// Source : https://leetcode.com/problems/range-sum-query-immutable/
// Author : Calinescu Valentin, Hao Chen
// Date   : 2015-11-10

/*************************************************************************************** 
 *
 * Given an integer array nums, find the sum of the elements between indices i and j
 * (i ≤ j), inclusive.
 * 
 * Example:
 * Given nums = [-2, 0, 3, -5, 2, -1]
 * 
 * sumRange(0, 2) -> 1
 * sumRange(2, 5) -> -1
 * sumRange(0, 5) -> -3
 * Note:
 * You may assume that the array does not change.
 * There are many calls to sumRange function.
 *               
 ***************************************************************************************/

class NumArray {
/* 
 * Solution
 * =========
 *
 * The sum of all the elements starting from position 0 to position i is stored in
 * sums[i]. This way we can reconstruct the sum from position i to position j by
 * subtracting sums[i - 1] from sums[j], leaving us with the sum of the desired elements.
 *
 * Note: we can add a dummy sum at then beginning to simplify the code
 * 
 */
private:
    int size;
    vector <long long> sums;
public:
    NumArray(vector<int> &nums): size(nums.size()), sums(size+1, 0) {
        for(int i=0; i<size; i++) {
            sums[i+1] = sums[i] + nums[i];
        } 
    }
    int sumRange(int i, int j) {
        return sums[j+1] - sums[i];
    }
};


// Your NumArray object will be instantiated and called as such:
// NumArray numArray(nums);
// numArray.sumRange(0, 1);
// numArray.sumRange(1, 2);