Question
Given an integer array `nums`, return a new array `counts` where counts[i] is the number of elements to the RIGHT of nums[i] that are strictly smaller than nums[i]. Values may be negative. Length up to 10^5, so an O(n^2) double loop is too slow — use a modified merge sort (count cross-pair inversions) or a Binary Indexed Tree over compressed values for O(n log n).
count_smaller(nums: list[int]) → list[int][[5,2,6,1]]out[2,1,1,0]State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.