Splay

Splay - AcWing 950 - 郁闷的出纳员

之前做过这道题目，当时是用权值线段树做的。本题还可以用splay做，splay用于维护一些区间问题。这是第一道凭个人记忆打出的splay模板，可以说对于splay有一个基本的理解了。

#include <bits/stdc++.h>
using namespace std;

const int N = 100010,INF = 1e9;

int n,m,k;
int root,idx;
int delta,tot;
char op[2];

struct Node{
    int s[2],p,v;
    int size;
    void init(int _p,int _v){
        p = _p;
        v = _v;
    }
    
}tr[N];



inline int ws(int x){
    return tr[tr[x].p].s[1] == x;
}

void push_up(int x){
    tr[x].size = tr[tr[x].s[0]].size + tr[tr[x].s[1]].size + 1;
}

void rotate(int x){
    int y = tr[x].p;
    int z = tr[y].p;
    int k = ws(x);
    
    // modify z
    tr[z].s[ws(y)] = x;
    
    // modify y
    tr[y].p = x;
    tr[y].s[k] = tr[x].s[k^1];
    
    // modify m
    tr[tr[x].s[k^1]].p = y;
    
    // modify x
    tr[x].p = z;
    tr[x].s[k^1] = y;
    
    push_up(y);
    push_up(x);
}

void splay(int x,int k){
    while(tr[x].p != k){
        int y = tr[x].p;
        int z = tr[y].p;
        if(z != k){
            if(ws(x) ^ ws(y)){
                rotate(x);
            }else{
                rotate(y);
            }
        }
        rotate(x);
    }
    
    if(k == 0) root = x;
}

int insert(int v){
    int u = root;
    int p = 0;
    while(u){
        p = u;
        u = tr[u].s[v > tr[u].v];
    }
    u = ++idx;
    if(p) tr[p].s[v > tr[p].v] = u;
    tr[u].init(p,v);
    splay(u,0);
    return u;
}

int get_k(int k){
    int u = root;
    while(u){
        if(tr[tr[u].s[0]].size >= k){
            u = tr[u].s[0];
        }else if(tr[tr[u].s[0]].size + 1 == k){
            return u;
        }else{
            k -= tr[tr[u].s[0]].size + 1;
            u = tr[u].s[1];
        }
    }
    return -1;
}


// find the max one that leq than v
int get_v(int v){
    int res = -1;
    int u = root;
    while(u){
        if(tr[u].v >= v){
            res = u;
            u = tr[u].s[0];
        }else{
            u = tr[u].s[1];
        }
    }
    return res;
}


int main(){
    scanf("%d%d",&n,&m);
    
    int L = insert(-INF), R = insert(INF);
    
    while(n--){
        scanf("%s%d",op,&k);
        
        if(*op == 'I'){
            if(k >= m){
                ++tot;
                insert(k-delta);
            }
        }else if(*op == 'A'){
            delta += k;
        }else if(*op == 'S'){
            delta -= k;
            // delete all less than m - delta
            R = get_v(m - delta);
            // [L,R]
            splay(R,0);
            splay(L,R);
            tr[L].s[1] = 0;
            push_up(L);
            push_up(R);
        }else{
            if(tr[root].size - 2 < k){
                puts("-1");
            }else{
                // tr[root].size - k
                int test = get_k(tr[root].size - k);
                printf("%d
",tr[test].v + delta);
            }
        }
    }
    
    printf("%d
",tot-(tr[root].size-2));
    return 0;
}