Segment Tree for range add and minimum query

starrysky.h

#pragma once

#include <vector>
#include <algorithm>
#include <limits>

template<class T>
class starrysky {
public:
	struct node { T add; T min; };
	explicit starrysky(size_t N=1, T add_init=0, T min_init=std::numeric_limits<T>::max())
		: _add_init(add_init), _min_init(min_init), _N(N), _tree(2*N-1,{add_init,add_init}) {}
	void add(size_t i, size_t j, T data) {
		_add(i,j,data,0,0,_N);
	}
	T min(size_t i, size_t j) {
		return _min(i,j,0,0,_N);
	}
private:
	void _add(size_t i, size_t j, T data, size_t k, size_t l, size_t r) {
		if(j <= l || r <= i) return;
		if(i <= l && r <= j) {
			_tree[k].add += data;
			while(k>0) {
				k = (k - 1) / 2;
				const T vleft = _tree[2*k+1].min + _tree[2*k+1].add;
				const T vright = _tree[2*k+2].min + _tree[2*k+2].add;
				_tree[k].min = std::min(vleft, vright);
			}
		} else {
			_add(i,j,data,k*2+1,l,(l+r)/2);
			_add(i,j,data,k*2+2,(l+r)/2,r);
		}
	}
	T _min(size_t i, size_t j, size_t k, size_t l, size_t r) {
		if(r <= i || j <= l) return _min_init;
		if(i <= l && r <= j) return _tree[k].min + _tree[k].add;
		else {
			const T vleft = _min(i,j,k*2+1,l,(l+r)/2);
			const T vright = _min(i,j,k*2+2,(l+r)/2,r);
			return std::min(vleft,vright) + _tree[k].add;
		}
	}
private:
	T _add_init, _min_init;
	size_t _N;
	std::vector<node> _tree;
};