BFS traversal and applications in Data Structures Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the queue for BFS traversal.

Data Structures Theory

queue = [[1]]

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

Agraph

Bvisited

Cstart_node

DNone

Attempts:

3 left

💡 Hint

Common Mistakes

Starting the queue with an empty list or None.

Using the visited set instead of the start node.

In BFS, the queue starts with the starting node to begin traversal.

2fill in blank

medium

Complete the code to mark a node as visited during BFS.

Data Structures Theory

visited.add([1])

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Agraph

Bneighbor

Cqueue

Dcurrent_node

Attempts:

3 left

💡 Hint

Common Mistakes

Adding the entire graph or queue to visited.

Adding neighbors before checking if they are visited.

We mark the current node as visited to avoid revisiting it.

3fill in blank

hard

Fix the error in the BFS neighbor check condition.

Data Structures Theory

if neighbor not in [1]:

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Avisited

Bgraph

Cqueue

Dstart_node

Attempts:

3 left

💡 Hint

Common Mistakes

Checking if neighbor is not in the graph or queue instead of visited.

Forgetting to check if neighbor is visited.

We only add neighbors to the queue if they have not been visited yet.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps nodes to their distances from the start node using BFS.

Data Structures Theory

distances = {node: [1] for node in graph if node [2] visited}

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A0

Bin

Cnot in

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'in' instead of 'not in' in the condition.

Assigning distance 0 to all nodes regardless of visitation.

We assign a default distance of 1 to nodes not yet visited.

The condition checks nodes not in visited.

5fill in blank

hard

Fill all three blanks to complete the BFS function that returns the shortest path length from start to goal.

Data Structures Theory

def bfs_shortest_path(graph, start, goal):
    queue = [(start, 0)]
    visited = set([start])
    while queue:
        current, depth = queue.pop(0)
        if current == goal:
            return [1]
        for neighbor in graph[current]:
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append((neighbor, [2]))
    return [3]

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

Adepth

Bdepth + 1

C-1

Ddepth - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning depth + 1 instead of depth when goal is found.

Appending neighbors with the same depth instead of incremented.

Returning 0 instead of -1 when goal is unreachable.

Return the current depth when goal is found.

Append neighbors with depth increased by 1.

Return -1 if goal is not reachable.

Practice

1. What is the main data structure used in BFS (Breadth-First Search) traversal of a graph?

easy

A. Queue

B. Stack

C. Priority Queue

D. Hash Map

Solution

1. Step 1: Understand BFS traversal method

   BFS explores nodes level by level, which requires processing nodes in the order they are discovered.

2. Step 2: Identify the suitable data structure

   A queue follows First-In-First-Out (FIFO) order, perfect for level-wise exploration in BFS.

3. Final Answer:

   Queue -> Option A

4. Quick Check:

   BFS uses a queue = Queue [OK]

Hint: BFS uses FIFO order, so it needs a queue [OK]

Common Mistakes:

• Confusing BFS with DFS which uses a stack
• Thinking BFS uses a priority queue
• Assuming BFS uses a hash map as main structure

2. Which of the following is the correct way to mark a node as visited in BFS to avoid revisiting it?

easy

A. Add node to a stack after visiting

B. Add node to a visited set or list immediately when enqueued

C. Add node to the queue only after processing all neighbors

D. Do not mark nodes; revisit all nodes

Solution

1. Step 1: Understand when to mark nodes visited in BFS

   Nodes should be marked visited when they are enqueued to prevent multiple enqueues of the same node.

2. Step 2: Identify correct marking method

   Adding nodes to a visited set immediately when enqueued ensures no duplicates in the queue.

3. Final Answer:

   Add node to a visited set or list immediately when enqueued -> Option B

4. Quick Check:

   Mark visited on enqueue = Add node to a visited set or list immediately when enqueued [OK]

Hint: Mark nodes visited when enqueued, not after dequeued [OK]

Common Mistakes:

• Marking nodes visited only after dequeuing
• Using a stack instead of a visited set
• Not marking nodes visited at all

3. Consider the following graph edges:
0 - 1, 0 - 2, 1 - 3, 2 - 3
If BFS starts at node 0, what is the order of nodes visited?

medium

A. [0, 1, 2, 3]

B. [0, 2, 1, 3]

C. [0, 3, 1, 2]

D. [1, 0, 2, 3]

Solution

1. Step 1: Start BFS from node 0

   Enqueue 0, visited order starts with 0.

2. Step 2: Enqueue neighbors of 0 in order

   Neighbors are 1 and 2, enqueue 1 then 2.

3. Step 3: Dequeue 1 and enqueue its neighbor 3

   3 is neighbor of 1, enqueue 3.

4. Step 4: Dequeue 2, neighbor 3 already visited

   No new nodes added.

5. Step 5: Dequeue 3, no new neighbors

   Traversal ends.

6. Final Answer:

   [0, 1, 2, 3] -> Option A

7. Quick Check:

   BFS order = [0, 1, 2, 3] [OK]

Hint: Visit neighbors in order they appear, enqueue before dequeue [OK]

Common Mistakes:

• Visiting neighbors in wrong order
• Adding nodes multiple times
• Starting BFS from wrong node

4. The following BFS code snippet has a bug. What is the error?

visited = set()
queue = [start]
visited.add(start)
while queue:
    node = queue.pop()
    for neighbor in graph[node]:
        if neighbor not in visited:
            queue.append(neighbor)
            visited.add(neighbor)

medium

A. Not marking start node as visited before loop

B. Queue should be a stack for BFS

C. Visited nodes added after enqueueing neighbors

D. Using pop() removes from the end, causing DFS behavior

Solution

1. Step 1: Analyze queue operations

   pop() without argument removes last element, making it LIFO (stack), not FIFO (queue).

2. Step 2: Understand BFS requires FIFO

   BFS needs to remove from front (pop(0)) to process nodes level by level.

3. Final Answer:

   Using pop() removes from the end, causing DFS behavior -> Option D

4. Quick Check:

   pop() without index = DFS, not BFS [OK]

Hint: Use pop(0) for queue behavior in BFS [OK]

Common Mistakes:

• Using pop() instead of pop(0)
• Forgetting to mark start node visited
• Confusing stack and queue roles

5. You want to find the shortest path in an unweighted graph from node A to node B using BFS. Which of the following modifications is necessary to track the actual path?

hard

A. Run BFS twice, once from A and once from B, then combine results

B. Use a stack instead of a queue to track the path

C. Store each node's parent when enqueuing it, then backtrack from B to A

D. Mark nodes visited only after dequeuing them

Solution

1. Step 1: Understand BFS finds shortest path length

   BFS explores nodes level by level, so the first time B is found is shortest path length.

2. Step 2: Track path by storing parents

   When a node is enqueued, record which node led to it (its parent). After BFS, backtrack from B to A using parents.

3. Final Answer:

   Store each node's parent when enqueuing it, then backtrack from B to A -> Option C

4. Quick Check:

   Parent tracking + backtrack = shortest path [OK]

Hint: Save parents on enqueue, backtrack from target [OK]

Common Mistakes:

• Using stack instead of queue for BFS
• Marking visited too late causing duplicates
• Running BFS twice unnecessarily