UVALive - 4730 Kingdom(并查集+线段树)

题目连接：https://vjudge.net/problem/UVALive-4730

思路：用并查集来维护每一个州的城市数目，最上面城市的y坐标maxy，最下面城市的y坐标miny，当在城市之间连接一条路时，如果这两个城市已经在同一个州内，就不用处理了，如果不在同一个州内，首先要现在线段树中删除这两个州的信息，注意如果这个州只有一个城市不用删除，因为线段树内并没有记录只有一个城市的州的信息，然后合并这两个州，再把合并之后的州的信息更新到线段树上，区间更新，查询的时候单点查询

#include <bits/stdc++.h>

using namespace std;
#define lson num << 1
#define rson num << 1 | 1
#define MAXN 2000006

struct node1
{
	int l,r;
	int state,city;
	int lazy1,lazy2;
}tree[MAXN << 2];
void pushup(int num)
{
	tree[num].state = tree[lson].state + tree[rson].state;
	tree[num].city = tree[lson].city + tree[rson].city;
}
void pushdown(int num)
{
	if(tree[num].lazy1) {
		tree[lson].state += tree[num].lazy1;
		tree[rson].state += tree[num].lazy1;
		tree[lson].lazy1 += tree[num].lazy1;
		tree[rson].lazy1 += tree[num].lazy1;
		tree[num].lazy1 = 0;
	}
	if(tree[num].lazy2) {
		tree[lson].city += tree[num].lazy2;
		tree[rson].city += tree[num].lazy2;
		tree[lson].lazy2 += tree[num].lazy2;
		tree[rson].lazy2 += tree[num].lazy2;
		tree[num].lazy2 = 0;
	}
}
void build(int num,int l,int r)
{
	tree[num].l = l;
	tree[num].r = r;
	tree[num].lazy1 = tree[num].lazy2 = 0;
	tree[num].state = tree[num].city = 0;
	if(l == r) return;
	int mid = (l + r) >> 1;
	build(lson,l,mid);
	build(rson,mid + 1,r);
}
void update(int num,int l,int r,int state,int city)
{
	if(tree[num].l == l && tree[num].r == r) {
		tree[num].state += state;
		tree[num].city += city;
		tree[num].lazy1 += state;
		tree[num].lazy2 += city;
		return;
	}
	pushdown(num);
	int mid = (tree[num].l + tree[num].r) >> 1;
	if(r <= mid) update(lson,l,r,state,city);
	else if(l > mid) update(rson,l,r,state,city);
	else {
		update(lson,l,mid,state,city);
		update(rson,mid + 1,r,state,city);
	}
	pushup(num);
}
int query(int num,int pos)
{
	if(tree[num].l == pos && tree[num].r == pos) {
		return num;
	}
	pushdown(num);
	int mid = (tree[num].l + tree[num].r) >> 1;
	if(pos <= mid) query(lson,pos);
	else query(rson,pos);
}
struct node2
{
	int maxy,miny;
	int num,pre;
}un[MAXN];
int findset(int x) 
{
	if(x == un[x].pre) return x;
	else return un[x].pre = findset(un[x].pre);
}
void join(int x,int y)
{
	int fx = findset(x);
	int fy = findset(y);
	if(fx != fy) {
		if(un[fx].num > 1) update(1,un[fx].miny,un[fx].maxy,-1,-un[fx].num);
		if(un[fy].num > 1) update(1,un[fy].miny,un[fy].maxy,-1,-un[fy].num);
		un[fy].pre = fx;
		un[fx].num += un[fy].num;
		un[fx].miny = min(un[fy].miny,un[fx].miny);
		un[fx].maxy = max(un[fy].maxy,un[fx].maxy); 
		update(1,un[fx].miny,un[fx].maxy,1,un[fx].num);
	}
}
int main(void)
{
	int T,n,m;
	int x,y,id;
	double li;
	int Max;
	char op[10];
	scanf("%d",&T);
	while(T--) {
		scanf("%d",&n);
		Max = 0;
		for(int i = 0; i < n; i++) {
			scanf("%d %d",&x,&y);
			un[i].pre = i;
			un[i].maxy = un[i].miny = (y << 1);
			un[i].num = 1;
			Max = max(Max,y << 1);
		}
		build(1,0,Max);
		scanf("%d",&m);
		while(m--) {
			scanf("%s",&op);
			if(op[0] == 'r') {
				scanf("%d %d",&x,&y);
				join(x,y);
			}
			else {
				scanf("%lf",&li); li *= 2; 
				if((int)(li) > Max) printf("0 0\n"); 
				else{ 
					id = query(1,(int)li);
					printf("%d %d\n",tree[id].state,tree[id].city); 
				}
			}
		}
	}
	return 0;
}