Delete Node in a BST

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:

1. Search for a node to remove.

2. If the node is found, delete the node.

Note: Time complexity should be O(height of tree).

Example:

root = [5,3,6,2,4,null,7]
key = 3

    5
   / \
  3   6
 / \   \
2   4   7

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 following BST.

    5
   / \
  4   6
 /     \
2       7

Another valid answer is [5,2,6,null,4,null,7].

    5
   / \
  2   6
   \   \
    4   7

class Solution {
    public TreeNode deleteNode(TreeNode root, int key) {
        if (root == null)
            return null;

        if (root.val > key)
            root.left = deleteNode(root.left, key);
        else if (root.val < key)
            root.right = deleteNode(root.right, key);
        else {
            if (root.left == null)
                return root.right;
            if (root.right == null)
                return root.left;

            TreeNode rightSmallest = root.right;
            while (rightSmallest.left != null)
                rightSmallest = rightSmallest.left;
            rightSmallest.left = root.left;
            return root.right;
        }
        return root;
    }
}