Delete Node in a BST

Delete Node in a BST is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the Tree Traversal Patterns (DFS & BFS) pattern, in the Recursive Inorder Traversal subpattern.

Problem statement

Given root, the root of a binary search tree, and key, remove the node whose value equals key and return the root of the resulting tree. A binary search tree is a binary tree where every value in a node's left subtree is smaller than the node's value, and every value in its right subtree is larger.

If the node to remove has no children, remove it directly. If it has one child, connect its parent to that child. If it has two children, replace its value with a suitable value from one subtree—such as the smallest value in its right subtree or the largest value in its left subtree—and then remove that replacement node.

All values are unique. The returned tree must be a valid binary search tree containing exactly the original values except key. If key does not occur in the tree, return the tree unchanged. The returned value is the new root; it may be null when the resulting tree is empty.

Example 1:

Input: root = [8,3,10,1,6,null,14,null,null,4,7,13], key = 3 Output: [8,4,10,1,6,null,14,null,null,null,7,13] Explanation: The node 3 has two children. Replacing it with its in-order successor 4 and removing the original 4 preserves the search-tree ordering.

Example 2:

Input: root = [5,2,9,null,3,7,12], key = 12 Output: [5,2,9,null,3,7] Explanation: The target is a leaf, so it can be removed without changing any other links.

Example 3:

Input: root = [6,4,11,2,5,8,13], key = 10 Output: [6,4,11,2,5,8,13] Explanation: No node has value 10, so the original tree is returned unchanged.

Constraints:

- 0 <= number of nodes in root <= 5000 - -10^5 <= node values <= 10^5 - -10^5 <= key <= 10^5 - All node values in root are unique - root represents a valid binary search tree - The tree is encoded in level order, using null for missing children

Topics and companies

Topics: Binary Search Tree, Binary Tree, Tree, Recursion.

How to practise Delete Node in a BST on Thita.ai

Starter code is provided in C#, C++, Go, Java, JavaScript and Python. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(h), where h is the height of the tree; O(n) in the worst case. time and O(h) for recursive call stack; O(n) in the worst case. space.

Open Delete Node in a BST in the code editor, or read the Delete Node in a BST editorial for a worked solution with its approach and complexity analysis.

Where Delete Node in a BST sits in the DSA pattern sheet

Problems related to Delete Node in a BST

Other problems that use the same Recursive Inorder Traversal and Tree Traversal Patterns (DFS & BFS) techniques:

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