I went straight for the O(n^2) brute force, two nested loops, check every pair.
Start by clarifying the problem and constraints, then propose an efficient divide-and-conquer algorithm like merge sort that counts inversions during the merge step. Explain the algorithm's logic, complexity, and why it's optimal, and be prepared to discuss alternative approaches and edge cases.
Pro tip: Mention that the inversion count can be used to measure similarity between rankings, which is relevant for data science applications like recommendation systems. Also, emphasize that while a brute-force O(n^2) solution is straightforward, the O(n log n) merge sort approach is preferred for large datasets.
Confirm that the array contains distinct integers and that an inversion is defined as i < j and A[i] > A[j]. Ask about input size and whether the array can be modified.
Mention the brute-force O(n^2) solution using nested loops to count inversions, but note its inefficiency for large n.
Explain the divide-and-conquer approach using a modified merge sort that counts inversions during the merge step, achieving O(n log n) time.
Describe how to count inversions when merging two sorted halves: when an element from the right half is chosen before an element from the left half, all remaining elements in the left half form inversions with it.
State the time and space complexity, and discuss edge cases like empty array, single element, already sorted, and reverse sorted arrays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.