Segment Tree Modify

For a Maximum Segment Tree, which each node has an extra value max to store the maximum value in this node's interval.

Implement a modify function with three parameter root,index and value to change the node's value with [start, end] = [index, index] to the new given value. Make sure after this change, every node in segment tree still has the max attribute with the correct value.

Have you met this question in a real interview? 

Yes

Example

For segment tree:

                      [1, 4, max=3]
                    /                \
        [1, 2, max=2]                [3, 4, max=3]
       /              \             /             \
[1, 1, max=2], [2, 2, max=1], [3, 3, max=0], [4, 4, max=3]

if call modify(root, 2, 4), we can get:

                      [1, 4, max=4]
                    /                \
        [1, 2, max=4]                [3, 4, max=3]
       /              \             /             \
[1, 1, max=2], [2, 2, max=4], [3, 3, max=0], [4, 4, max=3]

or call modify(root, 4, 0), we can get:

                      [1, 4, max=2]
                    /                \
        [1, 2, max=2]                [3, 4, max=0]
       /              \             /             \
[1, 1, max=2], [2, 2, max=1], [3, 3, max=0], [4, 4, max=0]

Note

We suggest you finish problem Segment Tree Build and Segment Tree Query first.

Challenge

Do it in O(h) time, h is the height of the segment tree.

/**

 * Definition of SegmentTreeNode:

 * public class SegmentTreeNode {

 *     public int start, end, max;

 *     public SegmentTreeNode left, right;

 *     public SegmentTreeNode(int start, int end, int max) {

 *         this.start = start;

 *         this.end = end;

 *         this.max = max

 *         this.left = this.right = null;

 *     }

 * }

 */

public class Solution {

    /**

     *@param root, index, value: The root of segment tree and 

     *@ change the node's value with [index, index] to the new given value

     *@return: void

     */

    public void modify(SegmentTreeNode root, int index, int value) {

        // write your code here

        if(root == null || root.start > index || root.end < index) return;

        

        if(root.start == root.end) {

            root.max = value;

            return;

        }    

        int mid = (root.start + root.end) / 2;

        if(mid + 1 <= index){

            modify(root.right, index, value);

        } else {

            modify(root.left, index, value);

        }

        

        root.max = Math.max(root.left.max, root.right.max);

    }

}