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package g0301_0400.s0307_range_sum_query_mutable;

// #Medium #Array #Design #Segment_Tree #Binary_Indexed_Tree
// #2023_03_31_Time_92_ms_(90.27%)_Space_75.3_MB_(16.68%)

/**
 * 307 - Range Sum Query - Mutable\.
 *
 * Medium
 *
 * Given an integer array `nums`, handle multiple queries of the following types:
 *
 * 1.  **Update** the value of an element in `nums`.
 * 2.  Calculate the **sum** of the elements of `nums` between indices `left` and `right` **inclusive** where `left <= right`.
 *
 * Implement the `NumArray` class:
 *
 * *   `NumArray(int[] nums)` Initializes the object with the integer array `nums`.
 * *   `void update(int index, int val)` **Updates** the value of `nums[index]` to be `val`.
 * *   `int sumRange(int left, int right)` Returns the **sum** of the elements of `nums` between indices `left` and `right` **inclusive** (i.e. `nums[left] + nums[left + 1] + ... + nums[right]`).
 *
 * **Example 1:**
 *
 * **Input**
 *
 *     ["NumArray", "sumRange", "update", "sumRange"]
 *     [[[1, 3, 5]], [0, 2], [1, 2], [0, 2]]
 *
 * **Output:** [null, 9, null, 8]
 *
 * **Explanation:**
 *
 *     NumArray numArray = new NumArray([1, 3, 5]);
 *     numArray.sumRange(0, 2); // return 1 + 3 + 5 = 9
 *     numArray.update(1, 2); // nums = [1, 2, 5]
 *     numArray.sumRange(0, 2); // return 1 + 2 + 5 = 8 
 *
 * **Constraints:**
 *
 * *   1 <= nums.length <= 3 * 10⁴
 * *   `-100 <= nums[i] <= 100`
 * *   `0 <= index < nums.length`
 * *   `-100 <= val <= 100`
 * *   `0 <= left <= right < nums.length`
 * *   At most 3 * 10⁴ calls will be made to `update` and `sumRange`.
**/
public class NumArray {
    private int[] tree;
    private int[] nums;

    public NumArray(int[] nums) {
        tree = new int[nums.length + 1];
        this.nums = nums;
        // copy the array into the tree
        System.arraycopy(nums, 0, tree, 1, nums.length);
        for (int i = 1; i < tree.length; i++) {
            int parent = i + (i & -i);
            if (parent < tree.length) {
                tree[parent] += tree[i];
            }
        }
    }

    public void update(int index, int val) {
        int currValue = nums[index];
        nums[index] = val;
        index++;
        while (index < tree.length) {
            tree[index] = tree[index] - currValue + val;
            index = index + (index & -index);
        }
    }

    private int sum(int i) {
        int sum = 0;
        while (i > 0) {
            sum += tree[i];
            i -= (i & -i);
        }
        return sum;
    }

    public int sumRange(int left, int right) {
        return sum(right + 1) - sum(left);
    }
}

/*
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(index,val);
 * int param_2 = obj.sumRange(left,right);
 */