# 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](https://en.wikipedia.org/wiki/Segment_tree)

[Interval Tree](https://en.wikipedia.org/wiki/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]
```

## Analysis

求出中间值，再分别对left，right进行build，递归调用build，生成子树。

## Solution

```java
/**
 * 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;
    }
}
```