DSA Graphs - Practice Questions 2026

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Core Concepts: Here, we dive into the engines of graph theory: Breadth-First Search (BFS) and Depth-First Search (DFS). You will be tested on traversal orders, stack/queue implementations, and the basic properties of trees vs. graphs.

Intermediate Concepts: This module covers connectivity and cycle detection. You will solve problems related to finding Connected Components, detecting cycles in both directed and undirected graphs using DFS and Disjoint Set Union (DSU).

Advanced Concepts: Focuses on Shortest Path algorithms and Minimum Spanning Trees. Expect rigorous questions on Dijkstra’s algorithm, Bellman-Ford, Floyd-Warshall, and Prim/Kruskal algorithms.

Real-world Scenarios: This section challenges you to apply graph theory to practical problems like social network analysis, network routing, and dependency resolution (Topological Sorting).

Mixed Revision / Final Test: A comprehensive evaluation that mixes all levels of difficulty to simulate a real-world coding interview or academic exam environment.

Option 2: Topological Sort using Kahn's Algorithm

Option 3: Prim’s Algorithm

Option 4: Bellman-Ford Algorithm

Option 5: Kruskal’s Algorithm

Option 3: Prim’s Algorithm is used for finding the Minimum Spanning Tree (MST) in a weighted undirected graph.

Option 4: Bellman-Ford is a shortest-path algorithm that can handle negative weights but does not produce a linear ordering of vertices.

Option 5: Kruskal’s is an MST algorithm based on edges and the Disjoint Set Union data structure.

Option 2: The shortest path is undefined because you can infinitely reduce the path cost.

Option 3: BFS will find the shortest path regardless of weights.

Option 4: Only Floyd-Warshall can detect the cycle but cannot run.

Option 5: The graph must be undirected for a negative cycle to exist.

Option 3: BFS only finds the shortest path in unweighted graphs (where all weights are considered 1).

Option 4: Floyd-Warshall can detect negative cycles (by checking if the diagonal elements of the distance matrix become negative), but it is not the only algorithm that can do so.

Option 5: Negative cycles can exist in both directed and undirected graphs (though an undirected negative edge effectively acts as a cycle itself).

Option 2: $O(E^2)$

Option 3: $O(V + E)$

Option 4: $O(V \times E)$

Option 5: $O(log V)$

Option 2: $O(E^2)$ is significantly slower than BFS and usually represents poorly optimized nested loops over edges.

Option 4: $O(V \times E)$ is the complexity of the Bellman-Ford algorithm, which is much slower than a simple traversal.

Option 5: $O(log V)$ is the complexity of operations in binary search trees or heaps, not a full graph traversal.