Binary tree terminology in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the sentence: A node with no children is called a {{BLANK_1}}.

Data Structures Theory

A node with no children is called a [1].

Drag options to blanks, or click blank then click option'

Aroot

Bparent

Cleaf

Dsibling

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing leaf with root node.

Thinking a parent node has no children.

A node with no children is called a leaf node in a binary tree.

2fill in blank

medium

Complete the sentence: The topmost node of a binary tree is called the {{BLANK_1}}.

Data Structures Theory

The topmost node of a binary tree is called the [1].

Drag options to blanks, or click blank then click option'

Asibling

Broot

Cchild

Dleaf

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing root with leaf node.

Thinking root is a child node.

The root is the topmost node of a binary tree from which all other nodes descend.

3fill in blank

hard

Fix the error in the sentence: A node's {{BLANK_1}} is the node directly above it in the tree.

Data Structures Theory

A node's [1] is the node directly above it in the tree.

Drag options to blanks, or click blank then click option'

Aleaf

Bsibling

Cchild

Dparent

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing parent with child or sibling.

Using leaf instead of parent.

The node directly above a given node is called its parent.

4fill in blank

hard

Fill both blanks to complete the definition: Nodes that share the same {{BLANK_1}} are called {{BLANK_2}}.

Data Structures Theory

Nodes that share the same [1] are called [2].

Drag options to blanks, or click blank then click option'

Aparent

Bchildren

Csiblings

Dancestors

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing siblings with children or ancestors.

Mixing up parent and children.

Nodes that share the same parent are called siblings.

5fill in blank

hard

Fill all three blanks to complete the sentence: The {{BLANK_1}} of a node is the number of edges from the node to the {{BLANK_2}}, and the {{BLANK_3}} is the number of edges on the longest path from the node to a leaf.

Data Structures Theory

The [1] of a node is the number of edges from the node to the [2], and the [3] is the number of edges on the longest path from the node to a leaf.

Drag options to blanks, or click blank then click option'

Adepth

Broot

Cheight

Dleaf

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up depth and height definitions.

Confusing root with leaf in depth definition.

The depth of a node is the number of edges from the node to the root. The height is the number of edges on the longest path from the node to a leaf.

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