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.start == root.end) {

             root.max = value;

             return;

         }

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

         if (index <= mid) modify(root.left, index, value);

         else modify(root.right, index, value);

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

     }

 }