【luogu P1801 黑匣子_NOI导刊2010提高（06）】 题解

题目链接：https://www.luogu.org/problemnew/show/P1801

替罪羊树吼啊！

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define il inline
using namespace std;
const int maxn = 2000001;
const int alpha = 0.7;
struct scapegoat{
    int son[2], val, valid, below;
    bool del;
}e[maxn];
int cur[maxn], memory[maxn], root, pool, posi, cnt, to_rebuild, a[maxn], u[maxn], n, m;
il bool isbad(int now)
{
    if((double)e[now].valid*alpha <= (double)max(e[e[now].son[0]].valid, e[e[now].son[1]].valid)) return true;
    return false;
}
void dfs(int now)
{
    if(!now) return;
    dfs(e[now].son[0]);
    if(e[now].del) cur[++posi] = now;
    else memory[++pool] = now;
    dfs(e[now].son[1]);
}
void build(int l, int r, int &now)
{
    int mid = l+r>>1;
    now = cur[mid];
    if(l == r)
    {
        e[now].son[0] = e[now].son[1] = 0;
        e[now].valid = e[now].below = 1;
        return;
    }
    if(l < mid) build(l,mid-1,e[now].son[0]);
    else e[now].son[0] = 0;
    build(mid+1, r, e[now].son[1]);
    e[now].below = e[e[now].son[0]].below+e[e[now].son[1]].below+1;
    e[now].valid = e[e[now].son[0]].valid+e[e[now].son[1]].valid+1;
}
il void rebuild(int &now)
{
    posi = 0;
    dfs(now);
    if(posi) build(1,posi,now);
    else now = 0;
}
il int find_rank(int tar)
{
    int now = root;
    int ans = 1;
    while(now)
    {
        if(e[now].val >= tar) now = e[now].son[0];
        else
        {
            ans+=e[e[now].son[0]].valid+e[now].del;
            now = e[now].son[1];
        }
    }
    return ans;
}
void insert(int &now, int val)
{
    if(!now)
    {
        now = memory[pool--]; e[now].val = val;
        e[now].below = e[now].valid = e[now].del = 1;
        e[now].son[0] = e[now].son[1] = 0;
        return;
    }
    e[now].below++, e[now].valid++;
    if(e[now].val >= val) insert(e[now].son[0], val);
    else insert(e[now].son[1], val);
    if(!isbad(now))
    {
        if(to_rebuild)
        {
            if(e[now].son[0] == to_rebuild) rebuild(e[now].son[0]);
            else rebuild(e[now].son[1]);
            to_rebuild = 0;
        }
    }
    else to_rebuild = now;
}
void delete_pos(int &now, int tar)
{
    if(e[now].del && e[e[now].son[0]].valid + 1 == tar)
    {
        e[now].del = false; e[now].valid--; return;
    }
    e[now].valid--;
    if(e[e[now].son[0]].valid+e[now].del >= tar) delete_pos(e[now].son[0],tar);
    else delete_pos(e[now].son[1], tar-e[e[now].son[0]].valid-e[now].del);
}
il void delete_val(int tar)
{
    delete_pos(root, find_rank(tar));
    if((double)e[root].below*alpha > e[root].valid) rebuild(root);
}
il int kth(int tar)
{
    int now = root;
    while(now)
    {
        if(e[now].del&&e[e[now].son[0]].valid+1==tar) return e[now].val;
        else if(e[e[now].son[0]].valid >= tar) now = e[now].son[0];
        else
        {
            tar-=e[e[now].son[0]].valid+e[now].del;
            now = e[now].son[1];
        }
    }
}
int main()
{
    root = 0;
    for(int i = 2000000; i >= 1; i--)
    memory[++pool] = i;
    scanf("%d%d",&n,&m);
    for(int i = 1; i <= n; i++) scanf("%d",&a[i]);
    for(int i = 1; i <= m; i++) scanf("%d",&u[i]);
    int qaq = 1;

    for(int i = 1; i <= m; i++)
    {
        while(qaq <= u[i])
    	{
    	    insert(root, a[qaq]);
            qaq++;
        }
        printf("%d\n",kth(i));
    }
    return 0;
}