12.10. Analysis of Time Complexity

Try these first

1. 1.

   Define the divide and conquer strategy in one sentence.

   Hint

   Think about how to tackle a large task.

2. 2.

   What is an inversion in the context of rankings?

   Hint

   Consider how preferences can differ between two people.

3. 3.

   What is the time complexity of the brute force method for counting inversions?

   • O(n)
   • O(n log n)
   • O(n²)

   Hint

   Consider how many comparisons are made.

4. 4.

   True or False: Merge sort can be modified to count inversions.

   • True
   • False

   Hint

   Reflect on what happens when sorting two halves.

5. 5.

   Given the rankings [3, 1, 4, 2] and [1, 4, 2, 3], calculate the number of inversions and explain each step.

   Hint

   Map each of the ranking pairs and see which are inverted.

6. 6.

   Describe how you would implement a counting inversions algorithm from scratch, including planning for edge cases.

   Hint

   Think about how to handle empty or very small input lists effectively.