# Step-by-Step Guide to Find the Kth Smallest Element in a Binary Search Tree

Whether a developer is just starting out or is a veteran in coding, this guide will provide an insight into how to find the kth smallest element in a binary search tree.

### What is a Binary Search Tree?

A binary search tree (BST) is a binary tree data structure in computer science that has several useful applications. The BST is useful for searching and sorting elements quickly.

### What is the Kth Smallest Element?

The kth smallest element is the kth largest element when sorting in ascending order. It refers to the kth largest element in terms of the total number of elements in a BST.

### How to find the Kth Smallest Element in a Binary Search Tree?

1. Start by checking if the root node is NULL. If it is, then the kth smallest element does not exist.
2. If the root node is not NULL, calculate the size of the left subtree and store it in an integer variable.
3. If the size of the left subtree is equal to k, then the kth smallest element is the root node.
4. If the size of the left subtree is greater than k, then the kth smallest element is in the left subtree of the BST.
5. If the size of the left subtree is less than k, then the kth smallest element is in the right subtree of the BST and the value of k should be decremented by the size of the left subtree plus one (1).
6. Repeat steps 2 to 5 with the left and right subtree as the root node until the kth smallest element is found.

Here is a link to a helpful tutorial on finding the Kth smallest element in a binary search tree.

### FAQ

#### What is a Binary Search Tree?

A binary search tree (BST) is a binary tree data structure in computer science that is useful for searching and sorting elements quickly.

#### What does the Kth smallest element refer to?

The Kth smallest element refers to the Kth largest element in terms of the total number of elements in a BST when sorting in ascending order.

#### What is the algorithm for finding Kth smallest element in a binary search tree?

1. Start by checking if the root node is NULL. If it is, then the kth smallest element does not exist.
2. If the root node is not NULL, calculate the size of the left subtree and store it in an integer variable.
3. If the size of the left subtree is equal to k, then the kth smallest element is the root node.
4. If the size of the left subtree is greater than k, then the kth smallest element is in the left subtree of the BST.
5. If the size of the left subtree is less than k, then the kth smallest element is in the right subtree of the BST and the value of k should be decremented by the size of the left subtree plus one (1).
6. Repeat steps 2 to 5 with the left and right subtree as the root node until the kth smallest element is found.

#### How do I know if the kth smallest element exists in the binary search tree?

Start by checking if the root node is NULL. If it is, then the kth smallest element does not exist.

#### Where can I find additional resources on finding the kth smallest element in a binary search tree?

You can find helpful tutorials and resources on GeeksforGeeks.

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