# 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

## 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 A: a list of integer
* @return: The root of Segment Tree
*/
public SegmentTreeNode build(int[] A) {
if (A.length < 1) return null;
SegmentTreeNode root = build(0, A.length - 1);
setMax(A, root);
return root;
}

private SegmentTreeNode build(int start, int end) {
if (start > end) {
return null;
}
SegmentTreeNode node = new SegmentTreeNode(start, end);
if (start == end) {
return node;
}

node.left = build(start, (start + end) / 2);
node.right = build((start + end) / 2 + 1, end);

return node;
}

private int setMax(int[] A, SegmentTreeNode node) {
if (node.start == node.end) {
node.max = A[node.start];

} else {
node.max = Math.max(setMax(A, node.left), setMax(A, node.right));

}
return node.max;
}
}