20. Kth Smallest Element in a BST.cpp

/*

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?

*/

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    int kthSmallest(TreeNode* root, int k) 
    {
        int a[2]={0}; //will store the index of inorder traversal and value
        inorder(root,a,k);
        
    return a[1];
    }
    
    void inorder(TreeNode* root, int a[], int k)
    {
        if(root==NULL) return;
        
        inorder(root->left,a,k); //left tree traversal
    
        a[0]++; //incrementing index of traversal 
        if((a[0])==k) //if index==k
        {  
            a[1] = root->val; //found answer
            return;
        }
        
        inorder(root->right,a,k); //right tree traversal
    }
};