Leetcode450-Delete Node in a BST

Description

Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.

Basically, the deletion can be divided into two stages:

• Search for a node to remove.
• If the node is found, delete the node.

Example

Example 1:

Input: root = [5,3,6,2,4,null,7], key = 3
Output: [5,4,6,2,null,null,7]
Explanation: Given key to delete is 3. So we find the node with value 3 and delete it.
One valid answer is [5,4,6,2,null,null,7], shown in the above BST.
Please notice that another valid answer is [5,2,6,null,4,null,7] and it's also accepted.

Example 2:

Input: root = [5,3,6,2,4,null,7], key = 0
Output: [5,3,6,2,4,null,7]
Explanation: The tree does not contain a node with value = 0.

Example 3:

Input: root = [], key = 0
Output: []

Constraints:

• The number of nodes in the tree is in the range [0, 104].
• -105 <= Node.val <= 105
• Each node has a unique value.
• root is a valid binary search tree.
• -105 <= key <= 105

Solution

• Time Complexity: $O(logN)$ or $O(H)$
• Space Complexity: $O(N)$

// O(logN) = O(H)
class Solution {
    public TreeNode deleteNode(TreeNode root, int key) {
        if (root == null) return null;
        
        if (key < root.val){
            root.left = deleteNode(root.left, key);
        }
        else if (key > root.val){
            root.right = deleteNode(root.right, key);
        }
        else{
            if (root.left == null && root.right == null){
                root = null;
            }
            else if (root.right != null){
                root.val = nextLarger(root);
                root.right = deleteNode(root.right, root.val);
            }
            else {
                root.val = preSmaller(root);
                root.left = deleteNode(root.left, root.val);
            }
        }
        return root;
    }
    
    private int nextLarger(TreeNode root){
        root = root.right;
        while(root.left != null) root = root.left;
        return root.val;
    }
    
    private int preSmaller(TreeNode root){
        root = root.left;
        while(root.right != null) root = root.right;
        return root.val;
    }
}

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