Count of Smaller Numbers After Self

Problem Statement
You are given an integer array nums. Return an integer array counts where counts[i] is the number of elements to the right of nums[i] that are smaller than it. This is LeetCode problem 315, commonly appearing in Google interviews with tags like Array, Binary Search, Merge Sort, Segment Tree, and Binary Indexed Tree (Fenwick Tree).[1][2][7]

Example 1
Input: nums = [5,2,6,1]
Output: [2,1,1,0]
Explanation: To the right of 5 are 2 smaller elements (2,1); right of 2 is 1 smaller (1); right of 6 is 1 smaller (1); right of 1 is 0 smaller.[5][7][9]

Example 2
Input: nums = [-1]
Output: [0]
Explanation: No elements to the right.[9]

Example 3
Input: nums = [-1,-1]
Output: [0,0]
Explanation: No strictly smaller elements to the right (equal doesn't count).[9]

Constraints

• 1 <= nums.length <= 10^5
• -10^4 <= nums[i] <= 10^4
  These allow O(n log n) solutions like merge sort or Fenwick Tree but rule out O(n^2) brute force.[2][7]