data_structure/range_tree.hpp

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• Last update: 2024-07-28 17:15:59+09:00
• Include: #include "data_structure/range_tree.hpp"

Depends on

• data_structure/compress.hpp
• template/const.hpp
• template/inout_old.hpp
• template/template.hpp
• template/utils.hpp

Verified with

• test/data_structure/Point_Add_Rectangle_Sum.test.cpp

Code

#pragma once

#include"../template/template.hpp"
#include"../data_structure/compress.hpp"

namespace noya2 {

template<class M, template<class MM> class data_structure, typename Idx = ll>
struct range_tree {
    using DS = data_structure<M>;
    using T = typename M::value_type;
    void join(Idx x, Idx y){ ps.emplace_back(x,y); }
    void build(){
        for (auto &[x, y] : ps) xs.add(x);
        xs.build();
        //siz = bit_ceil(xs.size());
        siz = 1; while (siz < (int)(xs.size())) siz <<= 1;
        ys.resize(siz*2);
        for (auto &[x, y] : ps){
            int xid = xs.id(x) + siz;
            ys[xid].add(y);
            while (xid > 1){
                xid >>= 1;
                ys[xid].add(y);
            }
        }
        for (int i = 0; i < 2*siz; i++){
            ys[i].build();
            ds.emplace_back(ys[i].size());
        }
    }
    void set(Idx p, Idx q, T val){
        int i = xs.id(p) + siz;
        ds[i].set(ys[i].id(q),val);
        while (i > 1){
            i >>= 1;
            T lr = M::e();
            int i0 = ys[2*i+0].contains_id(q), i1 = ys[2*i+1].contains_id(q);
            if (i0 != -1) lr = M::op(lr, ds[2*i+0].get(i0));
            if (i1 != -1) lr = M::op(lr, ds[2*i+1].get(i1));
            ds[i].set(ys[i].id(q),lr);
        }
    }
    T get(Idx p, Idx q){
        int ip = xs.contains_id(p);
        if (ip == -1) return M::e();
        int i = ip + siz;
        int iq = ys[i].contains_id(q);
        if (iq == -1) return M::e();
        return ds[i].get(iq);
    }
    T prod(Idx lp, Idx rp, Idx lq, Idx rq){
        T res = M::e();
        int li = xs.lb(lp), ri = xs.lb(rp);
        for (li += siz, ri += siz; li < ri; li >>= 1, ri >>= 1){
            if (li & 1) res = M::op(res,ds[li].prod(ys[li].lb(lq),ys[li].lb(rq))), ++li;
            if (ri & 1) --ri, res = M::op(res,ds[ri].prod(ys[ri].lb(lq),ys[ri].lb(rq)));
        }
        return res;
    }
    int siz;
    vector<pair<Idx,Idx>> ps;
    compress<Idx> xs;
    vector<compress<Idx>> ys;
    vector<DS> ds;
};

} // namespace noya2

#line 2 "data_structure/range_tree.hpp"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "data_structure/compress.hpp"

#line 5 "data_structure/compress.hpp"

namespace noya2{

template<typename T>
struct compress {
    std::vector<T> raws;
    compress () {}
    compress (const vector<T> &_raws) : raws(_raws){ build(); }
    void build(){
        std::sort(raws.begin(), raws.end());
        raws.erase(std::unique(raws.begin(), raws.end()), raws.end());
    }
    int id(const T &raw){ return lb(raw); }
    T raw(const int &id){ return raws[id]; }
    void add(const T &raw){ raws.emplace_back(raw); }
    void reserve(size_t sz){ raws.reserve(sz); }
    size_t size(){ return raws.size(); }
    int lb(const T &raw){ return lower_bound(all(raws),raw) - raws.begin(); }
    int ub(const T &raw){ return upper_bound(all(raws),raw) - raws.begin(); }
    bool contains(const T &raw){
        int jd = lb(raw);
        if (jd < (int)size()) return raws[jd] == raw;
        return false;
    }
    int contains_id(const T &raw){
        int jd = lb(raw);
        if (jd < (int)size() && raws[jd] == raw) return jd;
        return -1;
    }
};

} // namespace noya2
#line 5 "data_structure/range_tree.hpp"

namespace noya2 {

template<class M, template<class MM> class data_structure, typename Idx = ll>
struct range_tree {
    using DS = data_structure<M>;
    using T = typename M::value_type;
    void join(Idx x, Idx y){ ps.emplace_back(x,y); }
    void build(){
        for (auto &[x, y] : ps) xs.add(x);
        xs.build();
        //siz = bit_ceil(xs.size());
        siz = 1; while (siz < (int)(xs.size())) siz <<= 1;
        ys.resize(siz*2);
        for (auto &[x, y] : ps){
            int xid = xs.id(x) + siz;
            ys[xid].add(y);
            while (xid > 1){
                xid >>= 1;
                ys[xid].add(y);
            }
        }
        for (int i = 0; i < 2*siz; i++){
            ys[i].build();
            ds.emplace_back(ys[i].size());
        }
    }
    void set(Idx p, Idx q, T val){
        int i = xs.id(p) + siz;
        ds[i].set(ys[i].id(q),val);
        while (i > 1){
            i >>= 1;
            T lr = M::e();
            int i0 = ys[2*i+0].contains_id(q), i1 = ys[2*i+1].contains_id(q);
            if (i0 != -1) lr = M::op(lr, ds[2*i+0].get(i0));
            if (i1 != -1) lr = M::op(lr, ds[2*i+1].get(i1));
            ds[i].set(ys[i].id(q),lr);
        }
    }
    T get(Idx p, Idx q){
        int ip = xs.contains_id(p);
        if (ip == -1) return M::e();
        int i = ip + siz;
        int iq = ys[i].contains_id(q);
        if (iq == -1) return M::e();
        return ds[i].get(iq);
    }
    T prod(Idx lp, Idx rp, Idx lq, Idx rq){
        T res = M::e();
        int li = xs.lb(lp), ri = xs.lb(rp);
        for (li += siz, ri += siz; li < ri; li >>= 1, ri >>= 1){
            if (li & 1) res = M::op(res,ds[li].prod(ys[li].lb(lq),ys[li].lb(rq))), ++li;
            if (ri & 1) --ri, res = M::op(res,ds[ri].prod(ys[ri].lb(lq),ys[ri].lb(rq)));
        }
        return res;
    }
    int siz;
    vector<pair<Idx,Idx>> ps;
    compress<Idx> xs;
    vector<compress<Idx>> ys;
    vector<DS> ds;
};

} // namespace noya2

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