Height and depth of trees in Data Structures Theory - Step-by-Step Execution

Concept Flow - Height and depth of trees

Start at Root Node

↓

Depth of Root = 0

↓

Move to Child Node

↓

Depth of Child = Depth of Parent + 1

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Repeat for all nodes

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Calculate Height

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Height = Max Depth among all nodes

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End

Start from the root node with depth 0, move down each child increasing depth by 1, and find the height as the maximum depth found.

Execution Sample

Data Structures Theory

Node A (root)
  |
  +-- Node B
  |     |
  |     +-- Node D
  +-- Node C
        |
        +-- Node E

A tree with root A, children B and C, and further children D and E to show depth and height.

Analysis Table

Step	Current Node	Depth	Action	Height So Far
1	A (root)	0	Start at root	0
2	B	1	Move to child of A	0
3	D	2	Move to child of B	0
4	Back to B	1	No more children	2
5	Back to A	0	Move to next child	2
6	C	1	Move to child of A	2
7	E	2	Move to child of C	2
8	Back to C	1	No more children	2
9	Back to A	0	No more children	2
10	-	-	Traversal complete	Height = 2

💡 All nodes visited; maximum depth found is 2, so height is 2.

State Tracker

Variable	Start	After Step 2	After Step 3	After Step 7	Final
Current Node	A	B	D	E	-
Depth	0	1	2	2	-
Height So Far	0	0	0	2	2

Key Insights - 3 Insights

Why is the root node depth 0 and not 1?

Depth counts edges from root to node. Root has no edges above it, so depth is 0 (see Step 1 in execution_table).

How is height different from depth?

Depth is distance from root to a node; height is the longest depth among all nodes (see Height So Far column in execution_table).

Why does height update only after visiting leaf nodes?

Height depends on maximum depth found, which is known after reaching leaves (see Steps 4 and 7 where height updates to 2).

Visual Quiz - 3 Questions

Look at the execution_table at Step 3. What is the depth of node D?

A 2

B 1

C 0

D 3

💡 Hint

Check the Depth column at Step 3 in execution_table.

At which step does the height first update to 2?

A Step 2

B Step 7

C Step 4

D Step 9

💡 Hint

Look at the Height So Far column in execution_table rows.

If node E had a child node F, how would the final height change?

A Height would remain 2

B Height would become 3

C Height would become 1

D Height would become 4

💡 Hint

Height is maximum depth; adding a child to E increases max depth by 1 (see variable_tracker Depth values).

Concept Snapshot

Height and Depth of Trees:
- Depth: number of edges from root to a node (root depth = 0)
- Height: maximum depth among all nodes
- Calculate depth by adding 1 moving down each level
- Height is found after visiting all nodes
- Useful for understanding tree structure size

Full Transcript

This visual execution shows how to find the depth and height of a tree. Starting at the root node with depth zero, we move down each child node, increasing depth by one each time. We track the current node and its depth step-by-step. The height is the maximum depth found after visiting all nodes. For example, node D and node E have depth 2, so the height is 2. The root node has depth zero because it has no edges above it. Height updates after reaching leaf nodes, as shown in the execution table. If a new child is added deeper in the tree, the height increases accordingly.