范 GIT的使用非常的灵活,但是灵活就导致在使用的过程中有各种各样的情况,根据现有项目组的情况,使用GITFLOW流程规范作为项目开发流程规范. 该规范参考地址: 深入理解学习Gi ...
- Packet flow in l2(receive and transmit)
Receive 1. napi && none napi 讲网络收报过程,必然要涉及到网卡收报模型发展历史.总体上看,网络收报过经历了如下发展过程: 轮询 ---à 中断 ---à ...
- 03: saltstack和ansible的区别和原理
1.1 SaltStack.Ansible.Puppet比较 1.SaltStack 1. saltStack由Python编写,为server-client模式的系统,自己本身支持多master. ...
- python中几个常见的魔法方法
首先,什么是魔法方法呢?在python中方法名如果是__xxxx__()的,那么就有特殊的功能,因此叫做"魔法"方法. __ init__()方法 当一个实例被创建的时候调用的初始 ...
- python3小demo
总结常用的功能小实例,快速学习并掌握python技能 1.墨迹天气 import requests from lxml.html import etree import json import tim ...
- Restful 架构方式的 web service
现在公司项目用的apache wink 搭建的web service ,感觉挺好用的.顺便学习一个这种架构方式 . 个人理解apache 实现Restful 架构方式技术有两种,如果有其他新的知识或不 ...
- 机器学习python常用模块
.Pickle模块 打包,解压训练模型 .pysnooper 调试打印日志
- Heshen's Account Book HihoCoder - 1871 2018北京区域赛B题(字符串处理)
Heshen was an official of the Qing dynasty. He made a fortune which could be comparable to a whole c ...
- Zookeeper客户端使用(使用原生zookeeper)
Zookeeper客户端使用 一.使用原生zookeeper 在pom.xml中加入依赖 <dependency> <groupId>org.apache.zookeeper& ...