Splay入门

伸展树-Splay

对于本题的区间flip操作，线段树难以实现；用splay来做非常合适。

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

const int N = 1e5+50;

int n,m;
struct Node{
    int s[2],p,v;
    int size,flag;
    
    void init(int _v,int _p){
        v = _v;
        p = _p;
        size = 1;
    }
}tr[N];

int root,idx;

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

void push_down(int x){
    if(tr[x].flag){
        swap(tr[x].s[0],tr[x].s[1]);
        tr[tr[x].s[0]].flag ^= 1;
        tr[tr[x].s[1]].flag ^= 1;
        tr[x].flag = 0;
    }
}

void rotate(int x){
    int y = tr[x].p;
    int z = tr[y].p;
    int k = tr[y].s[1] == x;
    tr[z].s[tr[z].s[1] == y] = x;
    tr[x].p = z;
    
    tr[y].s[k] = tr[x].s[k^1];
    tr[tr[x].s[k^1]].p = y;
    
    tr[x].s[k^1] = y;
    tr[y].p = x;
    
    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((tr[y].s[1] == x) ^ (tr[z].s[1] == y)){
                rotate(x);
            }else{
                rotate(y);
            }
        }
        rotate(x);
    }
    if(!k) root = x;
}

void 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(v,p);
    splay(u,0);
}


int get_k(int k){
    int u = root;
    while(1){
        push_down(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;
}

void output(int u){
    push_down(u);
    if(tr[u].s[0])output(tr[u].s[0]);
    if(tr[u].v >= 1 && tr[u].v <= n) printf("%d ",tr[u].v); // 不是哨兵就输出
    if(tr[u].s[1])output(tr[u].s[1]);
}

int main(){
    
    scanf("%d%d",&n,&m);
    for(int i = 0; i <= n+1; ++i){
        insert(i);
    }
    
    while(m--){
        int l,r;
        scanf("%d%d",&l,&r);
        l = get_k(l);
        r = get_k(r+2);
        splay(l,0);
        splay(r,l);
        tr[tr[r].s[0]].flag = 1;
    }
    
    output(root);
    return 0;
}