450. Delete Node in a BST

Problem:

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

Analysis:
When we found the target node, we need to use the smallest node on its right branch to replace it. Then we need to call deleteNode again to delete the smallest node.

Solution:

 class Solution {  
   public TreeNode deleteNode(TreeNode root, int key) {  
           if (root == null)  
                return null;  
           if (root.val < key)  
                root.right = deleteNode(root.right, key);  
           else if (root.val > key)  
                root.left = deleteNode(root.left, key);  
           else {  
                if (root.left == null)  
                     return root.right;  
                else if (root.right == null)  
                     return root.left;  
                root.val = findMin(root.right);  
                root.right = deleteNode(root.right, root.val);  
           }  
           return root;  
      }  
      private int findMin(TreeNode root) {  
           if (root.left == null)  
                return root.val;  
           return findMin(root.left);  
      }  
 }