noya2_Library

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:heavy_check_mark: data_structure/binary_indexed_tree.hpp

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Code

#pragma once

#include"../template/template.hpp"
#include"../misc/concepts.hpp"

namespace noya2{

template <Group G>
struct binary_indexed_tree {
    using T = typename G::value_type;
    binary_indexed_tree (int _n = 0) : n(_n), d(_n + 1, G::e()) {}
    void add(int i, T val) {
        for (int x = i+1; x <= n; x += x & -x) {
            d[x] = G::op(d[x],val);
        }
    }
    T prod(int r){
        return prefix_prod(r);
    }
    T prod(int l, int r) {
        return G::op(G::inv(prefix_prod(l)),prefix_prod(r));
    }
    T get(int i){
        return prod(i,i+1);
    }
    void set(int i, T val){
        add(i,G::op(G::inv(get(i)),val));
    }
  private:
    int n;
    std::vector<T> d;
    T prefix_prod(int i) {
        assert(0 <= i && i <= n);
        T ret = G::e();
        for (int x = i; x > 0; x -= x & -x) {
            ret = G::op(ret,d[x]);
        }
        return ret;
    }
};

} // namespace noya2
#line 2 "data_structure/binary_indexed_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 "misc/concepts.hpp"

#include<concepts>

namespace noya2 {

template<class monoid>
concept Monoid = requires {
    typename monoid::value_type;
    {monoid::op(declval<typename monoid::value_type>(),declval<typename monoid::value_type>())} -> std::same_as<typename monoid::value_type>;
    {monoid::e()} -> std::same_as<typename monoid::value_type>;
};

template<class group>
concept Group = requires {
    requires Monoid<group>;
    {group::inv(declval<typename group::value_type>())} -> std::same_as<typename group::value_type>;
};

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

namespace noya2{

template <Group G>
struct binary_indexed_tree {
    using T = typename G::value_type;
    binary_indexed_tree (int _n = 0) : n(_n), d(_n + 1, G::e()) {}
    void add(int i, T val) {
        for (int x = i+1; x <= n; x += x & -x) {
            d[x] = G::op(d[x],val);
        }
    }
    T prod(int r){
        return prefix_prod(r);
    }
    T prod(int l, int r) {
        return G::op(G::inv(prefix_prod(l)),prefix_prod(r));
    }
    T get(int i){
        return prod(i,i+1);
    }
    void set(int i, T val){
        add(i,G::op(G::inv(get(i)),val));
    }
  private:
    int n;
    std::vector<T> d;
    T prefix_prod(int i) {
        assert(0 <= i && i <= n);
        T ret = G::e();
        for (int x = i; x > 0; x -= x & -x) {
            ret = G::op(ret,d[x]);
        }
        return ret;
    }
};

} // namespace noya2
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