BZOJ4923 K小值查询（splay）

　　容易想到建一棵平衡树，修改时打上标记即可。但是修改会导致平衡树结构被破坏。注意到实际上只有[k+1,2k)这一部分数在平衡树中的位置会被改变，所以对这一部分暴力修改，因为每次都会使其至少减小一半，复杂度非常正确。

　　开始写的玩意一个点要跑10s吓到我了，卡了半天常（最后也只是在darkbzoj上过了）造了半天bug，调的欲仙欲死，退役了。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cassert>
using namespace std;
#define ll long long
#define N 100010
#define inf 2000000001
#define lson tree[k].ch[0]
#define rson tree[k].ch[1]
char getc(){char c=getchar();while ((c<'A'||c>'Z')&&(c<'a'||c>'z')&&(c<'0'||c>'9')) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int n,m,a[N],root,cnt;
struct data{int x,ch[2],fa,s,lazy;
}tree[N<<5];
inline void up(int k){tree[k].s=tree[lson].s+tree[rson].s+1;}
inline void update(int k,int x){if (k) {if (tree[k].x<inf) tree[k].x-=x;tree[k].lazy+=x;}}
inline void down(int k){if (tree[k].lazy) update(lson,tree[k].lazy),update(rson,tree[k].lazy),tree[k].lazy=0;}
inline void push(int k){if (tree[k].fa) push(tree[k].fa);down(k);}
inline int whichson(int k){return tree[tree[k].fa].ch[1]==k;}
inline void move(int k)
{
    int fa=tree[k].fa,gf=tree[fa].fa,p=whichson(k);
    tree[gf].ch[whichson(fa)]=k,tree[k].fa=gf;
    tree[fa].ch[p]=tree[k].ch[!p],tree[tree[k].ch[!p]].fa=fa;
    tree[k].ch[!p]=fa,tree[fa].fa=k;
    up(fa),up(k);
}
void splay(int k,int rt)
{
    push(k);
    while (tree[k].fa!=rt)
    {
        int fa=tree[k].fa;
        if (tree[fa].fa!=rt)
            if (whichson(k)^whichson(fa)) move(k);
            else move(fa);
        move(k);
    }
    if (!rt) root=k;
}
void build(int &k,int l,int r)
{
    if (l>r) return;
    int mid=l+r>>1;
    k=++cnt;tree[k].x=a[mid],tree[k].s=r-l+1;
    build(lson,l,mid-1);build(rson,mid+1,r);
    tree[lson].fa=tree[rson].fa=k;
}
int find(int k,int x)
{
    if (tree[lson].s+1==x) return k;
    down(k);
    if (tree[lson].s+1>x) return find(lson,x);
    else return find(rson,x-tree[lson].s-1);
}
int qsuf(int k,int x)
{
    if (!k) return 0;
    down(k);
    if (tree[k].x<x) return qsuf(rson,x);
    else
    {
        int t=qsuf(lson,x);
        return t&&tree[t].x<=tree[k].x?t:k;
    }
}
int qpre(int k,int x)
{
    if (!k) return 0;
    down(k);
    if (tree[k].x>x) return qpre(lson,x);
    else
    {
        int t=qpre(rson,x);
        return t&&tree[t].x>=tree[k].x?t:k;
    }
}
void ins(int x)
{
    int k=root,fa=0;
    while (k) down(k),tree[k].s++,fa=k,k=tree[k].x<=x?rson:lson;
    k=++cnt;tree[k].x=x,tree[k].s=1,tree[k].fa=fa,tree[fa].ch[tree[fa].x<=x]=k;
    splay(k,0);
}
void dfs(int k,int x)
{
    if (!k) return;
    down(k);
    ins(tree[k].x-x);
    dfs(lson,x),dfs(rson,x);
}
void modify(int x) 
{
    int p=qpre(root,x),q=qsuf(root,2*x);
    splay(p,0);splay(q,p);
    int k=tree[q].ch[0];tree[q].ch[0]=0;up(q);up(p);update(q,x);
    dfs(k,x);
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj4923.in","r",stdin);
    freopen("bzoj4923.out","w",stdout);
    const char LL[]="%I64d
";
#else
    const char LL[]="%lld
";
#endif
    n=read(),m=read();
    for (int i=1;i<=n;i++) a[i]=read();
    a[0]=0,a[n+1]=inf;sort(a,a+n+1);
    build(root,0,n+1);
    for (int i=1;i<=m;i++)
    {
        int op=read(),x=read();
        if (op==1) printf("%d
",tree[find(root,x+1)].x);
        else modify(x);
    }
    return 0;
}