Question Type: Algorithm Analysis

Step-by-Step Solution:

• Selection Sort Algorithm: Selection sort works by repeatedly finding the minimum element from the unsorted part of the array and placing it at the beginning.
• Best-Case Complexity: The best-case scenario occurs when the input array is already sorted. In this case, the algorithm still needs to iterate through the array \(n-1\) times to confirm that it's sorted, making the best-case complexity \(O(n^2)\). While it might seem like it could be \(O(n)\), the nested loops inherent to selection sort prevent this. The algorithm still performs the comparisons.
• Worst-Case Complexity: The worst-case scenario occurs when the input array is sorted in reverse order. The algorithm will have to make all possible comparisons in the nested loops, resulting in a complexity of \(O(n^2)\).
• Why other options are incorrect:
  • \(O(n \log n)\): This is the complexity of more efficient sorting algorithms like merge sort and heap sort.
  • \(O(n)\): This is the complexity of linear time algorithms, which selection sort is not.
  • \(O(\log n)\): This is the complexity of algorithms that operate logarithmically, such as binary search.
• Conclusion: Both the best-case and worst-case time complexities of selection sort are \(O(n^2)\).

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