Comprehensive and Detailed Explanation From Exact Extract:
A sorting algorithm is correct if it consistently produces a sorted output (e.g., ascending order: [6, 8, 10] for input [10, 6, 8]). According to foundational programming principles, if an algorithm fails to sort any input correctly, it is considered incorrect for the general case.
Analysis:
Input: [10, 6, 8].
Output: [6, 10, 8].
Correct sorted output: [6, 8, 10] (ascending).
The algorithm’s output [6, 10, 8] is not sorted, as 10 > 8.
Option A: "The algorithm is incorrect." This is correct. Since the algorithm fails to sort [10, 6, 8] correctly, it is not a valid sorting algorithm for arbitrary inputs. A single failure proves incorrectness for the general case.
Option B: "The algorithm only works for [10, 6, 8]." This is incorrect. The algorithm does not “work” for [10, 6, 8], as it produces an incorrect output.
Option C: "The algorithm’s correctness is unknown." This is incorrect. The given example demonstrates incorrectness, so the algorithm is known to be incorrect.
Option D: "The algorithm is correct." This is incorrect. The algorithm fails to sort the given input correctly.
Certiport Scripting and Programming Foundations Study Guide (Section on Sorting Algorithms).
Cormen, T.H., et al., Introduction to Algorithms, 3rd Edition (Chapter 2: Sorting).
GeeksforGeeks: “Sorting Algorithms” (https://www.geeksforgeeks.org/sorting-algorithms/).
