[LeetCode][JavaScript]Range Sum Query

Range Sum Query - Mutable

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

The update(i, val) function modifies nums by updating the element at index i to val.

Example:

Given nums = [1, 3, 5]

sumRange(0, 2) -> 9
update(1, 2)
sumRange(0, 2) -> 8

Note:

1. The array is only modifiable by the update function.
2. You may assume the number of calls to update and sumRange function is distributed evenly

https://leetcode.com/problems/range-sum-query-mutable/

---

线段树。

举例来说[2, 4, 6, 8, 10]，如图所示建立线段树。

黑色为数组下标，红色是这个线段对应元素的和。

update和sumRange的复杂度都是O(logn)。

 

建立线段树：

root节点的长度就是入参数组的长度，找出middle，递归建立左子树和右子树。

update操作：

从上往下找到要更新的叶子节点，递归回溯的时候，把祖先的节点的val也一起更新了。

sumRange操作：

找到目标线段，返回val，如果结果分散在左右子树中，分开找到之后相加。 

/**
 * @constructor
 * @param {number[]} nums
 */
var NumArray = function(nums) {
    if(nums.length === 0) return;
    this._root = buildSegment(0, nums.length - 1);
    
    function buildSegment(start, end){
        var currNode = new Node(start, end);
        if(start === end){
            currNode.val = nums[start];
        }else{
            var middle = parseInt((start + end) / 2);
            currNode.left = buildSegment(start, middle);
            currNode.right = buildSegment(middle + 1, end);
            currNode.val = currNode.left.val + currNode.right.val;
        }
        return currNode;
    }
    function Node(start, end){
        this.start = start;
        this.end = end;
        this.val = null;
        this.left = null;
        this.right = null;
    }
};

/**
 * @param {number} i
 * @param {number} val
 * @return {void}
 */
NumArray.prototype.update = function(i, val) {
    updateNum(this._root, i);
    
    function updateNum(node, i){
        if(node.start === node.end && node.start === i){
            node.val = val;
            return node.val;
        }
        var middle = parseInt((node.start + node.end) / 2);
        if(i <= middle){
            node.val -= node.left.val;
            node.val += updateNum(node.left, i);
        }else{
            node.val -= node.right.val;
            node.val += updateNum(node.right, i);
        }
        return node.val;
    }    
};

/**
 * @param {number} i
 * @param {number} j
 * @return {number}
 */
NumArray.prototype.sumRange = function(i, j) {
    return findRange(this._root, i, j);
    
    function findRange(node, start, end){
        if(node.start === start && node.end === end){
            return node.val;
        }
        var result = 0, middle = parseInt((node.start + node.end) / 2);
        if(end <= middle){
            result += findRange(node.left, start, end);
        }else if(middle < start){
            result += findRange(node.right, start, end);
        }else{
            result += findRange(node.left, start, middle);
            result += findRange(node.right, middle + 1, end);
        }
        return result;
    }
};


/**
 * Your NumArray object will be instantiated and called as such:
 * var numArray = new NumArray(nums);
 * numArray.sumRange(0, 1);
 * numArray.update(1, 10);
 * numArray.sumRange(0, 2);
 */