BFS traversal and applications in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding BFS traversal order

Consider an undirected graph where BFS starts from node A. Which of the following sequences correctly represents a possible BFS traversal order?

A A, C, B, E, D

B A, D, B, C, E

C A, B, C, D, E

D A, E, D, C, B

💡 Hint

BFS explores neighbors level by level, visiting all nodes at the current distance before moving further.

BFS visits nodes in order of their distance from the start node. Option C shows a valid level order traversal. Other options mix nodes from different levels.

🚀 Application

intermediate

Shortest path in unweighted graph using BFS

Which BFS property allows it to find the shortest path in an unweighted graph?

A It explores nodes in increasing order of their distance from the start node.

B It uses a stack to remember nodes to visit next.

C It only visits nodes with the highest degree first.

D It visits nodes randomly to find the shortest path.

💡 Hint

Think about how BFS visits nodes layer by layer.

BFS explores nodes by their distance from the start node, so the first time it reaches a node, it has found the shortest path to it.

🔍 Analysis

advanced

BFS traversal on a directed graph with cycles

What happens when BFS is applied to a directed graph containing cycles?

A BFS always terminates immediately without visiting all nodes.

B BFS may enter an infinite loop if visited nodes are not tracked.

C BFS ignores cycles and treats the graph as acyclic.

D BFS cannot be applied to directed graphs.

💡 Hint

Consider what happens if BFS revisits nodes endlessly.

If BFS does not keep track of visited nodes, it can revisit nodes in cycles infinitely. Proper tracking prevents this.

❓ Comparison

advanced

BFS vs DFS in graph traversal

Which statement correctly compares BFS and DFS?

A BFS uses a queue and finds shortest paths in unweighted graphs; DFS uses a stack and explores deeply first.

B DFS uses a queue and finds shortest paths; BFS uses a stack and explores deeply first.

C Both BFS and DFS use stacks and find shortest paths in weighted graphs.

D BFS and DFS are identical in traversal order and data structures used.

💡 Hint

Recall the data structures each algorithm uses and their traversal style.

BFS uses a queue to explore neighbors level by level, useful for shortest paths in unweighted graphs. DFS uses a stack (or recursion) to explore as deep as possible before backtracking.

❓ Reasoning

expert

BFS application in social network analysis

In a social network graph, BFS is used to find all users within 3 degrees of connection from a given user. What is the main reason BFS is suitable for this task?

A BFS uses recursion to explore all possible paths simultaneously.

B BFS randomly jumps between users, quickly finding distant connections.

C BFS only visits direct friends and ignores further connections.

D BFS explores nodes in layers, so it naturally finds all users at each degree of separation efficiently.

💡 Hint

Think about how BFS visits nodes based on their distance from the start node.

BFS visits nodes in order of their distance from the start, making it ideal to find all users within a certain number of connections (degrees).