BST Find Minimum Element in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the minimum element in a Binary Search Tree (BST)?

The minimum element in a BST is the leftmost node because all smaller values are stored to the left.

beginner

How do you find the minimum element in a BST?

Start at the root and keep moving to the left child until you reach a node with no left child. That node is the minimum.

intermediate

Why does the minimum element in a BST always lie in the left subtree?

Because BST property states left child nodes have smaller values than their parents, so the smallest value is found by going left repeatedly.

intermediate

What is the time complexity to find the minimum element in a BST?

The time complexity is O(h), where h is the height of the BST. In the worst case (skewed tree), it can be O(n).

beginner

Show the TypeScript code snippet to find the minimum element in a BST node.

function findMin(root: TreeNode | null): TreeNode | null {
  if (!root) return null;
  while (root.left !== null) {
    root = root.left;
  }
  return root;
}

Where is the minimum element located in a BST?

A Root node

B Rightmost node

C Leftmost node

D Any leaf node

The minimum element is always the leftmost node in a BST.

What do you do if the BST root has no left child when finding the minimum?

A Return null

B Search both children

C Go to the right child

D Return the root node

If the root has no left child, it is the minimum element.

What is the time complexity to find the minimum element in a balanced BST with n nodes?

A O(log n)

B O(n)

C O(1)

D O(n log n)

In a balanced BST, height h is about log n, so finding minimum is O(log n).

Which of these is NOT true about the minimum element in a BST?

A It is always the root

B It is the leftmost node

C It has no left child

D It is smaller than all other nodes

The minimum element is not always the root; it depends on the tree structure.

What happens if you try to find the minimum in an empty BST?

A Return root

B Return null

C Throw an error

D Return a default value

If the BST is empty (root is null), the function returns null.

Explain step-by-step how to find the minimum element in a BST.

Think about the BST property and left children.

Write a simple TypeScript function to find the minimum element in a BST and explain its time complexity.

Use a loop to go left until no more left child.