12.3. Measuring Dissimilarity: Inversions

Try these first

1. 1.

   Define an inversion in the context of ranking.

   Hint

   Think about how preferences can differ.

2. 2.

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

   Hint

   Consider how many pairs you need to check.

3. 3.

   What is an inversion?

   • A pair of items in the same order
   • A pair of items in opposite order
   • A single ranked item

   Hint

   Consider how tastes can differ.

4. 4.

   The time complexity of the brute force method to count inversions is __________.

   • True
   • False

   Hint

   Think about the number of comparisons required.

5. 5.

   Design a modified merge sort algorithm to count inversions. Explain its steps and time complexity.

   Hint

   Consider how the merging process contributes to counting inversions.

6. 6.

   Propose a real-world application that utilizes inversion counting beyond recommendation systems.

   Hint

   Think about how preferences overlap in different scenarios.