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.

Practice

1. In a binary tree, what do we call the topmost node that has no parent?

easy

A. Root

B. Leaf

C. Internal node

D. Child

Solution

1. Step 1: Understand the position of nodes in a binary tree

   The topmost node in a binary tree is the starting point and has no parent node above it.

2. Step 2: Identify the term for the topmost node

   This node is called the root because it is the base from which all other nodes branch out.

3. Final Answer:

   Root -> Option A

4. Quick Check:

   Top node = Root [OK]

Hint: Top node with no parent is always the root [OK]

Common Mistakes:

• Confusing root with leaf
• Thinking root has a parent
• Calling root a child

2. Which of the following correctly describes a leaf node in a binary tree?

easy

A. The topmost node

B. A node with exactly two children

C. A node with one child

D. A node with no children

Solution

1. Step 1: Recall the definition of a leaf node

   A leaf node is a node that does not have any children, meaning it is at the end of a branch.

2. Step 2: Match the definition with the options

   A node with no children states the node has no children, which matches the leaf node definition.

3. Final Answer:

   A node with no children -> Option D

4. Quick Check:

   Leaf node = no children [OK]

Hint: Leaf nodes have zero children, no branches below [OK]

Common Mistakes:

• Thinking leaf has children
• Confusing leaf with root
• Assuming leaf has one child

3. Consider this binary tree node description:
Node A has two children: Node B (left) and Node C (right). Node B has no children. Node C has one child: Node D (left).
Which of these nodes is an internal node?

medium

A. Node B only

B. Node D only

C. Node A and Node C

D. Node A only

Solution

1. Step 1: Define internal nodes

   Internal nodes have at least one child. Leaf nodes have none.

2. Step 2: Analyze each node's children

   Node A has two children (B and C), so it is internal. Node B has no children, so it is a leaf. Node C has one child (D), so it is internal. Node D has no children, so it is a leaf.

3. Final Answer:

   Node A and Node C -> Option C

4. Quick Check:

   Internal nodes = nodes with children [OK]

Hint: Internal nodes have one or two children, leaves have none [OK]

Common Mistakes:

• Calling leaf nodes internal
• Ignoring nodes with one child
• Confusing node labels

4. Identify the error in this statement about binary trees:
"A leaf node can have one child."

medium

A. Leaf nodes cannot have any children, so the statement is false.

B. Leaf nodes are always the root, so the statement is false.

C. Leaf nodes can have two children, so the statement is false.

D. Leaf nodes must have exactly one child, so the statement is true.

Solution

1. Step 1: Recall the definition of a leaf node

   A leaf node is defined as a node with no children at all.

2. Step 2: Evaluate the statement

   The statement says a leaf node can have one child, which contradicts the definition. Therefore, the statement is false.

3. Final Answer:

   Leaf nodes cannot have any children, so the statement is false. -> Option A

4. Quick Check:

   Leaf node = no children [OK]

Hint: Leaf nodes have zero children, never one [OK]

Common Mistakes:

• Thinking leaf can have children
• Confusing leaf with internal node
• Misunderstanding node roles

5. You have a binary tree where every internal node has exactly two children, and all leaves are at the same depth. What is this type of binary tree called?

hard

A. Complete binary tree

B. Perfect binary tree

C. Balanced binary tree

D. Full binary tree

Solution

1. Step 1: Understand the definitions of binary tree types

   A full binary tree has every node with 0 or 2 children. A complete binary tree is filled level by level left to right. A balanced binary tree has heights of subtrees differ by at most one. A perfect binary tree is full and all leaves are at the same depth.

2. Step 2: Match the given conditions

   The tree described has every internal node with exactly two children (full) and all leaves at the same depth, which matches the perfect binary tree definition.

3. Final Answer:

   Perfect binary tree -> Option B

4. Quick Check:

   Full + all leaves same depth = Perfect tree [OK]

Hint: Full + all leaves same depth = Perfect binary tree [OK]

Common Mistakes:

• Confusing complete with perfect
• Mixing balanced with perfect
• Ignoring leaf depth condition