Segment Tree Build

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 hasstart=A.left, end=(A.left + A.right) / 2.
• The right child of node A hasstart=(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 two parameters start 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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Example

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

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

Given start=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]

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

/**

 * 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, end: Denote an segment / interval

     *@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);

        root.left = build(start, (start+end)/2);

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

        return root;

    }

}