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Convert Sorted Array to Binary Search Tree

Explore how to convert a sorted array into a height-balanced binary search tree by applying depth-first search methods. Understand the concept of maintaining balanced subtree heights to optimize BST operations. This lesson guides you through problem analysis and solution implementation to master this common coding interview pattern.

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Statement

Given an array of integers, nums, sorted in ascending order, your task is to construct a height-balanced binary search tree (BST) from this array.

In a height-balanced BST, the difference of heights of the left subtree and right subtree of any node is not more than 1.

Note: There can be multiple valid BSTs for a given input.

Constraints:

  • 1≤1 \leq nums.length ≤103\leq 10^3
  • −104≤-10^4 \leq nums[i] ≤104\leq 10^4
  • nums is sorted in strictly ascending order.

Examples

Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps us to check if you’re solving the correct problem:

Convert Sorted Array to a Binary Search Tree

1.

Select all valid BSTs that can be created with the given sorted array:

[5, 10, 15, 20] Multi-select

A.
  5
 / \
15  10
     \
      20
B.
  10
 /  \
5    15
      \
       20
C.
    15
   /  \
  5    20
 /   
10
D.
    15
   /  \
  10   20
 /
5
1 / 3

Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
1
2
3
4

Try it yourself

Implement your solution in the following coding playground.

Java
usercode > Solution.java
import java.util.*;
import ds_v1.BinaryTree.TreeNode;
// Definiton of a binary tree node class
// class TreeNode<T> {
//     T data;
//     TreeNode<T> left;
//     TreeNode<T> right;
//     TreeNode(T data) {
//         this.data = data;
//         this.left = null;
//         this.right = null;
//     }
// }
public class Solution {
    public static TreeNode<Integer> sortedArrayToBST(int[] nums) {
        // Replace this placeholder return statement with your code
        return new TreeNode<Integer>(-1);
    }
}
Convert Sorted Array to Binary Search Tree