108. Convert Sorted Array to Binary Search Tree

Given an array where elements are sorted in ascending order, convert it to a height balanced BST.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example:

Given the sorted array: [-10,-3,0,5,9],

One possible answer is: [0,-3,9,-10,null,5], which represents the following height balanced BST:

      0
     / \
   -3   9
   /   /
 -10  5

思路：

将有序数组变成bst，做法就是取出数组中的中位数当root节点，然后将root节点两边分别递归求bst，注意这里的中位数，如果是偶数个数组是向上取整，即[0, 1, 7, 8]的root是7,下标为2。

代码：

go：

/**

 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func sortedArrayToBST(nums []int) *TreeNode {
    if nums == nil || len(nums) == 0 {
        return nil
    }
    
    return recursion(nums, 0, len(nums))
}

func recursion(nums []int, low int, high int) *TreeNode {
	if low >= high { // leaf
		return nil
	}

	mid := (high-low)/2 + low

	return &TreeNode{
		Val:   nums[mid],
		Left:  recursion(nums, low, mid),
		Right: recursion(nums, mid+1, high)}
}