*[Lintcode]Segment Tree Build II

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 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.

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)

正向递归从上向下计算区间，用回溯算法从下向上计算区间内最大值，避免在区间内进行搜索。

/**
* 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) {
return helper(A, 0, A.length - 1);
}

private SegmentTreeNode helper(int[] A, int start, int end) {
if(start > end) return null;

SegmentTreeNode root = new SegmentTreeNode(start, end);
if(start == end) {
root.max = A[start];
return root;
}

root.left = helper(A, start, (start + end) / 2);
root.right = helper(A, (start + end) / 2 + 1, end);

//back tracking. Avoiding unnecessaary number.
root.max = Math.max(root.left.max, root.right.max);
return root;
}
}