src/binary_indexed_tree.hpp

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Last update: 2020-11-26 22:58:46+09:00
Include: #include "src/binary_indexed_tree.hpp"

Depends on

src/template.hpp

Verified with

test/binary_indexed_tree.test.cpp

Code

#pragma once
#include "template.hpp"

template<class ComumutativeMonoid>
struct BinaryIndexedTree {
  using T = typename ComumutativeMonoid::value_type;
  // 1-indexed
  ll n;
  vector<T> tree;
  const ComumutativeMonoid ope;

  BinaryIndexedTree(ll n_) : n(n_), ope(ComumutativeMonoid()) {
    tree.assign(n+1, ope.ide);
  }

  void add(ll p, T a) {
    for (ll x = p+1; x <= n; x += x&-x) {
      tree[x] = ope(tree[x], a);
    }
  }

  // sum [0, r)
  T sum(ll r) const {
    T sum = ope.ide;
    for (ll x = r; x > 0; x -= x&-x) {
      sum = ope(sum, tree[x]);
    }
    return sum;
  }

  /*
  // bit[1] + bit[2] + ... + bit[x] >= w;
  ll lower_bound(T w) const {
    if (w <= 0) return 0;
    ll x = 0, r = 1;
    while (r < n) r <<= 1;
    for (ll k = r; k > 0; k >>= 1){
      if(x+k <= n && tree[x+k] < w){
        w -= tree[x+k];
        x += k;
      }
    }
    return x+1;
  }
  */
};

#line 2 "src/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pl = pair<ll, ll>;
using vl = vector<ll>;
#define rep(i, n) for(ll i = 0; i < (ll)n; i++)
#define rep3(i, l, r) for(ll i = l; i < (ll)r; i++)
#define per(i, n) for(ll i = (ll)n-1; i >= 0; i--)
#define per3(i, l, r) for(ll i = (ll)r-1; i >= (ll)l; i--)
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
template<class T, class U> inline void cmax(T &a, U b) { if (a < b) a = b; }
template<class T, class U> inline void cmin(T &a, U b) { if (a > b) a = b; }
constexpr char el = '\n';
template<class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { os << p.first << " " << p.second; return os; }
template<class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { is >> p.first >> p.second; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { rep(i, v.size()) os << v[i] << (i+1 != (ll)v.size() ? " " : ""); return os; }
template<class T> istream &operator>>(istream &is, vector<T> &v) { for(T &i : v) is >> i; return is; }
struct IoSetup {
  IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(15); }
} io_setup;
#line 3 "src/binary_indexed_tree.hpp"

template<class ComumutativeMonoid>
struct BinaryIndexedTree {
  using T = typename ComumutativeMonoid::value_type;
  // 1-indexed
  ll n;
  vector<T> tree;
  const ComumutativeMonoid ope;

  BinaryIndexedTree(ll n_) : n(n_), ope(ComumutativeMonoid()) {
    tree.assign(n+1, ope.ide);
  }

  void add(ll p, T a) {
    for (ll x = p+1; x <= n; x += x&-x) {
      tree[x] = ope(tree[x], a);
    }
  }

  // sum [0, r)
  T sum(ll r) const {
    T sum = ope.ide;
    for (ll x = r; x > 0; x -= x&-x) {
      sum = ope(sum, tree[x]);
    }
    return sum;
  }

  /*
  // bit[1] + bit[2] + ... + bit[x] >= w;
  ll lower_bound(T w) const {
    if (w <= 0) return 0;
    ll x = 0, r = 1;
    while (r < n) r <<= 1;
    for (ll k = r; k > 0; k >>= 1){
      if(x+k <= n && tree[x+k] < w){
        w -= tree[x+k];
        x += k;
      }
    }
    return x+1;
  }
  */
};