TheAlgorithms-C-Plus-Plus/Range queries/bit.cpp

// Binary Indexed Tree.
#include<bits/stdc++.h>
using namespace std;

class Bit{
  int n;
  vector<int> bit;
  inline int offset(int x){ return (x & (-x)); }

	public:

		Bit(vector<int>& arr){
			n = arr.size();
			bit.assign(n+1,0);
			for(int i=0; i<n; ++i){
				update(i,arr[i]);
			}
		}
		Bit(int x){
			n = x;
			bit.assign(n+1,0);
		}

  void update(int id, int val){
    // Add val at id
    id++;
    while( id <= n ){
      bit[id] += val;
      id += offset(id);
    }
  }

  int sum(int id){
    // Get prefix sum upto id.
    id++;
    int res = 0;
    while( id > 0 ){
      res += bit[id];
      id -= offset(id);
    }
		return res;
  }

  int sum_range(int l, int r){
    return sum(r) - sum(l-1);
  }
};



int main(){

	int n = 5;
	vector<int> arr = {1,2,3,4,5};
	Bit x(arr);

	assert(x.sum_range(0,0) == 1);
	assert(x.sum_range(0,1) == 3);
	assert(x.sum_range(0,2) == 6);
	x.update(0,6);
	assert(x.sum_range(0,0) == 6);
	assert(x.sum_range(0,1) == 8);
	assert(x.sum_range(0,2) == 11);


}