Code Inspection Complexity Analysis

Code Inspection

The provided code snippet defines a function find_duplicates that takes a list of numbers as input. It initializes two sets, seen to store unique numbers encountered and duplicates to hold duplicate numbers found in the input list. The function iterates through the input list, adding each number to seen if it has not been encountered before. If a number is already in seen, it is added to the duplicates set. Finally, the function returns a list of duplicate numbers.

Complexity Analysis

• Time Complexity:

  • Best Case: O(n) when there are no duplicates in the input list.
  • Worst Case: O(n^2) when all elements are unique, and the code has to check each element against all previously seen elements.
  • Average Case: O(n^2) where each element is a duplicate, resulting in nested iterations through the list.

• Space Complexity:

  • The space complexity is O(n) as the sets seen and duplicates could grow linearly with the input list length n.

• Comments:

  • The if num in seen operation inside the loop contributes to the time complexity as it requires linear search in the set.
  • Record of seen numbers in the set is necessary to identify duplicates effectively and avoid adding them multiple times.

Average-Case Scenario Illustration

In an average-case scenario where half of the elements are duplicates, the algorithm will have to go through each element once and compare it to the seen numbers. In this case, the expected runtime complexity would be O(n^2) due to nested iterations through the list. The space complexity remains O(n) to store seen and duplicate numbers.

This practical input scenario showcases the algorithm's efficiency under typical conditions where duplicates make up a significant portion of the input list.