BST Insert Operation in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Binary Search Tree (BST)?

A Binary Search Tree is a tree data structure where each node has at most two children. For every node, all values in the left subtree are smaller, and all values in the right subtree are larger than the node's value.

beginner

What is the main rule to follow when inserting a new value into a BST?

Compare the new value with the current node's value. If smaller, go to the left child; if larger, go to the right child. Repeat until you find an empty spot to insert the new node.

intermediate

Why do we insert nodes recursively or iteratively in a BST?

Because we need to follow the BST property at each step, checking left or right child until we find the correct empty spot to insert the new node.

intermediate

What happens if you try to insert a value that already exists in the BST?

Usually, BSTs do not allow duplicate values. The insert operation can ignore the duplicate or handle it based on specific rules, like inserting duplicates to the right subtree.

intermediate

What is the time complexity of inserting a node in a BST?

The average time complexity is O(log n) when the tree is balanced, but in the worst case (like a skewed tree), it can be O(n), where n is the number of nodes.

When inserting a value into a BST, if the value is less than the current node, where do you go next?

A Replace current node

B Right child

C Left child

D Stop insertion

In a BST, smaller values go to the left child.

What is the first step when inserting a new value into an empty BST?

A Create a new root node with the value

B Search for the value

C Insert as left child

D Insert as right child

If the BST is empty, the new value becomes the root node.

What is the worst-case time complexity of inserting a node in a BST?

A O(log n)

B O(n)

C O(1)

D O(n log n)

In the worst case, the BST becomes skewed, making insertion O(n).

If a BST already contains the value you want to insert, what usually happens?

A Insert duplicate to the left

B Insert duplicate to the right

C Replace the existing node

D Ignore the duplicate

Most BST implementations ignore duplicates to keep unique values.

Which traversal method is NOT used to insert a node in a BST?

A In-order traversal

B Going left or right child based on comparison

C Following BST property by comparing values

D Pre-order traversal

In-order traversal is for visiting nodes, not for insertion.

Explain step-by-step how to insert a new value into a Binary Search Tree.

Think about how you decide where to place the new value by comparing it with nodes.

Describe the time complexity of inserting a node in a BST and what affects it.

Consider how the shape of the tree changes the steps needed.