Segment Tree Modify

Problem

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.

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.

Code - Java

/**
 * 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) {
        if (root == null) {
            return;
        }
        if (root.start == index && root.end == index) {
            root.max = value;
        } else {
            modify(root.left, index, value);
            modify(root.right, index, value);
            if (root.left != null && root.right != null) {
                root.max = Math.max(root.left.max, root.right.max);
            }
        }
    }
}