Delete Node in a BST — C++

// Time:  O(h)
// Space: O(h)

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* deleteNode(TreeNode* root, int key) {
        if (!root) {
            return nullptr;
        } 
        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) {
                auto right = root->right;
                delete root;
                return right;
            } else if (!root->right) {
                auto left = root->left;
                delete root;
                return left;
            } else {
                auto successor = root->right;
                while (successor->left) {
                    successor = successor->left;
                }
                root->val = successor->val;
                root->right = deleteNode(root->right, successor->val);
            }
        }
        return root;
    }
};