Graph algorithms are fundamental tools in computer science for solving problems involving graphs, which are structures made up of nodes (vertices) connected by edges. These algorithms enable efficient navigation, analysis, and optimization of complex networks, such as social media connections, transportation routes, or internet topologies.
At their core, graph algorithms manipulate relationships between nodes to perform tasks like:
– Traversal: Methods such as Breadth-First Search (BFS) and Depth-First Search (DFS) explore graphs by visiting nodes in a systematic order, useful for finding paths or detecting cycles.
– Shortest Paths: Algorithms like Dijkstra’s and A* compute the most efficient route between nodes in weighted graphs, essential for GPS navigation or network routing.
– Connectivity and Spanning Trees: Techniques such as Kruskal’s or Prim’s algorithm find minimum spanning trees, minimizing costs in networks like telecommunications.
– Flow and Matching: Algorithms like Ford-Fulkerson for maximum flow help optimize resource distribution, such as in traffic management or supply chains.
Graph algorithms are widely applied in fields like artificial intelligence, data mining, and bioinformatics, where they handle large-scale data to reveal patterns, predict outcomes, and solve real-world problems efficiently. Their efficiency often depends on the graph’s size and structure, making them a cornerstone of modern computing.
Table of Contents
- Part 1: OnlineExamMaker – Generate and Share Graph Algorithm Quiz with AI Automatically
- Part 2: 20 Graph Algorithm Quiz Questions & Answers
- Part 3: AI Question Generator – Automatically Create Questions for Your Next Assessment
Part 1: OnlineExamMaker – Generate and Share Graph Algorithm Quiz with AI Automatically
OnlineExamMaker is a powerful AI-powered assessment platform to create auto-grading Graph Algorithm skills assessments. It’s designed for educators, trainers, businesses, and anyone looking to generate engaging quizzes without spending hours crafting questions manually. The AI Question Generator feature allows you to input a topic or specific details, and it generates a variety of question types automatically.
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● Embed quizzes on websites, blogs, or share via email, social media (Facebook, Twitter), or direct links.
● Handles large-scale testing (thousands of exams/semester) without internet dependency, backed by cloud infrastructure.
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Part 2: 20 Graph Algorithm Quiz Questions & Answers
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1. Question: What is the time complexity of Breadth-First Search (BFS) on a graph with V vertices and E edges?
A. O(V + E)
B. O(V^2)
C. O(E log V)
D. O(V log E)
Answer: A
Explanation: BFS visits each vertex and edge once, resulting in O(V + E) time complexity for an adjacency list representation.
2. Question: In Depth-First Search (DFS), what data structure is typically used to keep track of the vertices to visit?
A. Queue
B. Stack
C. Priority Queue
D. Hash Table
Answer: B
Explanation: DFS uses a stack (either explicitly or via recursion) to explore as far as possible along each branch before backtracking.
3. Question: Which algorithm is used to find the shortest path in an unweighted graph?
A. Dijkstra’s Algorithm
B. Bellman-Ford Algorithm
C. BFS
D. Kruskal’s Algorithm
Answer: C
Explanation: BFS explores vertices level by level, making it ideal for finding the shortest path in terms of the number of edges in an unweighted graph.
4. Question: What does Dijkstra’s Algorithm compute?
A. Minimum Spanning Tree
B. Shortest paths from a source to all other vertices in a weighted graph
C. Topological order of a graph
D. Cycle detection
Answer: B
Explanation: Dijkstra’s Algorithm greedily selects the next closest vertex to find the shortest paths from a single source in a graph with non-negative weights.
5. Question: In a graph with negative weights but no negative cycles, which algorithm can be used to find shortest paths?
A. BFS
B. Prim’s Algorithm
C. Bellman-Ford Algorithm
D. Kruskal’s Algorithm
Answer: C
Explanation: Bellman-Ford handles negative weights by relaxing edges up to (V-1) times and can detect negative cycles.
6. Question: What is the primary purpose of Kruskal’s Algorithm?
A. Find shortest paths
B. Detect cycles
C. Find Minimum Spanning Tree
D. Perform topological sort
Answer: C
Explanation: Kruskal’s Algorithm sorts all edges by weight and adds the smallest edges that do not form cycles, resulting in a Minimum Spanning Tree.
7. Question: Prim’s Algorithm starts from a vertex and grows the Minimum Spanning Tree by adding the nearest vertex. What data structure is commonly used?
A. Queue
B. Stack
C. Priority Queue
D. Linked List
Answer: C
Explanation: A priority queue is used to always select the edge with the minimum weight that connects a new vertex to the existing tree.
8. Question: For a directed acyclic graph (DAG), which algorithm is used to find a linear ordering of vertices?
A. BFS
B. DFS
C. Topological Sort
D. Dijkstra’s Algorithm
Answer: C
Explanation: Topological Sort uses DFS or Kahn’s algorithm to order vertices such that for every directed edge uv, vertex u comes before v in the ordering.
9. Question: In a graph, how does BFS differ from DFS in terms of traversal order?
A. BFS uses recursion, DFS uses a queue
B. BFS explores level by level, DFS explores depth first
C. BFS is for undirected graphs only
D. DFS is faster than BFS
Answer: B
Explanation: BFS processes all neighbors of a vertex before moving to the next level, while DFS goes as deep as possible along a path.
10. Question: What condition must a graph satisfy for Dijkstra’s Algorithm to work correctly?
A. It must be directed
B. It must have no cycles
C. Edge weights must be non-negative
D. It must be connected
Answer: C
Explanation: Dijkstra’s Algorithm assumes non-negative weights; negative weights can lead to incorrect results as it does not re-evaluate paths.
11. Question: Which of the following is true about Floyd-Warshall Algorithm?
A. It works only for undirected graphs
B. It finds shortest paths between all pairs of vertices
C. It uses a priority queue
D. It is suitable only for sparse graphs
Answer: B
Explanation: Floyd-Warshall computes the shortest paths in a weighted graph by considering all possible intermediate vertices for every pair.
12. Question: In Kruskal’s Algorithm, how are edges selected?
A. By breadth-first order
B. By sorting and adding without forming cycles
C. By depth-first order
D. Randomly
Answer: B
Explanation: Edges are sorted by weight, and the algorithm adds them one by one if they do not create a cycle, ensuring the minimum total weight.
13. Question: What is the output of a BFS traversal on a graph?
A. A spanning tree
B. A breadth-first search tree
C. A minimum spanning tree
D. A topological order
Answer: B
Explanation: BFS produces a breadth-first search tree that includes the shortest paths from the source to all reachable vertices.
14. Question: Bellman-Ford Algorithm can detect negative cycles. How?
A. If a shorter path is found after (V-1) iterations
B. If the graph is disconnected
C. If there are multiple sources
D. If the graph has loops
Answer: A
Explanation: After (V-1) relaxations, if any edge can still be relaxed, it indicates a negative cycle.
15. Question: For a graph with V vertices, what is the time complexity of Prim’s Algorithm using a binary heap?
A. O(V + E)
B. O(E log V)
C. O(V^2)
D. O(1)
Answer: B
Explanation: Prim’s Algorithm with a binary heap involves sorting edges with a priority queue, leading to O(E log V) complexity.
16. Question: In a directed graph, how is a strongly connected component defined?
A. A subgraph where every vertex is reachable from every other
B. A cycle in the graph
C. A path from source to sink
D. An undirected edge
Answer: A
Explanation: A strongly connected component is a maximal subgraph where there is a directed path from every vertex to every other vertex.
17. Question: Which algorithm is most efficient for finding the shortest path in a dense graph?
A. BFS
B. Floyd-Warshall
C. Dijkstra’s with Fibonacci heap
D. Bellman-Ford
Answer: B
Explanation: Floyd-Warshall has O(V^3) complexity, which is efficient for dense graphs where E is close to V^2.
18. Question: What happens if you run DFS on a graph with a cycle?
A. It will terminate immediately
B. It may enter an infinite loop if not handled properly
C. It always finds the shortest path
D. It requires a priority queue
Answer: B
Explanation: Without tracking visited vertices, DFS on a graph with cycles can loop indefinitely; proper implementation uses a visited set.
19. Question: In topological sorting, what must the graph be?
A. Undirected and connected
B. Directed and acyclic
C. Weighted and sparse
D. Cyclic
Answer: B
Explanation: Topological sorting is only possible on Directed Acyclic Graphs (DAGs), as cycles would prevent a valid ordering.
20. Question: Which of the following is an application of graph algorithms?
A. Sorting arrays
B. Finding routes in GPS
C. Matrix multiplication
D. Binary search
Answer: B
Explanation: Graph algorithms like Dijkstra’s are used in GPS for finding the shortest routes between locations.
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