<p>Given an integer array <code>nums</code>, return<em> an integer array </em><code>counts</code><em> where </em><code>counts[i]</code><em> is the number of smaller elements to the right of </em><code>nums[i]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,6,1]
<strong>Output:</strong> [2,1,1,0]
<strong>Explanation:</strong>
To the right of 5 there are <b>2</b> smaller elements (2 and 1).
To the right of 2 there is only <b>1</b> smaller element (1).
To the right of 6 there is <b>1</b> smaller element (1).
To the right of 1 there is <b>0</b> smaller element.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1]
<strong>Output:</strong> [0]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [-1,-1]
<strong>Output:</strong> [0,0]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

#include <vector>
using namespace std;

class Solution {
private:
    void mergeSortAndCount(vector<int>& nums, int start, int end, vector<int>& result, vector<int>& indices) {
        if (start >= end) return;
        
        int mid = start + (end - start) / 2;
        mergeSortAndCount(nums, start, mid, result, indices);
        mergeSortAndCount(nums, mid + 1, end, result, indices);
        
        int leftPos = start, rightPos = mid + 1;
        int numElemsRightArrayLessThanLeftArray = 0;
        vector<int> merged;
        vector<int> tempIndices;
        
        while (leftPos <= mid && rightPos <= end) {
            if (nums[indices[leftPos]] > nums[indices[rightPos]]) {
                ++numElemsRightArrayLessThanLeftArray;
                tempIndices.push_back(indices[rightPos++]);
            } else {
                result[indices[leftPos]] += numElemsRightArrayLessThanLeftArray;
                tempIndices.push_back(indices[leftPos++]);
            }
        }
        
        while (leftPos <= mid) {
            result[indices[leftPos]] += numElemsRightArrayLessThanLeftArray;
            tempIndices.push_back(indices[leftPos++]);
        }
        
        while (rightPos <= end) {
            tempIndices.push_back(indices[rightPos++]);
        }
        
        for (int i = start; i <= end; ++i) {
            indices[i] = tempIndices[i - start];
        }
    }
    
public:
    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        if (n == 0) return {};
        
        vector<int> result(n, 0);
        vector<int> indices(n);
        for (int i = 0; i < n; ++i) {
            indices[i] = i;
        }
        
        mergeSortAndCount(nums, 0, n - 1, result, indices);
        
        return result;
    }
};

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