Graph Algorithms: Interview Readiness Quiz Quiz

1. Q1

   Which graph representation is generally preferred for sparse graphs due to its space efficiency?

   1. Adjacency Matrix
   2. Incident Matrix
   3. Adjacency List
   4. Incidence List

2. Q2

   What data structure is typically used to implement Breadth-First Search in a graph?

   1. Stack
   2. Queue
   3. Priority Queue
   4. Heap

3. Q3

   Which of the following algorithms can be used to detect cycles in a directed graph?

   1. Dijkstra's Algorithm
   2. Prim's Algorithm
   3. Topological Sorting
   4. Bellman-Ford Algorithm

4. Q4

   Dijkstra's algorithm finds the shortest path from a single source to all other vertices. What key property must the edge weights have for Dijkstra's algorithm to work correctly?

   1. Must be negative
   2. Must be positive
   3. Must be non-negative
   4. Can be any value

5. Q5

   Which algorithm is used to find the minimum spanning tree of a weighted, undirected graph?

   1. Bellman-Ford Algorithm
   2. Depth-First Search
   3. Kruskal's Algorithm
   4. Breadth-First Search

6. Q6

   Which of the following algorithms can handle graphs with negative edge weights and detect negative cycles?

   1. Dijkstra’s algorithm
   2. Prim's algorithm
   3. Bellman-Ford Algorithm
   4. Kruskal’s algorithm

7. Q7

   In a directed graph, what is a strongly connected component?

   1. A subgraph with no cycles
   2. A subgraph where every vertex is reachable from every other vertex
   3. A subgraph with a single source node
   4. A subgraph with a single sink node

8. Q8

   Which of these real-world applications makes use of graph algorithms to calculate efficient routes?

   1. Social media platforms
   2. Database management systems
   3. Navigation systems
   4. Operating systems

9. Q9

   What is the time complexity of Depth-First Search for a graph represented using an adjacency list, where V is the number of vertices and E is the number of edges?

   1. O(V)
   2. O(E)
   3. O(V + E)
   4. O(V * E)

10. Q10

    Which algorithm is commonly used to perform topological sorting on a directed acyclic graph?

    1. Dijkstra's Algorithm
    2. Bellman-Ford Algorithm
    3. Depth-First Search
    4. Breadth-First Search

11. Q11

    In graph theory, what is the definition of a 'cut'?

    1. A path that visits every vertex exactly once
    2. A path that visits every edge exactly once
    3. A partition of the vertices of a graph into two disjoint sets
    4. A cycle that includes all vertices

12. Q12

    Which of the following describes Prim's algorithm's approach to finding a minimum spanning tree?

    1. Starts with a set of isolated vertices and iteratively adds edges with minimum weight.
    2. Starts with all edges and iteratively removes the edge with highest weight.
    3. Randomly selects edges until a spanning tree is formed.
    4. Always selects the edge connected to the starting node.

13. Q13

    What distinguishes a directed graph from an undirected graph?

    1. Directed graphs have no edges.
    2. The edges in a directed graph have a specific direction, while edges in an undirected graph do not.
    3. Undirected graphs have no cycles.
    4. Directed graphs can have more than one edge between two vertices.

14. Q14

    What is the primary advantage of using an adjacency matrix representation for a graph?

    1. Space efficiency for sparse graphs
    2. Easy to iterate through all edges
    3. Fast lookup of the existence of an edge between two vertices
    4. Simple implementation of DFS

15. Q15

    Which algorithm is used to determine whether a graph is bipartite?

    1. Dijkstra's
    2. Kruskal's
    3. Breadth-First Search
    4. Depth-First Search