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# Segment Tree Build II

## Problem

The structure of Segment Tree is a binary tree which each node has two attributes start and end denote an segment / interval.

start and end are both integers, they should be assigned in following rules:

• The root's start and end is given by build method.
• The left child of node A has `start=A.left`, `end=(A.left + A.right) / 2`.
• The right child of node A has `start=(A.left + A.right) / 2 + 1`, `end=A.right`.
• if start equals to end, there will be no children for this node.

Implement a build method with a given array, so that we can create a corresponding segment tree with every node value represent the corresponding interval max value in the array, return the root of this segment tree.

### Example

Given `[3,2,1,4]`. The segment tree will be:

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

### Note

Segment Tree (a.k.a Interval Tree) is an advanced data structure which can support queries like:

which of these intervals contain a given point

which of these points are in a given interval