[hdu 3018] Ant Trip

Problem Description

Ant Country consist of N towns.There are M roads connecting the towns.

Ant Tony,together with his friends,wants to go through every part of the country.

They intend to visit every road , and every road must be visited for exact one time.However,it may be a mission impossible for only one group of people.So they are trying to divide all the people into several groups,and each may start at different town.Now tony wants to know what is the least groups of ants that needs to form to achieve their goal.

Input

  Input contains multiple cases.Test cases are separated by several blank lines. Each test case starts with two integer N(1<=N<=100000),M(0<=M<=200000),indicating that there are N towns and M roads in Ant Country.Followed by M lines,each line contains two integers a,b,(1<=a,b<=N) indicating that there is a road connecting town a and town b.No two roads will be the same,and there is no road connecting the same town.

Solution

题目大意:给一张无向图,求最少几笔描过所有边。

欧拉路径裸题,考虑每一个强连通分量,如果分量内度数均是偶数证明可以一笔遍历完分量内的边。

反之,如果有k个奇度点,那么一定可以画\left \lfloor \frac{k}{2} \right \rfloor笔遍历完分量内的边。

于是tarjan搞搞即可。时间复杂度O(N+M)

 

发表评论