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

Concept Flow - Tree Terminology Root Leaf Height Depth Level

Start at Root Node

↓

Check if Node has Children

↓

Go to Child

↓

Repeat for all Children

↓

Calculate Height and Depth

↓

Assign Level Based on Depth

Start from the root node, explore children to find leaves, then calculate height, depth, and level for each node.

Execution Sample

DSA Javascript

class Node {
  constructor(value) {
    this.value = value;
    this.children = [];
  }
}

Defines a simple tree node with a value and list of children.

Execution Table

Step	Current Node	Children Present?	Action	Height	Depth	Level
1	A (Root)	Yes	Go to children B and C	?	0	0
2	B	Yes	Go to children D and E	?	1	1
3	D	No	Leaf node found	0	2	2
4	E	No	Leaf node found	0	2	2
5	B	After children processed	Calculate height = max(0,0)+1=1	1	1	1
6	C	No	Leaf node found	0	1	1
7	A	After children processed	Calculate height = max(1,0)+1=2	2	0	0
8	End	-	All nodes processed	-	-	-

💡 All nodes visited, heights and depths calculated, levels assigned based on depth.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	After Step 7	Final
Current Node	-	A	B	D	E	B	C	A	-
Height	-	?	?	0	0	1	0	2	-
Depth	-	0	1	2	2	1	1	0	-
Level	-	0	1	2	2	1	1	0	-

Key Moments - 3 Insights

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

Depth counts edges from root down, so root is 0. Height counts edges down to farthest leaf, so root height is max child height + 1 (2 here). See execution_table rows 1 and 7.

Why do leaf nodes have height 0?

Leaf nodes have no children, so height is 0 by definition. This is shown in execution_table rows 3, 4, and 6.

How is level related to depth?

Level is the same as depth here, counting edges from root. Both are assigned together as shown in execution_table columns Depth and Level.

Visual Quiz - 3 Questions

Look at the execution_table at Step 3, what is the height of node D?

A 0

B 1

C 2

D Undefined

💡 Hint

Check the Height column at Step 3 in execution_table.

At which step does the condition 'Children Present?' become No for node C?

A Step 2

B Step 6

C Step 4

D Step 7

💡 Hint

Look at the Current Node and Children Present? columns in execution_table.

If node B had one more child, how would the height of node A change?

A It would decrease

B It would increase by 1

C It would stay the same

D Cannot determine

💡 Hint

Height depends on the maximum child height, see calculation in Step 7 of execution_table.

Concept Snapshot

Tree Terminology Quick Reference:
- Root: Top node, depth 0
- Leaf: Node with no children, height 0
- Depth: Edges from root to node
- Height: Edges from node to deepest leaf
- Level: Same as depth here
- Height(node) = max height(children) + 1

Full Transcript

This visual execution traces tree terminology concepts. Starting at the root node A, we check if it has children. Since it does, we move to children B and C. Node B has children D and E, which are leaves with height 0. We calculate heights bottom-up: leaves have height 0, their parents have height 1, and root has height 2. Depth counts edges from root down, so root is 0, its children 1, and leaves 2. Level matches depth. This helps understand how root, leaf, height, depth, and level relate in a tree.