Count Total Nodes in Binary Tree in DSA Typescript - Execution Trace

Concept Flow - Count Total Nodes in Binary Tree

Start at root node

↓

Is node null?

Yes→Return 0

No↓

Count left subtree nodes

↓

Count right subtree nodes

↓

Sum left + right + 1 (current node)

↓

Return total count

The process visits each node starting from the root, counts nodes in left and right subtrees recursively, then sums them with the current node.

Execution Sample

DSA Typescript

function countNodes(node: TreeNode | null): number {
  if (node === null) return 0;
  return 1 + countNodes(node.left) + countNodes(node.right);
}

This function counts all nodes in a binary tree by recursively summing nodes in left and right subtrees plus the current node.

Execution Table

Step	Operation	Node Visited	Left Subtree Count	Right Subtree Count	Total Count	Visual State
1	Start at root	1	-	-	-	1 / \ 2 3
2	Go left	2	-	-	-	1 / 2
3	Go left	4	-	-	-	4 (leaf)
4	Left null	null	0	-	-	null
5	Right null	null	-	0	-	null
6	Count node 4	4	0	0	1	4 (leaf) counted
7	Back to 2, go right	5	-	-	-	5 (leaf)
8	Left null	null	0	-	-	null
9	Right null	null	-	0	-	null
10	Count node 5	5	0	0	1	5 (leaf) counted
11	Count node 2	2	1	1	3	2 subtree counted
12	Back to root, go right	3	-	-	-	3 (leaf)
13	Left null	null	0	-	-	null
14	Right null	null	-	0	-	null
15	Count node 3	3	0	0	1	3 (leaf) counted
16	Count root node 1	1	3	1	5	Full tree counted
17	End	-	-	-	-	Total nodes = 5

💡 All nodes visited; recursion ends when null nodes are reached.

Variable Tracker

Variable	Start	After Step 6	After Step 10	After Step 11	After Step 15	After Step 16	Final
node	1 (root)	4 (leaf)	5 (leaf)	2 (subtree root)	3 (leaf)	1 (root)	null (end)
left subtree count	-	0	0	1	0	3	3
right subtree count	-	0	0	1	0	1	1
total count	-	1	1	3	1	5	5

Key Moments - 3 Insights

Why do we return 0 when the node is null?

Returning 0 at null nodes (see steps 4,5,8,9,13,14) means no nodes exist there, so they don't add to the count.

How does the function count nodes in left and right subtrees separately?

The function calls itself recursively on node.left and node.right (steps 2,3 for left; steps 12,13 for right), counting nodes in each subtree before summing.

Why do we add 1 after counting left and right subtrees?

Adding 1 (step 16) accounts for the current node itself, ensuring it is included in the total count.

Visual Quiz - 3 Questions

Look at the execution table, what is the total count after counting node 2 (step 11)?

A 1

B 5

C 3

D 0

💡 Hint

Check the 'Total Count' column at step 11 in the execution_table.

At which step does the function return 0 for a null node on the right subtree of node 3?

A Step 13

B Step 14

C Step 15

D Step 16

💡 Hint

Look for 'Right null' operation on node 3 in the execution_table.

If the tree had no right child for the root, how would the total count at step 16 change?

A It would be 4

B It would be 5

C It would be 3

D It would be 1

💡 Hint

Consider the right subtree count column and how missing right child affects total count.

Concept Snapshot

Count Total Nodes in Binary Tree:
- Use recursion starting at root
- If node is null, return 0
- Count nodes in left subtree
- Count nodes in right subtree
- Return sum of left + right + 1 (current node)
- Visits all nodes exactly once

Full Transcript

To count total nodes in a binary tree, start at the root node. If the node is null, return 0 because there are no nodes to count. Otherwise, recursively count nodes in the left subtree and right subtree. Add these counts together and add 1 for the current node. This process repeats until all nodes are visited. The final sum is the total number of nodes in the tree.