307. 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:
The array is only modifiable by the update function.
You may assume the number of calls to update and sumRange function is distributed evenly.

Solution：Segment Tree

思路：
Time Complexity: O(N) O(logN) O(logN) Space Complexity: O(N)

Solution Code：

public class NumArray {

    class SegmentTreeNode {
        int start, end;
        SegmentTreeNode left, right;
        int sum;

        public SegmentTreeNode(int start, int end) {
            this.start = start;
            this.end = end;
            this.left = null;
            this.right = null;
            this.sum = 0;
        }
    }
      
    SegmentTreeNode root = null;
   
    public NumArray(int[] nums) {
        root = buildTree(nums, 0, nums.length-1);
    }

    private SegmentTreeNode buildTree(int[] nums, int start, int end) {
        if (start > end) {
            return null;
        } else {
            SegmentTreeNode ret = new SegmentTreeNode(start, end);
            if (start == end) {
                ret.sum = nums[start];
            } else {
                int mid = start  + (end - start) / 2;             
                ret.left = buildTree(nums, start, mid);
                ret.right = buildTree(nums, mid + 1, end);
                ret.sum = ret.left.sum + ret.right.sum;
            }         
            return ret;
        }
    }
   
    void update(int i, int val) {
        update(root, i, val);
    }
   
    void update(SegmentTreeNode root, int pos, int val) {
        if (root.start == root.end) {
           root.sum = val;
        } else {
            int mid = root.start + (root.end - root.start) / 2;
            if (pos <= mid) {
                 update(root.left, pos, val);
            } else {
                 update(root.right, pos, val);
            }
            root.sum = root.left.sum + root.right.sum;
        }
    }

    public int sumRange(int i, int j) {
        return sumRange(root, i, j);
    }
    
    public int sumRange(SegmentTreeNode root, int start, int end) {
        if (root.end == end && root.start == start) {
            return root.sum;
        } else {
            int mid = root.start + (root.end - root.start) / 2;
            if (end <= mid) {
                return sumRange(root.left, start, end);
            } else if (start >= mid+1) {
                return sumRange(root.right, start, end);
            }  else {    
                return sumRange(root.right, mid+1, end) + sumRange(root.left, start, mid);
            }
        }
    }
}