[tree cover] [learning notes]

thought

Tree cover tree, like his name, is a tree cover another tree. Use an outer tree to maintain something like intervals. Then each node of the outer tree is an inner tree. That's it.

A template question

bzoj3196

thinking

This is a template problem of line tree set balance tree. The outer layer uses a line segment tree to maintain the section operation. Then each node of the line tree is a balance tree

Operation 1: query the number smaller than k from l to r, and then output + 1

Action 2: split the answer and find the maximum value of ranking less than or equal to k

Action 3: delete the original value first, and then add a new value

Operation 4: query the precursor in each sub interval, and the largest one is the precursor in the current interval

Operation 5: similar to operation 4, query the successor in each subinterval, and then the smallest one is the successor in the current interval.

PS: do not forget to change the value in the original array during operation 3, or you will make an error when you delete it later. 2 hours 2333 in this place

Code

/*
* @Author: wxyww
* @Date:   2018-12-11 08:29:48
* @Last Modified time: 2018-12-11 10:44:01
*/
#include<cstdio>
#include<iostream>
#include<cstdlib>
#include<cmath>
#include<ctime>
#include<bitset>
using namespace std;
typedef long long ll;
#define ls TR[cur].ch[0]
#define rs TR[cur].ch[1]
const int N = 100000 + 100,INF = 2147483647;
ll read() {
    ll 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*10+c-'0';
        c=getchar();
    }
    return x*f;
}
namespace treap {
    struct node {
        int val,siz,ch[2],id,cnt;
    }TR[N * 20];
    void up(int cur) {
        TR[cur].siz = TR[ls].siz + TR[rs].siz + TR[cur].cnt;
    }
    int tot = 0;
    void rotate(int &cur,int f) {
        int son = TR[cur].ch[f];
        TR[cur].ch[f] = TR[son].ch[f ^ 1];
        TR[son].ch[f ^ 1] = cur;
        up(cur);
        cur = son;
        up(cur);
    }
    void insert(int &cur,int val) {
        if(!cur) {
            cur = ++tot;
            TR[cur].val = val;
            TR[cur].siz = TR[cur].cnt = 1;
            TR[cur].id = rand();
            return;
        }
        TR[cur].siz++;
        if(val == TR[cur].val) {TR[cur].cnt++;return;}
        int d = val > TR[cur].val;
        insert(TR[cur].ch[d],val);
        if(TR[TR[cur].ch[d]].id < TR[cur].id) rotate(cur,d);
    }
    void del(int &cur,int val) {
        if(!cur) return;
        if(TR[cur].val == val) {
            if(TR[cur].cnt > 1) {TR[cur].cnt--;TR[cur].siz--;return;}
            if(!ls || !rs) {cur = ls + rs;return;}
            rotate(cur,TR[rs].id < TR[ls].id);
            del(cur,val);
            return;
        }
        TR[cur].siz--;
        del(TR[cur].ch[val > TR[cur].val],val);
    }
    int Rank(int cur,int val) {
        int ans = 0;
        while(cur) {
            if(val < TR[cur].val) cur = ls;
            else if(val == TR[cur].val) return ans + TR[ls].siz;
            else ans += TR[ls].siz + TR[cur].cnt,cur = rs;
        }
        return ans;
    }
    int pred(int cur,int val) {
        if(!cur) return -INF;
        if(val > TR[cur].val) return max(pred(rs,val),TR[cur].val);
        else return pred(ls,val);
    }
    int nex(int cur,int val) {
        if(!cur) return INF;
        if(val < TR[cur].val) return min(nex(ls,val),TR[cur].val);
        else return nex(rs,val);
    }
}
using namespace treap;
int tree[N << 2];
int a[N];
int n;
void build(int rt,int l,int r) {
    if(l == r) {
        insert(tree[rt],a[l]);
        return;
    }
    int mid = (l + r) >> 1;
    for(int i = l;i <= r;++i) insert(tree[rt],a[i]);
    build(rt << 1,l,mid);
    build(rt << 1 | 1,mid + 1,r);
}
void delet(int rt,int l,int r,int pos,int c) {
    if(l == r) {
        insert(tree[rt],c);
        del(tree[rt],a[pos]);
        return;
    }
    insert(tree[rt],c);
    del(tree[rt],a[pos]);
    int mid = (l + r) >> 1;
    if(pos <= mid) delet(rt << 1,l,mid,pos,c);
    else delet(rt << 1 | 1,mid + 1,r,pos,c);
}
int getrank(int rt,int l,int r,int L,int R,int val) {
    if(L <= l && R >= r) return Rank(tree[rt],val);
    int mid = (l + r) >> 1;
    int ans = 0;
    if(L <= mid) ans += getrank(rt << 1,l,mid,L,R,val);
    if(R > mid) ans += getrank(rt << 1 | 1,mid + 1,r,L, R,val);
    return ans;
}
int getpred(int rt,int l,int r,int L,int R,int val) {
    if(L <= l && R >= r) return pred(tree[rt],val);
    int mid = (l + r) >> 1;
    int ans = -INF;
    if(L <= mid) ans = max(ans,getpred(rt << 1,l,mid,L,R,val));
    if(R > mid) ans = max(ans,getpred(rt << 1 | 1,mid + 1,r,L, R,val));
    return ans;
}
int getnex(int rt,int l,int r,int L,int R,int val) {
    if(L <= l && R >= r) return nex(tree[rt],val);
    int mid = (l + r) >> 1;
    int ans = INF;
    if(L <= mid) ans = min(ans,getnex(rt << 1,l,mid,L,R,val));
    if(R > mid) ans = min(ans,getnex(rt << 1 | 1,mid + 1,r,L,R,val));
    return ans;
}
int MAX = -INF;
int getkth(int L,int R,int x) {
    int l = 0,r = INF;
    int ans = 0;
    while(l <= r) {
        int mid = (l + r) >> 1;
        if(getrank(1,1,n,L,R,mid) + 1<= x) ans = mid,l = mid + 1;
        else r = mid - 1;
    }
    return ans;
}
int main() {

    n = read();
    int m = read();
    for(int i = 1;i <= n;++i) a[i] = read();
    build(1,1,n);
    while(m--) {
        int opt = read();
        if(opt == 1) {
            int l = read(),r = read(),k = read();
            printf("%d\n",getrank(1,1,n,l,r,k) + 1);
        }
        if(opt == 2) {
            int l = read(),r = read(),k = read();
            printf("%d\n",getkth(l,r,k));
        }
        if(opt == 3) {
            int pos = read(),k = read();
            delet(1,1,n,pos,k);
            a[pos] = k;//!!!
        }
        if(opt == 4) {
            int l = read(),r = read(),k = read();
            printf("%d\n",getpred(1,1,n,l,r,k));
        }
        if(opt == 5) {
            int l = read(),r = read(),k = read();
            printf("%d\n",getnex(1,1,n,l,r,k));
        }
    }
    return 0;
}

Tags: C++ less

Posted on Tue, 03 Dec 2019 19:44:21 -0500 by florida_guy99