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Dijkstra and Shortest Path Algorithms - Implementations in C++ - Higher Difficulty Problems

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Dijkstra and Shortest Path Algorithms - Implementations in C++ - Higher Difficulty Problems MCQ & Objective Questions

Understanding Dijkstra and Shortest Path Algorithms is crucial for students aiming to excel in their exams. These algorithms are not only fundamental in computer science but also frequently appear in competitive exams. Practicing MCQs and objective questions on this topic enhances your problem-solving skills and boosts your confidence, ensuring you are well-prepared for important questions in your exams.

What You Will Practise Here

  • Fundamentals of Dijkstra's Algorithm and its applications
  • Implementation of Shortest Path Algorithms in C++
  • Complexity analysis of Dijkstra's Algorithm
  • Graph representations: Adjacency matrix and adjacency list
  • Handling edge cases and negative weights in graphs
  • Comparison of Dijkstra's Algorithm with other shortest path algorithms
  • Real-world applications of shortest path algorithms

Exam Relevance

Dijkstra and Shortest Path Algorithms are significant topics in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect questions that assess their understanding of algorithm implementation, complexity, and practical applications. Common question patterns include coding problems, theoretical explanations, and scenario-based questions that require a deep understanding of the concepts.

Common Mistakes Students Make

  • Confusing the differences between Dijkstra's Algorithm and other shortest path algorithms like Bellman-Ford.
  • Overlooking the importance of graph representation, leading to incorrect implementations.
  • Misunderstanding the time complexity and its implications on algorithm performance.
  • Failing to account for negative weights in graphs, which can lead to incorrect results.

FAQs

Question: What is the primary use of Dijkstra's Algorithm?
Answer: Dijkstra's Algorithm is primarily used to find the shortest path from a source node to all other nodes in a weighted graph.

Question: Can Dijkstra's Algorithm handle negative weight edges?
Answer: No, Dijkstra's Algorithm cannot handle graphs with negative weight edges; it is designed for graphs with non-negative weights only.

Ready to master Dijkstra and Shortest Path Algorithms? Dive into our practice MCQs and test your understanding to score better in your exams. Your success is just a question away!

Q. In a graph represented as an adjacency list, what is the space complexity of storing the graph?
  • A. O(V)
  • B. O(E)
  • C. O(V + E)
  • D. O(V^2)
Q. In Dijkstra's algorithm, what data structure is typically used to keep track of the shortest path estimates?
  • A. Array
  • B. Linked List
  • C. Stack
  • D. Priority Queue
Q. What is the main disadvantage of Dijkstra's algorithm compared to the A* algorithm?
  • A. Dijkstra's algorithm is slower.
  • B. Dijkstra's algorithm cannot handle graphs with cycles.
  • C. Dijkstra's algorithm does not use heuristics.
  • D. Dijkstra's algorithm is less accurate.
Q. What is the primary purpose of the 'visited' array in Dijkstra's algorithm?
  • A. To store the shortest path from the source to each vertex.
  • B. To keep track of which vertices have been processed.
  • C. To hold the distances from the source to each vertex.
  • D. To maintain the priority queue.
Q. Which of the following is NOT a valid implementation of Dijkstra's algorithm?
  • A. Using an adjacency matrix.
  • B. Using an adjacency list with a binary heap.
  • C. Using a linked list for the priority queue.
  • D. Using a Fibonacci heap.
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