codeforces 731C 并查集

C. Socks

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

Arseniy is already grown-up and independent. His mother decided to leave him alone for m days
and left on a vacation. She have prepared a lot of food, left some money and washed all Arseniy's clothes.
Ten minutes before her leave she realized that it would be also useful to prepare instruction of which particular clothes to wear on each of the days she will be absent. Arseniy's
family is a bit weird so all the clothes is enumerated. For example, each of Arseniy's n socks
is assigned a unique integer from 1 to n.
Thus, the only thing his mother had to do was to write down two integers li and ri for
each of the days — the indices of socks to wear on the day i (obviously, li stands
for the left foot and ri for
the right). Each sock is painted in one of kcolors.
When mother already left Arseniy noticed that according to instruction he would wear the socks of different colors on some days. Of course, that is a terrible mistake cause by a
rush. Arseniy is a smart boy, and, by some magical coincidence, he posses k jars
with the paint — one for each of k colors.
Arseniy wants to repaint some of the socks in such a way, that for each of m days
he can follow the mother's instructions and wear the socks of the same color. As he is going to be very busy these days he will have no time to change the colors of any socks so he has to finalize the colors now.
The new computer game Bota-3 was just realised and Arseniy can't wait to play it. What is the minimum number of socks that need their color to be changed in order to make it possible
to follow mother's instructions and wear the socks of the same color during each of m days.

Input
The first line of input contains three integers n, m and k (2 ≤ n ≤ 200 000, 0 ≤ m ≤ 200 000, 1 ≤ k ≤ 200 000) —
the number of socks, the number of days and the number of available colors respectively.
The second line contain n integers c1, c2,
..., cn (1 ≤ ci ≤ k) —
current colors of Arseniy's socks.
Each of the following m lines
contains two integers li and ri (1 ≤ li, ri ≤ n, li ≠ ri) —
indices of socks which Arseniy should wear during thei-th day.

Output
Print one integer — the minimum number of socks that should have their colors changed in order to be able to obey the instructions and not make people laugh from watching the socks
of different colors.

Examples

input

3 2 3
1 2 3
1 2
2 3

output

2

input

3 2 21 1 21 22 1

output

0

Note
In the first sample, Arseniy can repaint the first and the third socks to the second color.
In the second sample, there is no need to change any colors.
题意：有n只袜子，总共有m天，袜子总共有k种颜色，标记为1-k，下面一行给出n只袜子的颜色，接下来几行给出m天，每天左右脚要穿第几只袜子即Li和Ri，问你求至少需要改变几只袜子的颜色，保证每天传的袜子同色
思路：用并查集来吧每天要穿的袜子合并在一起，然后统计相同根下每种袜子颜色的数目是多少，然后求每个根下的所有种数袜子数目最大值，根的总大小减去数目最多的那一种，剩下就是要改变的；
代码：

/*
Author:fanmeng
Lang:C++
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <vector>
#include <set>

using namespace std;

int fa[200005];
map<int,int>mp[200005];//用来统计具有相同根的每种袜子的数目
int n,m,k;
int color[200005];//每只袜子的颜色
int tol;

int found(int x) {
return x==fa[x]?x:fa[x]=found(fa[x]);//路径压缩了
}

int main() {
cin >> n >> m >> k;
for(int i = 1; i <= n; i++) {
cin >> color[i];
fa[i] = i;
}
int a,b;
tol = 0;
while(m--) {
cin >> a >> b;
a = found(a);
b = found(b);
fa[max(a,b)] = min(a,b);//并在一起
}
for(int i = 1;i <= n;i++){
mp[found(i)][color[i]]++;//统计具有相同根的每种袜子的数目
}
for(int i = 1;i<=n;i++){
int s = 0;//根的总大小
int mx = 0;//数目最大的是多少
for(map<int,int>::iterator it = mp[i].begin();it !=mp[i].end();it++){
s += it->second;
mx = max(mx,it->second);
}
tol += s-mx;
}
cout << tol << endl;
return 0;
}

ps：这题要好好想想，思想很简单，但就是想不清楚怎么做的，也是醉。。。。。。。。。。。。