BST Find Minimum Element in DSA Typescript - Execution Trace

Concept Flow - BST Find Minimum Element

Start at root

↓

Check if left child exists?

No→Current node is minimum

Yes↓

Move to left child

↩Back to check left child

Start at the root node and keep moving left until no left child exists. The last node reached is the minimum.

Execution Sample

DSA Typescript

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

This code finds the smallest value in a BST by moving left until no left child exists.

Execution Table

Step	Operation	Current Node Value	Pointer Changes	Visual State
1	Start at root	10	current = root (10)	10 / \ 5 15
2	Check left child of current (10)	10	left child exists (5)	10 / \ 5 15
3	Move current to left child	5	current = 5	10 / \ 5 15
4	Check left child of current (5)	5	left child exists (2)	10 / \ 5 15 / 2
5	Move current to left child	2	current = 2	10 / \ 5 15 / 2
6	Check left child of current (2)	2	left child does not exist	10 / \ 5 15 / 2
7	Return current value as minimum	2	return 2	10 / \ 5 15 / 2

💡 Left child of current node (2) is null, so current node is minimum.

Variable Tracker

Variable	Start	After Step 3	After Step 5	Final
current	10 (root)	5	2	2

Key Moments - 3 Insights

Why do we keep moving left to find the minimum?

In a BST, smaller values are always on the left. The execution_table rows 2, 4 show checking left child to move left until none exists.

What if the tree is empty?

The code returns null immediately (see execution_sample line 2). No steps happen in execution_table because root is null.

Why do we stop when current.left is null, not current itself?

Because the minimum is the leftmost node. If current.left is null, current is the smallest. See execution_table step 6 where left child is null.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'current' after step 5?

A 10

B 2

C 5

D 15

💡 Hint

Check variable_tracker column 'After Step 5' and execution_table step 5.

At which step does the algorithm find that there is no left child?

A Step 6

B Step 4

C Step 3

D Step 7

💡 Hint

Look at execution_table step 6 where left child does not exist.

If the root had no left child, what would be the minimum value returned?

A The right child's value

B null

C The root's value

D The smallest leaf node

💡 Hint

Refer to concept_flow and execution_table step 2 where no left child means current node is minimum.

Concept Snapshot

BST Find Minimum Element:
- Start at root node
- Move left while left child exists
- When no left child, current node is minimum
- Return current node's value
- Handles empty tree by returning null

Full Transcript

To find the minimum element in a Binary Search Tree (BST), start at the root node. Keep moving to the left child because smaller values are always on the left in a BST. When you reach a node that has no left child, that node contains the minimum value. If the tree is empty, return null immediately. This process is shown step-by-step in the execution table, where the current pointer moves from the root (10) to 5, then to 2, and stops because 2 has no left child. The minimum value found is 2.