Q. In the coin change problem, which approach does a greedy algorithm use?
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A.
Always take the largest denomination first
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B.
Take the smallest denomination first
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C.
Randomly select coins
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D.
Take coins in pairs
Solution
A greedy algorithm for the coin change problem typically takes the largest denomination first to minimize the number of coins.
Correct Answer:
A
— Always take the largest denomination first
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Q. In the context of greedy algorithms, what does 'local optimum' refer to?
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A.
The best solution overall
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B.
The best solution in a local neighborhood
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C.
The worst solution possible
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D.
A solution that is not feasible
Solution
A local optimum is the best solution within a local neighborhood, which may not lead to the global optimum.
Correct Answer:
B
— The best solution in a local neighborhood
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Q. What is a greedy algorithm?
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A.
An algorithm that makes the best choice at each step
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B.
An algorithm that explores all possible solutions
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C.
An algorithm that uses dynamic programming
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D.
An algorithm that always finds the optimal solution
Solution
A greedy algorithm makes the best choice at each step with the hope of finding the global optimum.
Correct Answer:
A
— An algorithm that makes the best choice at each step
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Q. What is the key difference between greedy algorithms and dynamic programming?
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A.
Greedy algorithms use recursion
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B.
Dynamic programming considers all possible solutions
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C.
Greedy algorithms are always optimal
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D.
Dynamic programming is faster
Solution
The key difference is that dynamic programming considers all possible solutions, while greedy algorithms make local optimal choices.
Correct Answer:
B
— Dynamic programming considers all possible solutions
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Q. What is the main drawback of greedy algorithms?
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A.
They are too slow
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B.
They may not produce the optimal solution
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C.
They require more memory
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D.
They are difficult to implement
Solution
The main drawback of greedy algorithms is that they may not produce the optimal solution for all problems.
Correct Answer:
B
— They may not produce the optimal solution
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Q. What is the time complexity of Prim's algorithm for finding the minimum spanning tree using an adjacency matrix?
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A.
O(V^2)
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B.
O(E log V)
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C.
O(V + E)
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D.
O(V^3)
Solution
Prim's algorithm has a time complexity of O(V^2) when using an adjacency matrix.
Correct Answer:
A
— O(V^2)
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Q. Which greedy algorithm is used to solve the activity selection problem?
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A.
Dijkstra's algorithm
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B.
Kruskal's algorithm
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C.
Interval scheduling maximization
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D.
Prim's algorithm
Solution
The activity selection problem is solved using the interval scheduling maximization greedy algorithm.
Correct Answer:
C
— Interval scheduling maximization
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Q. Which of the following is a common application of greedy algorithms?
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A.
Sorting data
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B.
Finding the shortest path
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C.
Job scheduling
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D.
All of the above
Solution
Job scheduling is a common application of greedy algorithms, particularly in maximizing resource utilization.
Correct Answer:
C
— Job scheduling
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Q. Which of the following is NOT a characteristic of greedy algorithms?
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A.
They make decisions based on current information
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B.
They do not reconsider previous decisions
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C.
They guarantee an optimal solution for all problems
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D.
They are often faster than other algorithms
Solution
Greedy algorithms do not guarantee an optimal solution for all problems; they work well for specific types of problems.
Correct Answer:
C
— They guarantee an optimal solution for all problems
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Q. Which of the following problems can be solved using a greedy algorithm?
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A.
Knapsack problem
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B.
Minimum spanning tree
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C.
Shortest path in a graph
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D.
All of the above
Solution
The minimum spanning tree can be solved using a greedy algorithm, while the knapsack problem is not always solvable by greedy methods.
Correct Answer:
B
— Minimum spanning tree
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