Tree Terminology Root Leaf Height Depth Level in DSA Typescript - Execution Trace

Concept Flow - Tree Terminology Root Leaf Height Depth Level

Start at Root Node

↓

Check if Node has Children

Yes No↓

Go to Child

↓

Calculate Height

↓

Calculate Depth

↓

Assign Level

↓

Repeat for all Nodes

↓

End

This flow shows how to identify root, leaf nodes and calculate height, depth, and level for each node in a tree.

Execution Sample

DSA Typescript

class TreeNode {
  value: number;
  children: TreeNode[] = [];
  constructor(value: number) { this.value = value; }
}

Defines a simple tree node with a value and children array.

Execution Table

Step	Node	Is Root?	Is Leaf?	Depth	Height	Level
1	A	Yes	No	0	2	0
2	B	No	No	1	1	1
3	D	No	Yes	2	0	2
4	E	No	Yes	2	0	2
5	C	No	Yes	1	0	1
6	End	-	-	-	-	-

💡 All nodes processed; root identified; leaves found; depth, height, and level assigned.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
Node	None	A	B	D	E	C	All nodes visited
Is Root?	N/A	Yes	No	No	No	No	Set for all nodes
Is Leaf?	N/A	No	No	Yes	Yes	Yes	Set for all leaves
Depth	N/A	0	1	2	2	1	Assigned per node
Height	N/A	2	1	0	0	0	Calculated bottom-up
Level	N/A	0	1	2	2	1	Same as depth here

Key Moments - 3 Insights

Why is the root node's depth 0 but height 2?

Depth counts edges from root down, so root is 0. Height counts edges from node down to deepest leaf, so root has height 2 (see execution_table step 1).

How do we know a node is a leaf?

A leaf has no children. In the table, nodes D, E, and C have 'Is Leaf?' as Yes because they have no children (steps 3,4,5).

Are level and depth always the same?

In this example, yes. Level is often defined as depth from root, so they match here (see variable_tracker Level and Depth rows).

Visual Quiz - 3 Questions

Look at the execution table, what is the height of node B at step 2?

A 1

B 0

C 2

D 3

💡 Hint

Check the 'Height' column for step 2 in the execution_table.

At which step does the node become identified as a leaf?

A Step 2

B Step 3

C Step 1

D Step 5

💡 Hint

Look for 'Is Leaf?' marked Yes in the execution_table.

If node C had children, how would its 'Is Leaf?' value change in the table?

A It would stay Yes

B It would become Root

C It would change to No

D It would have depth 0

💡 Hint

Leaves have no children, so adding children changes 'Is Leaf?' to No (see key_moments explanation).

Concept Snapshot

Tree Terminology Quick Reference:
- Root: top node, depth 0
- Leaf: node with no children
- Depth: edges from root to node
- Height: edges from node to deepest leaf
- Level: often same as depth
Use these to understand tree structure clearly.

Full Transcript

This visual execution traces tree terminology concepts. We start at the root node, which has depth 0 and height equal to the longest path to a leaf. Nodes with no children are leaves. Depth counts edges from root down, height counts edges from node down to deepest leaf. Level is often the same as depth. The execution table shows each node's properties step by step. Variable tracker records changes as we visit nodes. Key moments clarify common confusions like why root depth is zero but height is not, how leaves are identified, and the relation between level and depth. The quiz tests understanding by referencing the execution table and variable tracker. This helps beginners see how tree terms apply in practice.