library

This documentation is automatically generated by online-judge-tools/verification-helper

Project maintained by tko919 Hosted on GitHub Pages — Theme by mattgraham

:heavy_check_mark: 2D Segment Tree
(DataStructure/2dsegtree.hpp)

Depends on

Verified with

Code

#pragma once
#include "DataStructure/segtree.hpp"


template<typename M,typename N,M (*f)(M,M),M (*g)(M,N),M (*m1)()>struct SegmentTree2D{
    int n;
    vector<SegmentTree<M,N,f,g,m1>> st;
    vector<vector<int>> ys;
    SegmentTree2D(){}
    int id(int x,int y){return lower_bound(ALL(ys[x]),y)-ys[x].begin();}
    using P=pair<int,int>;
    vector<int> xs; vector<P> ps;
    void push(int x,int y){
        ps.push_back({x,y});
    }
    void init(){
        for(auto& [x,y]:ps)xs.push_back(x);
        sort(ALL(xs));
        xs.erase(unique(ALL(xs)),xs.end());
        n=xs.size();
        ys.resize(n*2);
        for(auto& [x,y]:ps){
            int i=lower_bound(ALL(xs),x)-xs.begin();
            for(i+=n;i;i>>=1)ys[i].push_back(y);
        }
        for(int i=0;i<n*2;i++){
            sort(ALL(ys[i]));
            ys[i].erase(unique(ALL(ys[i])),ys[i].end());
            st.push_back(SegmentTree<M,N,f,g,m1>(ys[i].size()));
        }
    }
    void update(int x,int y,N w){
        x=(lower_bound(ALL(xs),x)-xs.begin())+n;
        st[x].update(id(x,y),w);
        M cur=st[x][id(x,y)];
        int pos=x;
        while(x>>=1){
            M opp=st[pos^1].query(id(pos^1,y),id(pos^1,y+1));
            cur=f(cur,opp);
            st[x].set(id(x,y),cur);
            pos>>=1;
        }
    }
    M query(int x0,int x1,int y0,int y1){
        x0=lower_bound(ALL(xs),x0)-xs.begin();
        x1=lower_bound(ALL(xs),x1)-xs.begin();
        M res=m1();
        for(x0+=n,x1+=n;x0<x1;x0>>=1,x1>>=1){
            if(x0&1)res=f(res,st[x0].query(id(x0,y0),id(x0,y1))),x0++;
            if(x1&1)x1--,res=f(res,st[x1].query(id(x1,y0),id(x1,y1)));
        }
        return res;
    }
};

/**
 * @brief 2D Segment Tree
 */
#line 2 "DataStructure/segtree.hpp"

template <typename M, typename N, M (*f)(M, M), M (*g)(M, N), M (*m1)()>
struct SegmentTree {
    int sz, n;
    vector<M> data;
    SegmentTree(int _n = 0) : n(_n) {
        sz = 1;
        while (sz < _n)
            sz <<= 1;
        data.assign(2 * sz, m1());
    }
    void run(vector<M> &v) {
        for (int i = 0; i < (int)v.size(); i++)
            data[i + sz] = v[i];
        for (int k = sz - 1; k > 0; k--)
            data[k] = f(data[2 * k], data[2 * k + 1]);
    }
    void set(int k, const M &x) {
        k += sz;
        data[k] = x;
        while (k >>= 1)
            data[k] = f(data[2 * k], data[2 * k + 1]);
    }
    void update(int k, const N &x) {
        k += sz;
        data[k] = g(data[k], x);
        while (k >>= 1)
            data[k] = f(data[2 * k], data[2 * k + 1]);
    }
    M query(int a, int b) {
        M L = m1(), R = m1();
        for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
            if (a & 1)
                L = f(L, data[a++]);
            if (b & 1)
                R = f(data[--b], R);
        }
        return f(L, R);
    }
    M operator[](const int &k) const {
        return data[k + sz];
    }
    vector<M> get() {
        return {data.begin() + sz, data.begin() + sz + n};
    }
    template <class F> int max_right(int L, F ch) const {
        int l = sz + L, w = 1;
        M ansL = m1();
        for (; L + w <= sz; l >>= 1, w <<= 1)
            if (l & 1) {
                if (not ch(f(ansL, data[l])))
                    break;
                ansL = f(ansL, data[l++]);
                L += w;
            }
        while (l <<= 1, w >>= 1) {
            if (L + w <= sz && ch(f(ansL, data[l]))) {
                ansL = f(ansL, data[l++]);
                L += w;
            }
        }
        return L;
    }
    template <class F> int min_left(int R, F ch) const {
        int r = sz + R, w = 1;
        M ansR = m1();
        for (; R - w >= 0; r >>= 1, w <<= 1)
            if (r & 1) {
                if (not ch(f(data[r - 1], ansR)))
                    break;
                ansR = f(data[--r], ansR);
                R -= w;
            }
        while (r <<= 1, w >>= 1) {
            if (R - w >= 0 && ch(f(data[r - 1], ansR))) {
                ansR = f(data[--r], ansR);
                R -= w;
            }
        }
        return R;
    }
};

/**
 * @brief Segment Tree
 */
#line 3 "DataStructure/2dsegtree.hpp"

template<typename M,typename N,M (*f)(M,M),M (*g)(M,N),M (*m1)()>struct SegmentTree2D{
    int n;
    vector<SegmentTree<M,N,f,g,m1>> st;
    vector<vector<int>> ys;
    SegmentTree2D(){}
    int id(int x,int y){return lower_bound(ALL(ys[x]),y)-ys[x].begin();}
    using P=pair<int,int>;
    vector<int> xs; vector<P> ps;
    void push(int x,int y){
        ps.push_back({x,y});
    }
    void init(){
        for(auto& [x,y]:ps)xs.push_back(x);
        sort(ALL(xs));
        xs.erase(unique(ALL(xs)),xs.end());
        n=xs.size();
        ys.resize(n*2);
        for(auto& [x,y]:ps){
            int i=lower_bound(ALL(xs),x)-xs.begin();
            for(i+=n;i;i>>=1)ys[i].push_back(y);
        }
        for(int i=0;i<n*2;i++){
            sort(ALL(ys[i]));
            ys[i].erase(unique(ALL(ys[i])),ys[i].end());
            st.push_back(SegmentTree<M,N,f,g,m1>(ys[i].size()));
        }
    }
    void update(int x,int y,N w){
        x=(lower_bound(ALL(xs),x)-xs.begin())+n;
        st[x].update(id(x,y),w);
        M cur=st[x][id(x,y)];
        int pos=x;
        while(x>>=1){
            M opp=st[pos^1].query(id(pos^1,y),id(pos^1,y+1));
            cur=f(cur,opp);
            st[x].set(id(x,y),cur);
            pos>>=1;
        }
    }
    M query(int x0,int x1,int y0,int y1){
        x0=lower_bound(ALL(xs),x0)-xs.begin();
        x1=lower_bound(ALL(xs),x1)-xs.begin();
        M res=m1();
        for(x0+=n,x1+=n;x0<x1;x0>>=1,x1>>=1){
            if(x0&1)res=f(res,st[x0].query(id(x0,y0),id(x0,y1))),x0++;
            if(x1&1)x1--,res=f(res,st[x1].query(id(x1,y0),id(x1,y1)));
        }
        return res;
    }
};

/**
 * @brief 2D Segment Tree
 */
Back to top page