The structure of Segment Tree is a binary tree which each node has two attributesstartandenddenote 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 abuildmethod 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.

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Clarification

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

See wiki:
Segment Tree
Interval 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)

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/**
 * 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) {
        // write your code here
        if (A == null || A.length == 0) {
            return null;
        }

        return divideConquer(A, 0, A.length - 1);
    }

    public SegmentTreeNode divideConquer(int[] A, int start, int end) {
        //exit
        if (start == end) {
            return new SegmentTreeNode(start, start, A[start]);
        }


        SegmentTreeNode root = new SegmentTreeNode(start, end, 0);

        int mid = (start + end) / 2;

        SegmentTreeNode left = divideConquer(A, start, mid);
        SegmentTreeNode right = divideConquer(A, mid + 1, end);

        root.left = left;
        root.right = right;

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

    }


}