BFS and DFS Algorithm Explained with Examples for GATE, ISRO, EMRS, STET, and IFO Exams

BFS and DFS Algorithm Explained for GATE, ISRO, EMRS, STET, and IFO Exams

In computer science, **graph traversal** is one of the most important topics in **Data Structures and Algorithms (DSA)**. For competitive exams like GATE, ISRO, EMRS, STET, and IFO (International Informatics Olympiad), questions on BFS (Breadth First Search) and DFS (Depth First Search) are frequently asked. These two algorithms are fundamental for exploring nodes and edges in a graph or tree.

🌐 What is a Graph?

A graph is a data structure that consists of:

• A set of vertices (nodes)
• A set of edges (connections between vertices)

Graphs can be directed or undirected, and may contain cycles. Traversing a graph means visiting all its vertices and edges in a systematic way.

🔹 1. Breadth First Search (BFS)

BFS is a level-order traversal technique that explores all neighboring vertices first before moving to the next level.

Approach:
1️⃣ Start with a selected node (source).
2️⃣ Visit all its adjacent (neighbor) nodes.
3️⃣ Move level by level, using a Queue data structure.
4️⃣ Mark visited nodes to avoid repetition.

💡 Example Graph

Suppose the graph has edges like: A → B, A → C, B → D, C → E

BFS Traversal (starting from A): A → B → C → D → E

🧮 BFS Algorithm (Pseudocode)

BFS(G, start): create a queue Q mark start as visited enqueue start to Q while Q is not empty: node = Q.dequeue() print(node) for each neighbor in adjacency[node]: if neighbor is not visited: mark neighbor as visited Q.enqueue(neighbor)

📘 Complexity:
Time: O(V + E) Space: O(V) (for queue and visited list)

🔹 2. Depth First Search (DFS)

DFS explores as far as possible along one branch before backtracking. It uses a Stack (explicitly or via recursion) to track visited nodes.

Approach:
1️⃣ Start with a selected node.
2️⃣ Visit a neighbor and go deeper until no unvisited neighbor remains.
3️⃣ Backtrack and continue with the remaining nodes.

💡 Example Graph

For the same graph: A → B, A → C, B → D, C → E

DFS Traversal (starting from A): A → B → D → C → E

🧮 DFS Algorithm (Recursive Form)

DFS(G, node): mark node as visited print(node) for each neighbor in adjacency[node]: if neighbor is not visited: DFS(G, neighbor)

📘 Complexity:
Time: O(V + E) Space: O(V) (recursion stack)

📊 BFS vs DFS — Comparison Table

Feature	BFS	DFS
Data Structure Used	Queue	Stack / Recursion
Traversal Order	Level-wise	Depth-wise
Memory Usage	More (stores entire level)	Less (stores path)
Path Finding	Finds shortest path in unweighted graph	Does not guarantee shortest path
Applications	Shortest path, Web crawlers, Networking	Cycle detection, Maze solving, Topological sort

🧩 Visualization Tip for Exams

In exams like GATE or ISRO, BFS and DFS questions are often asked in the form of:

• Traversal sequence for a given graph
• Number of edges or levels traversed
• Stack/Queue content after certain steps
• Recursive call order

Always draw a clear adjacency list and mark visited nodes carefully.

🚀 Applications in Real Life

• BFS – Used in GPS navigation systems to find the shortest route.
• DFS – Used in puzzle solving, maze generation, and backtracking algorithms.
• Both are fundamental for AI, networking, and compiler design.

🧠 Exam Tip: In GATE, you might see a question: “For the given graph, what is the DFS traversal starting from vertex 1?” — always simulate step by step.

📘 Example GATE Question

Question: For the graph: 1 → 2, 1 → 3, 2 → 4, 3 → 5 Find BFS and DFS traversals starting from node 1.

Answer:
BFS: 1, 2, 3, 4, 5 DFS: 1, 2, 4, 3, 5

💡 Key Points for EMRS, ISRO, and STET Exams

• Questions are often asked to identify correct traversal order.
• ISRO focuses on iterative DFS using stack.
• STET/EMRS may include theoretical MCQs about graph types and traversal uses.
• IFO exams test logic of recursion and queue-based BFS.

📚 Summary

• BFS → Uses Queue → Level-order traversal → Finds shortest path.
• DFS → Uses Stack/Recursion → Depth-wise traversal → Explores complete path.
• Both algorithms have O(V + E) complexity.
• Commonly asked in GATE, ISRO, EMRS, STET, and IFO exams.

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