【BZOJ 2733】 [HNOI2012]永无乡

思路

并查集+线段树合并
时间复杂度$O(n\log^2n+q\log n)$

代码

#include <cstdio>
#include <iostream>
#include <algorithm>
#define mid ((l+r)>>1)
using namespace std;
const int maxn = 100010;
struct node{
    int val;
    node *ch[2];
}pool[maxn*25], *null, *root[maxn];
int fa[maxn], sz[maxn], ct, n, m, q, v[maxn];
node *get(int val){
    node *now = &pool[++ct];
    now->ch[0] = now->ch[1] = null;
    now->val = val;
    return now;
}
void build(node *now, int l, int r, int pos){
    if(l == r) return;
    int wh = 0; if(pos >= mid+1) wh = 1;
    now->ch[wh] = get(1);
    build(now->ch[wh], wh==0?l:mid+1, wh==0?mid:r, pos);
}
void merge_tree(node *fi, node *se, int l, int r){
    if(l == r) return;
    if(fi->ch[0] == null) fi->ch[0] = se->ch[0];
    else if(se->ch[0] != null){
        fi->ch[0]->val += se->ch[0]->val;
        merge_tree(fi->ch[0], se->ch[0], l, mid);
    }
    if(fi->ch[1] == null) fi->ch[1] = se->ch[1];
    else if(se->ch[1] != null){
        fi->ch[1]->val += se->ch[1]->val;
        merge_tree(fi->ch[1], se->ch[1], mid+1, r);
    }
}
int find(int x){return x == fa[x] ? x : fa[x] = find(fa[x]);}
void merge_fa(int x, int y){
    int fx = find(x), fy = find(y);
    if(fx == fy) return; 
    if(sz[fx] < sz[fy]) swap(fx, fy);
    merge_tree(root[fx], root[fy], 1, n);
    sz[fx] += sz[fy]; fa[fy] = fx;
}
void que(node *now, int l, int r, int k){
    if(l == r){
        if(k > now->val) printf("-1\n");
        else printf("%d\n", v[l]);
        return;
    }
    if(now->ch[0]->val >= k) que(now->ch[0], l, mid, k);
    else que(now->ch[1], mid+1, r, k - now->ch[0]->val);
}
int main(){
    null = pool, null->val = 0, null->ch[0] = null->ch[1] = null;
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i ++) root[i] = get(0);
    for(int i = 1; i <= n; i ++) fa[i] = i, sz[i] = 1;
    for(int i = 1, t; i <= n; i ++){
        scanf("%d", &t), v[t] = i;
        build(root[i], 1, n, t);
    }
    for(int i = 1, x, y; i <= m; i ++){
        scanf("%d%d", &x, &y);
        merge_fa(x, y);
    }
    scanf("%d", &q);
    for(int i = 1, x, y; i <= q; i ++){
        char ch[5];
        scanf("%s%d%d", ch+1, &x, &y);
        if(ch[1] == 'Q') que(root[find(x)], 1, n, y);
        else merge_fa(x, y);
    }
    return 0;
}