230. Kth Smallest Element in a BST

• Difficulty: Medium

• Topics: Binary Search, Tree

• Similar Questions:

  • Binary Tree Inorder Traversal

  • Second Minimum Node In a Binary Tree

Problem:

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Note:
You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

Example 1:

Input: root = [3,1,4,null,2], k = 1
   3
  / \
 1   4
  \
   2
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
       5
      / \
     3   6
    / \
   2   4
  /
 1
Output: 3

Follow up:
What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

Solutions:

/**
 * 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:
    int kthSmallest(TreeNode* root, int k) {
        int ret = 0;
        int count = 0;
        helper(root, k, ret, count);
        return ret;
    }

    bool helper(TreeNode* root, int k, int& ret, int& count) {
        if (root == NULL)   return false;
        if (helper(root->left, k, ret, count))  return true;
        ++count;
        if (count == k) {
            ret = root->val;
            return true;
        }
        return helper(root->right, k, ret, count);
    }
};