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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 understanding the depth-first search traversal and balancing conditions. Learn to build valid BSTs that ensure the height difference between subtrees is minimal, improving tree performance and structure.

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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.

C++
usercode > SortedArrayToBST.cpp
// Definition for a binary tree node
// template<class T>
// class TreeNode {
// public:
//     T data;
//     TreeNode<T>* left;
//     TreeNode<T>* right;
//     TreeNode(const T data) : data(data), left(nullptr), right(nullptr) {}
// };
TreeNode<int>* SortedArrayToBst(std::vector<int>& nums) {
    
    // Replace this placeholder return statement with your code
    return new TreeNode<int>(-1);
}
Convert Sorted Array to Binary Search Tree