# Segment Tree Build

## Question

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 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.

### 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 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]``````

## Solution

``````/**
* 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) {
if(start > end) {  // check core case
return null;
}

SegmentTreeNode root = new SegmentTreeNode(start, end);

if(start != end) {
int mid = (start + end) / 2;
root.left = build(start, mid);
root.right = build(mid + 1, end);
}
return root;
}
}``````

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