108. Convert Sorted Array to Binary Search Tree

Link

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

Solution

這題有個重要的關鍵要觀察到，就是每次要從中位數開始建立node，才可以確保整個tree是balanced

Find the middle, root is the middle. left subtree is left part of middle. right subtree is right part of middle.

之後就是找尋中位數，並從[start, mid-1]加入左子樹與從[mid+1, end]加入右子樹。重複至start > end，表示沒值可以放了回傳null

T: O(N)

class Solution {
    public TreeNode sortedArrayToBST(int[] nums) {
        if(nums.length == 0) return null;
        
        TreeNode root = helper(nums, 0, nums.length -1);
        return root;
    }
    
    public TreeNode helper(int[] nums, int start, int end){
        if(end < start) return null;
        
        int mid = start + (end - start)/2;
        
        TreeNode node = new TreeNode(nums[mid]);
        node.right = helper(nums, mid+1, end);
        node.left = helper(nums, start, mid-1);
        
        return node;
    }
}