Level-order traversal (BFS) in Data Structures Theory - Mini Project: Build & Apply

Level-order traversal (BFS)

📖 Scenario: Imagine you have a family tree represented as a simple tree structure. You want to visit each family member level by level, starting from the oldest ancestor down to the youngest generation.

🎯 Goal: Build a step-by-step understanding of how to perform a level-order traversal (Breadth-First Search) on a tree structure.

📋 What You'll Learn

Create a tree data structure with nodes and children

Set up a queue to help with the traversal

Implement the level-order traversal logic

Complete the traversal by collecting nodes in the correct order

💡 Why This Matters

🌍 Real World

Level-order traversal is used in many real-world applications like finding the shortest path in maps, organizing hierarchical data, and scheduling tasks.

💼 Career

Understanding BFS and tree traversal is important for software developers, data scientists, and anyone working with hierarchical or graph data structures.

1

Create the tree data structure

Create a dictionary called tree representing a simple tree with these nodes and their children exactly: "A": ["B", "C"], "B": ["D", "E"], "C": ["F"], "D": [], "E": [], "F": [].

Data Structures Theory

# Create the tree dictionary with nodes and children
# Your code here

Hint

Use a dictionary where each key is a node and the value is a list of its children.

2

Set up the queue for traversal

Create a list called queue and initialize it with the root node "A" to start the traversal.

Data Structures Theory

tree = {
    "A": ["B", "C"],
    "B": ["D", "E"],
    "C": ["F"],
    "D": [],
    "E": [],
    "F": []
}
# Create the queue list with the root node "A"
# Your code here

Hint

The queue helps us visit nodes level by level. Start it with the root node.

3

Implement the level-order traversal logic

Create an empty list called visited. Use a while loop that runs as long as queue is not empty. Inside the loop, remove the first node from queue and add it to visited. Then add all its children from tree to the end of queue.

Data Structures Theory

tree = {
    "A": ["B", "C"],
    "B": ["D", "E"],
    "C": ["F"],
    "D": [],
    "E": [],
    "F": []
}
queue = ["A"]
# Create visited list and write the while loop for BFS
# Your code here

Hint

Use pop(0) to remove the first item from the queue and extend() to add children.

4

Complete the traversal by collecting nodes

Add a final variable called level_order and set it equal to the visited list to represent the order of nodes visited in level-order traversal.

Data Structures Theory

tree = {
    "A": ["B", "C"],
    "B": ["D", "E"],
    "C": ["F"],
    "D": [],
    "E": [],
    "F": []
}
queue = ["A"]
visited = []
while queue:
    node = queue.pop(0)
    visited.append(node)
    queue.extend(tree[node])
# Set level_order equal to visited
# Your code here

Hint

This final step just saves the visited nodes as the level order traversal result.

Practice

1. What is the main data structure used in level-order traversal (BFS) of a binary tree?

easy

A. Linked List

B. Stack

C. Queue

D. Hash Table

Solution

1. Step 1: Understand traversal method

   Level-order traversal visits nodes level by level, which requires processing nodes in the order they appear.

2. Step 2: Identify suitable data structure

   A queue follows First-In-First-Out (FIFO) order, perfect for visiting nodes level by level.

3. Final Answer:

   Queue -> Option C

4. Quick Check:

   Level-order traversal uses a queue [OK]

Hint: Level-order uses FIFO structure: queue [OK]

Common Mistakes:

• Confusing queue with stack (LIFO)
• Thinking hash table stores order
• Assuming linked list is used directly

2. Which of the following is the correct syntax to enqueue a node n into a queue named q in Python during level-order traversal?

easy

A. q.append(n)

B. q.enqueue(n)

C. q.push(n)

D. q.insert(n)

Solution

1. Step 1: Identify Python queue implementation

   In Python, a list can be used as a queue where append() adds elements to the end.

2. Step 2: Confirm enqueue operation

   Using q.append(n) correctly adds node n to the queue's rear.

3. Final Answer:

   q.append(n) -> Option A

4. Quick Check:

   Python queue enqueue uses append() [OK]

Hint: Use append() to add nodes to Python queue [OK]

Common Mistakes:

• Using push() which is not a Python list method
• Using enqueue() which is not built-in
• Using insert() which adds at wrong position

3. Given the binary tree:

    1
   / \
  2   3
 /   / \
4   5   6

What is the output of a level-order traversal?

medium

A. [1, 3, 2, 6, 5, 4]

B. [1, 2, 3, 4, 5, 6]

C. [4, 2, 5, 3, 6, 1]

D. [1, 2, 4, 3, 5, 6]

Solution

1. Step 1: Traverse level by level

   Start at root: 1. Then next level: 2 and 3. Then next level: 4, 5, 6.

2. Step 2: List nodes in visiting order

   Collect nodes as visited: [1, 2, 3, 4, 5, 6].

3. Final Answer:

   [1, 2, 3, 4, 5, 6] -> Option B

4. Quick Check:

   Level-order visits nodes top to bottom, left to right [OK]

Hint: Visit nodes level by level, left to right [OK]

Common Mistakes:

• Mixing order of nodes in same level
• Listing nodes in depth-first order
• Reversing levels incorrectly

4. Consider this Python snippet for level-order traversal:

queue = [root]
while queue:
    node = queue.pop()
    print(node.value)
    if node.left:
        queue.append(node.left)
    if node.right:
        queue.append(node.right)

What is the main error in this code?

medium

A. Using pop() removes last element, not first

B. Appending children before popping node

C. Not checking if node is null

D. Printing node value before adding children

Solution

1. Step 1: Understand queue behavior

   Level-order traversal requires FIFO order, so nodes must be removed from the front.

2. Step 2: Identify pop() behavior

   pop() without index removes last element (LIFO), causing incorrect traversal order.

3. Final Answer:

   Using pop() removes last element, not first -> Option A

4. Quick Check:

   pop() removes from end, use pop(0) for queue [OK]

Hint: Use pop(0) to dequeue from front in Python list [OK]

Common Mistakes:

• Using pop() instead of pop(0)
• Ignoring queue order importance
• Assuming append order fixes pop issue

5. You want to find the shortest path from the root to a target node in a binary tree using level-order traversal. Which modification ensures you stop traversal as soon as the target is found?

hard

A. Continue traversal until queue is empty, then check target

B. Traverse only left children until target is found

C. Add all nodes to a stack and pop until target is found

D. Check each node during dequeue; stop and return path if target found

Solution

1. Step 1: Understand BFS for shortest path

   BFS visits nodes level by level, so the first time target is found is the shortest path.

2. Step 2: Implement early stopping

   Check each node when dequeued; if it matches target, stop traversal immediately and return path.

3. Final Answer:

   Check each node during dequeue; stop and return path if target found -> Option D

4. Quick Check:

   Stop BFS on target found for shortest path [OK]

Hint: Stop BFS immediately when target node is dequeued [OK]

Common Mistakes:

• Traversing entire tree unnecessarily
• Using stack instead of queue for shortest path
• Ignoring right children in traversal