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Delete a node in a BST given a key

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to delete a node with a given key from a Binary Search Tree (BST). Return the root node reference of the BST after deleting the node with the given key. A Binary Search Tree is a binary tree where for each node, all elements in its left subtree are less than the node's value, and all elements in its right subtree are greater than the node's value.

Example 1
    
  
  • Input: root = [5,3,6,2,4,null,7], key = 3
    • 
  
  • Output: [5,4,6,2,null,null,7]
    • 
  
  • Explanation: 
    
      
      
    • The tree before deletion:
       5
      / \
       3 6
      / \ \
       247
      • 
      
    • After deleting the node with key 3, the tree becomes:
      
        5
      
        / \
      
        4 6
      
        /
      
        2 \
      
        7
      • 
    
    
  
    •
Example 2
    
  
  • Input: root = [5,3,6,2,4,null,7], key = 5
    • 
  
  • Output: [6,3,7,2,4]
    • 
  
  • Explanation: 
    
      
      
    • The tree before deletion:
       5
      
        / \
      
        3 6
      
        / \ \
      
        2 4 7
      • 
      
    • After deleting the node with key 5, the tree becomes:
      
        6
      
        / \
      
        3 7
      
        / \
      
        2 4
      • 
    
    
  
    •
Constraints
    
  
  • The number of nodes in the tree is in the range [0, 10^4]
    • 
  
  • -10^5 ≤ Node.val ≤ 10^5
    • 
  
  • Each node has a unique value
    • 
  
  • The key to be deleted exists in the BST
    • 
  
  • Time Complexity: O(h) where h is the height of the tree. In the worst case, O(n) if the tree is skewed
    • 
  
  • Space Complexity: O(h) for the recursion stack
    •
TreeLTIMindtreeArctwist
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Hint
Solution

Solution Hints

    
  
  • Use the properties of a BST to locate the node to be deleted.
    • 
  
  • Handle three cases: node with no children, node with one child, and node with two children.
    • 
  
  • For a node with two children, find the successor (smallest value in the right subtree) or the predecessor (largest value in the left subtree).
    • 
  
  • Replace the node's value with the successor's value and then delete the successor.
    • 
  
  • Return the updated root of the tree.
    •

Steps to solve by this approach:

 Step 1: Check if the root is null. If yes, return null.
 Step 2: Compare the key with the current node's value to determine which subtree to search.
 Step 3: If the key is less than the current node's value, recursively delete from the left subtree.
 Step 4: If the key is greater than the current node's value, recursively delete from the right subtree.
 Step 5: If the key equals the current node's value, handle the deletion based on the number of children:
   - If the node has no children, simply return null.
   - If the node has only one child, return that child.
   - If the node has two children, find the smallest value in the right subtree (inorder successor).
 Step 6: Replace the current node's value with the inorder successor's value.
 Step 7: Recursively delete the inorder successor from the right subtree.

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