Which method exhaustively generates and checks every possible solution, often used as a baseline?

Which method exhaustively generates and checks every possible solution, often used as a baseline?

• A. Brute-force search
• B. Greedy algorithm
• C. Dynamic programming
• D. Random sampling

Answer: (A)

The method that exhaustively generates and checks every possible solution is known as a brute-force search. This approach systematically explores all potential solutions to a problem until it finds the best one or confirms that no viable solutions exist. Its thoroughness ensures that no possible option is overlooked, making it reliable as a baseline for solving optimization problems. While it can be computationally expensive and inefficient, particularly for larger datasets or complex problems, it serves as a foundational method against which the performance of more sophisticated algorithms can be compared. Other methods mentioned, like greedy algorithms and dynamic programming, employ different strategies that do not guarantee exhaustive exploration. Greedy algorithms aim for a local optimal solution at each step, which may not lead to a global optimum. Dynamic programming breaks a problem down into simpler subproblems and solves each of them just once, storing their solutions—thus not fully exploring every potential solution space but rather optimizing specific paths through the problem. Random sampling, on the other hand, relies on stochastic methods to approximate a solution, which inherently does not test all possibilities. Thus, brute-force search stands out as the method that exhaustively checks every potential solution.

The method that exhaustively generates and checks every possible solution is known as a brute-force search. This approach systematically explores all potential solutions to a problem until it finds the best one or confirms that no viable solutions exist. Its thoroughness ensures that no possible option is overlooked, making it reliable as a baseline for solving optimization problems. While it can be computationally expensive and inefficient, particularly for larger datasets or complex problems, it serves as a foundational method against which the performance of more sophisticated algorithms can be compared.

Other methods mentioned, like greedy algorithms and dynamic programming, employ different strategies that do not guarantee exhaustive exploration. Greedy algorithms aim for a local optimal solution at each step, which may not lead to a global optimum. Dynamic programming breaks a problem down into simpler subproblems and solves each of them just once, storing their solutions—thus not fully exploring every potential solution space but rather optimizing specific paths through the problem. Random sampling, on the other hand, relies on stochastic methods to approximate a solution, which inherently does not test all possibilities. Thus, brute-force search stands out as the method that exhaustively checks every potential solution.