LintCode "Interval Sum II"

struct Node
{
    Node(int rs, int re) : s(rs), e(re), left(nullptr), right(nullptr){}    
    int s;
    int e;
    long long sum;
    Node *left;
    Node *right;
};

class Solution {
    Node *root;
public:
    
    /**
     * @param A: An integer vector
     */
    Node * _build(int s, int e, vector<int> &A)
    {
    if(s > e) return nullptr;
    Node *p = new Node(s, e);
    if(s == e)
    {
        p->sum = A[s];
        return p;
    }
    int mid = (s + e) / 2;
    p->left = _build(s, mid, A);
    p->right= _build(mid+1, e, A);
    p->sum = p->left->sum + p->right->sum;
    
    return p;
    }
    Solution(vector<int> A) {
        root = _build(0, A.size() - 1, A);
    }
    
    /**
     * @param start, end: Indices
     * @return: The sum from start to end
     */
    long long _query(Node *p, int start, int end)
    {
    if(start == p->s && end == p->e)
    {
        return p->sum;
    }
    
    int mid = (p->s + p->e) / 2;
    if(end <= mid)
    {
        return _query(p->left, start, end);
    }
    else if(start > mid)
    {
        return _query(p->right, start, end);        
    }
    
    long long rl = _query(p->left, start, mid);
    long long rr = _query(p->right,mid+1, end);
    return rl + rr;
    }
    long long query(int start, int end) {
        return _query(root, start, end);
    }
    
    /**
     * @param index, value: modify A[index] to value.
     */
    int _modify(Node *p, int i, int val)
    {
    if(p->s == p->e && i == p->s)
    {
        int d = val - p->sum;
        p->sum = val;
        return d;
    }
    
    int mid = (p->s + p->e) / 2;
    int d = 0;
    if (i <= mid)
    {
        d = _modify(p->left, i, val);
    }
    else
    {
        d = _modify(p->right,i, val);
    }
    p->sum += d;
    return d;
    }
    void modify(int index, int value) {
        _modify(root, index, value);
    }
};