Kth Smallest Element in a BST

Desicription

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:

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

Example 2:

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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?

Solution

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/**
* 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 {
private:
int count = 0;
int result = 0;
void dfs(TreeNode* root, int k) {
if(root == nullptr || count > k) {
return ;
}
dfs(root->left, k);
count++;
if(k == count) {
result = root->val;
return ;
}
dfs(root->right, k);
}
public:
int kthSmallest(TreeNode* root, int k) {
dfs(root, k);
return result;
}
};