Graph Algorithms That Land Offers: BFS, DFS, Dijkstra & A*

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Graphs are everywhere—from social networks and maps to dependency resolution in compilers. And when it comes to technical interviews, they’re a favorite for testing a candidate’s ability to think in data structures and explore problem-solving depth.

If you're preparing for interviews at FAANG or any top-tier tech company, mastering a few key graph algorithms will take you a long way. Let's walk through four essential ones: BFS, DFS, Dijkstra, and A*—what they are, when to use them, and how to think about them in interview settings.

1. Breadth-First Search (BFS)

What it is:
An algorithm that explores a graph level by level, starting from a source node and visiting all neighbors before moving deeper.

Best for:

• Finding the shortest path in unweighted graphs

• Level-order traversal (e.g., in trees)

• Scenarios where the goal is "closest" in terms of steps

Common questions:

• Shortest path in an unweighted maze

• Word ladder / transformation problems

• Finding nearest resource in a grid (e.g., nearest exit)

Pro tip:
Use a queue and a visited set. In interview questions involving grids or transformations, always think "BFS first" when steps are involved.

2. Depth-First Search (DFS)

What it is:
An algorithm that dives deep along one branch before backtracking and exploring other paths.

Best for:

• Detecting cycles in graphs

• Exploring all paths between two nodes

• Topological sorting (in DAGs)

• Backtracking-style problems (e.g., puzzles)

Common questions:

• Island counting problems

• Graph traversal with cycle detection

• Path existence checks

Pro tip:
DFS can be implemented recursively or using a stack. Be ready to write both. Always track visited nodes to avoid infinite recursion.

3. Dijkstra’s Algorithm

What it is:
A greedy algorithm to find the shortest path from a source node to all other nodes in a weighted graph with non-negative weights.

Best for:

• Finding optimal cost routes

• Network routing, logistics problems

• Games and maps where path cost matters

Common questions:

• Shortest path in a weighted graph

• Travel time optimization

• Delivery scheduling

Pro tip:
Use a min-heap (priority queue) for optimal performance. Know the difference between Dijkstra (non-negative weights) and Bellman-Ford (can handle negative weights).

4. A* Search Algorithm

What it is:
An advanced pathfinding algorithm that uses both the actual cost (like Dijkstra) and a heuristic to guide the search more efficiently toward the goal.

Best for:

• Real-time pathfinding in games

• Map routing (e.g., Google Maps)

• Optimized search where destination is known

Common questions:
While less common in interviews, it can appear in system design or AI-focused roles.

Pro tip:
Requires a good heuristic function (like Manhattan or Euclidean distance). Combine the actual cost g(n) and estimated cost to goal h(n).

How to Prepare for Graph Questions

1. Practice Standard Problems: Focus on LeetCode, HackerRank, and GeeksforGeeks questions involving graphs, grids, and weighted edges.

2. Master Adjacency Representations: Know when to use adjacency lists vs. matrices.

3. Draw Before You Code: Always sketch a graph and label visited, distances, or path costs.

4. Know When to Use Which:

   • BFS: shortest path in unweighted

   • DFS: path finding or cycle detection

   • Dijkstra: weighted graphs with no negatives

   • A*: optimal path with known end point and good heuristic

Final Thoughts

Graphs can seem intimidating at first, but they follow predictable patterns. The key to cracking graph interview questions is not just knowing the algorithms—but knowing when to reach for each. With solid practice and clear strategies, you can confidently navigate whatever traversal or optimization puzzle comes your way.

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