Binary tree terminology in Data Structures Theory - Step-by-Step Execution

Concept Flow - Binary tree terminology

Start at Root Node

↓

Check Left Child?

Yes→Move to Left Child

↓

Check Left Child?

Yes→Move to Left Child

↓

Check Right Child?

Yes→Move to Right Child

↓

Check Right Child?

Yes→Move to Right Child

↓

Leaf Node

↓

End

This flow shows how to navigate a binary tree from the root, checking left and right children until reaching leaf nodes.

Execution Sample

Data Structures Theory

Node: 10
Left Child: 5
Right Child: 15
Left of 5: None
Right of 5: None
Left of 15: None
Right of 15: None

This shows a simple binary tree with root 10, left child 5, and right child 15, where 5 and 15 have no children.

Analysis Table

Step	Node Visited	Left Child	Right Child	Is Leaf?	Description
1	10	5	15	No	Start at root node 10
2	5	None	None	Yes	Left child of 10, no children, leaf node
3	15	None	None	Yes	Right child of 10, no children, leaf node
4	-	-	-	-	Traversal ends, all nodes visited

💡 All nodes visited; leaf nodes have no children to traverse

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
Current Node	None	10	5	15	-
Left Child	N/A	5	None	None	-
Right Child	N/A	15	None	None	-
Is Leaf	N/A	No	Yes	Yes	-

Key Insights - 3 Insights

Why is the root node not considered a leaf node?

Because the root node 10 has children (5 and 15), it is not a leaf. Leaf nodes have no children, as shown in execution_table rows 2 and 3.

What does it mean when a node's left or right child is 'None'?

It means that the node does not have a child on that side. For example, node 5 has left and right children as None, so it is a leaf node (execution_table row 2).

How do we know when to stop traversing the tree?

Traversal stops when all nodes have been visited and leaf nodes have no children to move to, as shown in execution_table row 4.

Visual Quiz - 3 Questions

Look at the execution_table, what is the left child of node 10 at step 1?

A 15

B 5

C None

D 10

💡 Hint

Check the 'Left Child' column in execution_table row 1

At which step does the traversal visit a leaf node for the first time?

A Step 2

B Step 1

C Step 3

D Step 4

💡 Hint

Look at the 'Is Leaf?' column in execution_table to find the first 'Yes'

If node 5 had a right child, how would the 'Is Leaf?' value change at step 2?

A It would remain 'Yes'

B It would become 'None'

C It would change to 'No'

D It would be 'Unknown'

💡 Hint

Leaf nodes have no children; adding a child means it is not a leaf (see execution_table rows 2 and 3)

Concept Snapshot

Binary Tree Terms:
- Root: top node (start)
- Child: node connected below
- Left/Right Child: left or right node
- Leaf: node with no children
- Traversal ends at leaves

Full Transcript

This visual execution trace shows the basic terminology of a binary tree. Starting at the root node 10, we check its left and right children, nodes 5 and 15. Both 5 and 15 have no children, so they are leaf nodes. The traversal ends after visiting all nodes. Key terms include root, child, left/right child, and leaf. Leaf nodes have no children, which is why traversal stops there. This helps understand the structure and navigation of binary trees.