题目

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

使用一个辅助方法来构建二分 查找树，方法中使用中序遍历的方式，递归调用本身来分别创建子树的根节点、左子树根、右子树根。由于数组已经排序，那么中间的数一定是树根。其实二分查找树的构建过程与二分查找某个数的过程是一样的。

代码

class Solution {
    public TreeNode sortedArrayToBST(int[] nums) {
        TreeNode head = createBST(nums,0,nums.length-1);
        return head;
    }

    public TreeNode createBST(int[] nums, int low ,int high){
    	if(low > high)//递归的退出条件
    		return null;
    	int mid = (low + high)/2;
    	TreeNode root = new TreeNode(nums[mid]);//创建子树根
    	root.left = createBST(nums , low , mid - 1);//递归创建左子树根
    	root.right = createBST(nums , mid + 1 ,high);
    	return root;

    }	
}

Runtime: 0 ms, faster than 100.00% of Java online submissions for Convert Sorted Array to Binary Search Tree.
Memory Usage: 37.9 MB, less than 39.69% of Java online submissions for Convert Sorted Array to Binary Search Tree.