Greedy Algorithms: Interactive Learning Quizzes for Computer Science MEng Students

Question 1

In Huffman coding, what strategy is employed to assign codewords to symbols?

Accepted Answer

Higher frequency symbols receive shorter codewords

Answer

Lower frequency symbols receive shorter codewords

Answer

Codewords are assigned randomly

Answer

Alphabetical order determines codeword assignment

Question 2

When evaluating the efficiency of a greedy algorithm, which factor is of primary importance?

Accepted Answer

Algorithm complexity

Answer

Input size

Answer

Output size

Answer

Hardware specifications

Question 3

Which problem type poses a challenge for greedy algorithms due to the absence of a clear locally optimal choice?

Accepted Answer

Finding the chromatic number of a graph

Answer

Finding the shortest path in a graph

Answer

Scheduling jobs to maximize profit

Answer

Finding the minimum spanning tree of a graph

Question 4

In the context of greedy algorithms, what is the fundamental trade-off between optimality and efficiency?

Accepted Answer

Trading optimality for faster computation

Answer

Trading efficiency for guaranteed optimality

Answer

No trade-off exists

Answer

Optimality and efficiency are directly proportional

Question 5

Which of the following is a notable advantage of utilizing greedy algorithms?

Accepted Answer

Simplicity and ease of implementation

Answer

Guaranteed optimality

Answer

Wide applicability

Answer

Always finds the unique optimal solution

Question 6

Which of the following **best** describes a property of greedy algorithms?

Accepted Answer

They provide an approximation to the optimal solution.

Answer

They always find the optimal solution.

Answer

They run in polynomial time.

Answer

They are easy to implement.

Question 7

What is the primary goal of Huffman coding?

Accepted Answer

To compress data by assigning shorter codes to more frequent symbols.

Answer

To detect errors in data transmission.

Answer

To encode data for transmission over noisy channels.

Answer

To improve the performance of search algorithms.

Question 8

Which of the following is an example of a problem **that can be** solved optimally using a greedy algorithm?

Accepted Answer

Finding the minimum spanning tree of a graph.

Answer

Finding the shortest path between two vertices in a graph.

Answer

Finding the maximum cut of a graph.

Answer

Finding the maximum clique of a graph.

Question 9

What is a trade-off often associated with using greedy algorithms?

Accepted Answer

Simplicity and efficiency versus optimality.

Answer

Accuracy and completeness versus speed.

Answer

Flexibility and scalability versus security.

Answer

Reliability and maintainability versus cost.

Question 10

Which technique is commonly used to analyze the performance of greedy algorithms?

Accepted Answer

Competitive analysis

Answer

Amortized analysis

Answer

Randomized analysis

Answer

Dynamic analysis

Question 11

What is a key benefit of using a greedy algorithm?

Accepted Answer

It is typically easy to implement and efficient.

Answer

It provides a guaranteed optimal solution.

Answer

It is robust to noise and errors.

Answer

It is suitable for large-scale problems.

Question 12

How do greedy algorithms differ from dynamic programming algorithms?

Accepted Answer

Greedy algorithms make locally optimal choices, while dynamic programming algorithms make globally optimal choices.

Answer

Dynamic programming algorithms are more efficient than greedy algorithms.

Answer

Greedy algorithms are more robust to noise and errors than dynamic programming algorithms.

Answer

Dynamic programming algorithms are suitable for problems without overlapping subproblems.

Question 13

Which of the following is a defining characteristic of greedy algorithms?

Accepted Answer

They make locally optimal choices at each step, aiming for an approximate solution.

Answer

They are guaranteed to find the optimal solution to every problem.

Answer

They always have a polynomial time complexity.

Answer

They are applicable to all types of optimization problems.

Question 14

What is the key insight used in Kruskal's algorithm to identify the minimum spanning tree?

Accepted Answer

Edges in the minimum spanning tree must form a cycle-free subgraph.

Answer

Edges in the minimum spanning tree must be sorted in ascending order of weight.

Answer

The sum of the weights of the edges in the minimum spanning tree must be minimized.

Answer

The minimum spanning tree must contain all vertices in the graph.

Question 15

Which of the following is a classic application of greedy algorithms?

Accepted Answer

Huffman coding (lossless data compression)

Answer

Branch and bound (optimization method)

Answer

Dynamic programming (optimization technique)

Answer

Backtracking (problem-solving approach)

Question 16

What is the key property of a greedy algorithm?

Accepted Answer

Each step optimizes the current state without considering future consequences

Answer

It is guaranteed to run in polynomial time

Answer

It always finds the optimal solution

Question 17

Which of the following can be a limitation of greedy algorithms?

Accepted Answer

They may not always produce the optimal solution

Answer

They are not useful in real-world applications

Answer

They require exponential memory

Answer

They are challenging to implement

Question 18

Kruskal's algorithm is a greedy algorithm used to:

Accepted Answer

Find a minimum spanning tree for a weighted graph

Answer

Solve the traveling salesman problem (finding the shortest route)

Answer

Pack items into a knapsack to maximize value

Answer

Schedule tasks on a processor to optimize efficiency

Question 19

Which of the following is a valid greedy approach to maximizing profit in a knapsack problem?

Accepted Answer

Always choose the item with the highest profit-to-weight ratio

Answer

Always choose the item with the highest profit

Answer

Always choose the item with the lowest weight

Question 20

Which of the following statements about greedy algorithms is inaccurate?

Accepted Answer

They never produce suboptimal solutions

Answer

They can be employed for a variety of optimization problems

Answer

They are suitable for scenarios where finding optimal solutions is challenging

Answer

They are generally easy to implement and analyze

Question 21

What is a key advantage of using a greedy algorithm over a dynamic programming algorithm?

Accepted Answer

Simplicity in implementation and analysis

Answer

Superior time complexity

Answer

Suitability for large-scale problems

Answer

Guaranteed optimality