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Sorted Array to a Binary Search Tree

Certification: Intermediate Level Accuracy: 100% Submissions: 1 Points: 12

Write a C++ program to implement the sortedArrayToBST(vector<int>& nums) function, which converts a sorted array into a height-balanced binary search tree (BST).

Example 1
    
  
  • Input: nums = [-10,-3,0,5,9]
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  • Output: [0,-3,9,-10,null,5]
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  • Explanation: 
    
      
      
    • The output represents the following height-balanced BST:

      Binary Search Tree with Root Node 0
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    •
Example 2
    
  
  • Input: nums = [1,3]
    • 
  
  • Output: [3,1]
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  • Explanation: 
    
      
      
    • The output represents the following height-balanced BST:

      Binary Search Tree with Root Node 3
      • 
    
    
  
    •
Constraints
    
  
  • 1 ≤ nums.length ≤ 10^4
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  • -10^4 ≤ nums[i] ≤ 10^4
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  • nums is sorted in a strictly increasing order
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  • Time Complexity: O(n)
    • 
  
  • Space Complexity: O(log n) for the recursion stack
    •
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Hint
Solution

Solution Hints

    
  
  • Use a divide-and-conquer approach to build the BST
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  • The middle element of the array will be the root of the BST
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  • The left subarray will form the left subtree, and the right subarray will form the right subtree
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  • Recursively apply this procedure to build the entire tree
    •

Steps to solve by this approach:

 Step 1: Use a divide-and-conquer approach to build a height-balanced BST.
 Step 2: Find the middle element of the array to use as the root of the tree.
 Step 3: Create a new TreeNode with the middle element as its value.
 Step 4: Recursively build the left subtree using the elements to the left of the middle.
 Step 5: Recursively build the right subtree using the elements to the right of the middle.
 Step 6: Return the root of the constructed BST.
 Step 7: Base case: if the subarray is empty (left > right), return null.

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