Height and depth of trees in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the sentence to define the depth of a node in a tree.

Data Structures Theory

The depth of a node is the number of edges from the root to the [1] node.

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

Aparent

Bleaf

Croot

Dtarget

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing depth with height.

Thinking depth counts edges from the node to the leaves.

The depth of a node is counted from the root down to the target node itself.

2fill in blank

medium

Complete the sentence to define the height of a node in a tree.

Data Structures Theory

The height of a node is the number of edges on the longest path from the node to a [1].

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

Aroot

Bparent

Cleaf

Dsibling

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up height and depth definitions.

Thinking height counts edges up to the root.

The height of a node measures the longest path down to a leaf node.

3fill in blank

hard

Fix the error in the statement about tree height.

Data Structures Theory

The height of the root node is always [1].

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

A0

Bequal to the depth of the tree

Cequal to the number of nodes

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming height is always 1 for the root.

Confusing height with depth.

The height of the root node is equal to the height of the tree, which is the longest path from the root to a leaf node.

4fill in blank

hard

Fill both blanks to complete the dictionary comprehension that maps nodes to their depths.

Data Structures Theory

depths = {node: [1] for node in nodes if node [2] root}

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

Adistance_from_root(node)

B==

C!=

Dis_leaf(node)

Attempts:

3 left

💡 Hint

Common Mistakes

Using equality instead of inequality to exclude root.

Using leaf check instead of distance calculation.

This comprehension assigns each node's depth by calculating its distance from the root, excluding the root itself.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension mapping nodes to their heights, excluding leaves.

Data Structures Theory

heights = {node: [1] for node in nodes if not [2] and node [3] root}

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

Aheight(node)

Bis_leaf(node)

C!=

Dis_root(node)

Attempts:

3 left

💡 Hint

Common Mistakes

Including leaves in the height calculation.

Confusing root exclusion condition.

This comprehension calculates the height for each node that is not a leaf and is not the root.

Practice

1. What does the depth of a node in a tree represent?

easy

A. The number of edges from the root to that node

B. The number of edges from that node to the farthest leaf

C. The total number of nodes in the tree

D. The number of children the node has

Solution

1. Step 1: Understand the definition of depth

   Depth is defined as the distance from the root node to the given node, measured in edges.

2. Step 2: Compare with other options

   Height measures distance to farthest leaf, not depth. Total nodes and children count are unrelated.

3. Final Answer:

   The number of edges from the root to that node -> Option A

4. Quick Check:

   Depth = edges from root to node [OK]

Hint: Depth counts edges from root down to the node [OK]

Common Mistakes:

• Confusing depth with height
• Thinking depth counts children
• Mixing depth with total nodes

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

easy

A. Height is always 1

B. Height is 0 because it has no children

C. Height equals the depth of the leaf

D. Height is the number of siblings it has

Solution

1. Step 1: Recall height definition for any node

   Height is the number of edges on the longest path from the node down to a leaf.

2. Step 2: Apply to leaf node

   A leaf node has no children, so the longest path down is zero edges, making height 0.

3. Final Answer:

   Height is 0 because it has no children -> Option B

4. Quick Check:

   Leaf height = 0 edges down [OK]

Hint: Leaf nodes always have height zero [OK]

Common Mistakes:

• Assuming height is 1 for leaves
• Confusing height with depth
• Counting siblings as height

3. Consider the following tree structure:

        A
       / \
      B   C
     /   / \
    D   E   F
           /
          G

What is the height of node C?

medium

A. 0

B. 1

C. 3

D. 2

Solution

1. Step 1: Identify the subtree rooted at node C

   Node C has children E and F; F has child G.

2. Step 2: Find longest path from C down to a leaf

   Paths: C->E (1 edge), C->F->G (2 edges). Longest path length is 2 edges.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Height of C = longest path down = 2 edges [OK]

Hint: Height = longest edges down from node [OK]

Common Mistakes:

• Counting number of children instead of edges
• Confusing height with depth
• Ignoring deeper descendants

4. A student wrote that the depth of the root node in any tree is 1. What is wrong with this statement?

medium

A. Depth depends on number of children, not fixed

B. Depth of root is always equal to height

C. Depth of root is always 0, not 1

D. Depth cannot be defined for root node

Solution

1. Step 1: Recall definition of depth for root

   Depth is edges from root to node; root is at distance zero from itself.

2. Step 2: Identify error in student's statement

   Student incorrectly assigns depth 1 to root; correct depth is 0.

3. Final Answer:

   Depth of root is always 0, not 1 -> Option C

4. Quick Check:

   Root depth = 0 edges [OK]

Hint: Root node depth is zero by definition [OK]

Common Mistakes:

• Assigning depth 1 to root
• Confusing depth with height
• Thinking depth depends on children

5. Given a tree where the root node has depth 0 and height 4, and a node at depth 3 has height 1, what is the height of a leaf node at depth 4?

hard

A. 0

B. 1

C. 3

D. 4

Solution

1. Step 1: Understand height of leaf nodes

   Leaf nodes have height 0 because they have no children below.

2. Step 2: Apply to leaf at depth 4

   Since the node at depth 3 has height 1, its child at depth 4 must be a leaf with height 0.

3. Final Answer:

   0 -> Option A

4. Quick Check:

   Leaf node height = 0 [OK]

Hint: Leaf nodes always have height zero regardless of depth [OK]

Common Mistakes:

• Assuming height equals depth
• Thinking height increases with depth
• Confusing height with number of siblings