# Leetcode 230:kth Smallest Element in a BST

Source: Internet
Author: User

Given A binary search tree, write a function to `kthSmallest` find thek-th smallest element in it.

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

What if the BST are modified (Insert/delete operations) often and you need to find the kth smallest frequently? How would optimize the Kthsmallest routine?

In binary search tree species, find the K element.

The algorithm is as follows:

1. Count left subtree elements.

2, left+1 = k, the root node is the K element

Left >=k, the first k element is

Left +1 <k, it is converted to the right subtree, looking for the k-left-1 element.

The code is as follows:

`Class Solution {Public:int calctreesize (treenode* root) {if (root = NULL) return 0;return 1+calctreesize (root->left) + Calctreesize (root->right);} int kthsmallest (treenode* root, int k) {if (root = NULL) return 0;int leftsize = Calctreesize (Root->left); if (k = = Left size+1) {return root->val;} else if (leftsize >= k) {return kthsmallest (root->left,k);} Else{return kthsmallest (Root->right, k-leftsize-1);}};`

Leetcode 230:kth Smallest Element in a BST

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