POJ-2985（树状数组 + 并查集 + 二分）

题目：http://poj.org/problem?id=2985

这题考察了两个点呢，组合并用到了并查集，求第K大的数用到了树状数组，刚开始WA了几次，发现是在组合并之后仅仅update(*, -1)了一次，因为是删除了两个组增加了一个组，应该是update(*, -1)两次，不细心啊。。。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define MAX	200005

int N, M, G;
int father[MAX] = {0};	//father[i]表示i所在group的首脑
int member[MAX] = {0};	//member[i]表示以i为首的group有多少个member
int group[MAX] = {0};	//group[i]表示成员有[i-lowbit(i)+1, i]个的group有多少个,

inline int lowbit(int x){ return x & -x; }
void update(int x, int v){
	for(; x <= N; x += lowbit(x)){
		group[x] += v;
	}
}
int sum(int x)
{
	int tot = 0;
	for(; x; x -= lowbit(x)) tot += group[x];
	return tot;
}
int query(int k)
{
	int l = 0, r = N;
	while(l + 1 < r){
		int m = (l + r) >> 1;
		if(sum(m) >= k) r = m;
		else l = m;
	}
	return r;
}
int find(int x){
	return x != father[x] ? father[x] = find(father[x]) : x;
}
void join(int x, int y)
{
	int fx = find(x), fy = find(y);
	if(fx == fy) return;

	if(member[fx] > member[fy]) swap(fx, fy);
	father[fx] =  fy;
	update(member[fy], -1);
	member[fy] += member[fx];
	update(member[fx], -1);
	member[fx] = 0;
	update(member[fy], 1);
	--G;
}
void init()
{
	for(int i = 1; i <= N; ++i) father[i] = i;
	for(int i = 1; i <= N; ++i) member[i] = 1;
	G = N;
	memset(group + 1, 0, N * sizeof(int));
	for(int i = 0; (1 << i) <= N; ++i) group[1 << i] = N;
}

int main()
{
	int c, x, y;
	while(~scanf("%d%d", &N, &M)){
		init();
		while(M--){
			scanf("%d%d", &c, &x);
			if(c) printf("%d\n", query(G - x + 1));
			else{
				scanf("%d", &y);
				join(x, y);
			}
		}
	}
	return 0;
}