s, the more optimized the data arrangement would be. Additionally, in search engines, the concept of inversion is used to improve search result rankings, for example in determining the best arrangement of URLs given a specific query.","hints":[{"hint":"We can use Merge Sort to count inversions efficiently in O(n log n). While merging, if nums[i] > nums[j], all elements from i onward in the left half form inversions with nums[j]."},{"hint":" If values in nums are bounded, a Fenwick Tree or Segment Tree can be used to count elements greater than nums[j] before index j in O(n log n)."}],"language":["cpp","java","python","javascript","csharp","go"],"topicTags":["Array","Divide and Conquer","Sorting"],"difficulty":"Hard","frequently_occuring_doubts":[{"answer":"While merging two halves, if left[i] > right[j], all remaining elements in left contribute to inversions because they are all greater than right[j].","question":"How does Merge Sort count inversions?"},{"answer":"The maximum inversions occur when the array is reverse sorted, which is n(n-1)/2.","question":"What is the worst-case inversion count?"}],"interview_followup_questions":[{"answer":"The number of inversions represents the minimum swaps needed to sort the array.","question":"How does this relate to sorting algorithms?"},{"answer":"Modify the merge function to return both sorted output and the inversion count.","question":"How can we modify Merge Sort to also return the sorted array alongside inversion count?"}]},"problem_type":"DSA","hasIDE":true},{"problem_id":"arrays_arrays_faqs(hard)_reversepairs","problem_name":"Reverse Pairs","problem_rank":3,"problem_slug":"reverse-pairs","misc":{"tags":["Zynga","Splunk","American Express","Unity Technologies","Walmart","Stripe","Robinhood","HCL Technologies","Alibaba","Databricks","Epic Systems","Activision Blizzard","OYO Rooms","Pinterest","Electronic Arts","PwC","Rockstar Games","Flipkart","Chewy","Boston Consulting Group","Riot Games","Broadcom","Swiggy","Visa","Uber","Google","Microsoft","Amazon","Meta","Apple","Netflix","Adobe"],"facts":"Fun Fact: While the problem of finding reverse pairs in an integer array might seem abstract, it actually finds use in data analysis and comparison-based sorting algorithms like Merge sort or Quick sort. In these cases, an efficient sorting of elements matters a lot, especially when dealing with large datasets. The concept of identifying and handling reverse pairs can be used to optimize these sorting algorithms, thereby improving the performance of software applications that rely on data processing, analysis, or management.","hints":[{"hint":"Similar to counting inversions, we divide the array into two halves and count reverse pairs while merging. During merging, count the number of nums[j] where nums[i] > 2 * nums[j] for all i < j."},{"hint":"If values in nums are bounded, a Fenwick Tree or Segment Tree can efficiently count elements <= 2 * nums[j] in O(log n)."}],"language":["cpp","java","python","javascript","csharp","go"],"topicTags":["Array","Binary Indexed Tree","Binary Search","Divide and Conquer","Merge Sort","Ordered Set","Segment Tree"],"difficulty":"Hard","similarProblems":[],"frequently_occuring_doubts":[{"answer":"

While merging, count the number of nums[j] where nums[i] > 2 * nums[j] before merging the two halves to maintain order.

","question":"How does Merge Sort help in counting reverse pairs?"},{"answer":"

If the array is in reverse sorted order with exponentially decreasing values, the count will be close to n(n-1)/2.

","question":"What is the worst-case number of reverse pairs?"}],"interview_followup_questions":[{"answer":"

Hash maps allow quick lookups, but they do not support range queries efficiently.

","question":"Can we use a hash map to store frequency counts instead of a Fenwick Tree?"},{"answer":"

Negative values affect 2 * nums[j], but sorting-based approaches still work.

","question":"What happens if the array contains negative numbers?"}]},"problem_type":"DSA","hasIDE":true},{"problem_id":"arrays_arrays_faqs(hard)_maximumproducts