<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>

struct NumSlot {
    int num;
    int index;
    int count;
};

class Solution {
public:
    vector<int> countSmaller(vector<int>& nums) {
        vector<NumSlot> arr(nums.size());
        for (int i = 0; i < nums.size(); i++) {
            arr[i].num = nums[i];
            arr[i].index = i;
            arr[i].count = 0;
        }
        mergeSort(arr.begin(), arr.end());
        vector<int> result(nums.size());
        for (int i = 0; i < nums.size(); i++) {
            result[arr[i].index] = arr[i].count;
        }
        return result;
    }
private:
    void mergeSort(vector<NumSlot>::iterator begin, vector<NumSlot>::iterator end) {
        if (begin + 1 == end) {
            return;
        }
        vector<NumSlot>::iterator mid = begin + (end - begin) / 2;
        mergeSort(begin, mid); mergeSort(mid, end);

        vector<NumSlot> mergeSpace(end - begin);
        vector<NumSlot>::iterator it1 = begin;
        vector<NumSlot>::iterator it2 = mid;
        vector<NumSlot>::iterator mit = mergeSpace.begin();
        int left_larger_than_right = 0;
        while (it1 < mid && it2 < end) {
            if (it1->num > it2->num) {
                *(mit++) = *(it2++);
                left_larger_than_right++;
            } else {
                it1->count += left_larger_than_right;
                *(mit++) = *(it1++);
            }
        }
        while (it1 < mid) {
            it1->count += left_larger_than_right;
            *(mit++) = *(it1++);
        }
        while (it2 < end) {
            *(mit++) = *(it2++);
        }
        copy(mergeSpace.begin(), mergeSpace.end(), begin);
    }
};
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