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 two parametersstart_and_end, so that we can create a corresponding segment tree with every node has the correct_start_and_end_value, 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

Givenstart=0, end=3. The segment tree will be:

               [0,  3]
             /        \
      [0,  1]           [2, 3]
      /     \           /     \
   [0, 0]  [1, 1]     [2, 2]  [3, 3]

Givenstart=1, end=6. The segment tree will be:

               [1,  6]
             /        \
      [1,  3]           [4,  6]
      /     \           /     \
   [1, 2]  [3,3]     [4, 5]   [6,6]
   /    \           /     \
[1,1]   [2,2]     [4,4]   [5,5]

divide and conquer

/**
 * Definition of SegmentTreeNode:
 * public class SegmentTreeNode {
 *     public int start, end;
 *     public SegmentTreeNode left, right;
 *     public SegmentTreeNode(int start, int end) {
 *         this.start = start, this.end = end;
 *         this.left = this.right = null;
 *     }
 * }
 */


public class Solution {
    /*
     * @param start: start value.
     * @param end: end value.
     * @return: The root of Segment Tree.
     */
    public SegmentTreeNode build(int start, int end) {
        // write your code here
        if (start > end) {
            return null;
        }

        if (start == end) {
            return new SegmentTreeNode(start, end);
        }

        SegmentTreeNode root = new SegmentTreeNode(start, end);

        int mid = (start + end) / 2;
        SegmentTreeNode left = build(start, mid);
        SegmentTreeNode right = build(mid + 1, end);

        root.left = left;
        root.right = right;
        return root;
    }
}