Problems

# 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.