<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>

class Solution {
public:
    void mergesort(vector<int>& arr, int l, int r, vector<int>& counts, vector<int>& indices) {
        if (r <= l) {
            return;
        }
        int mid = (l + r) / 2;
        mergesort(arr, l, mid, counts, indices);
        mergesort(arr, mid + 1, r, counts, indices);

        vector<int> tempIndices(r - l + 1);
        vector<int> temp(r - l + 1);
        int left = l;
        int right = mid + 1;
        int k = 0;

        while (left <= mid && right <= r) {
            if (arr[left] <= arr[right]) {
                temp[k] = arr[left];
                tempIndices[k] = indices[left];
                counts[indices[left]] += (right - mid - 1);
                left++;
            } else {
                temp[k] = arr[right];
                tempIndices[k] = indices[right];
                right++;
            }
            k++;
        }

        while (left <= mid) {
            temp[k] = arr[left];
            tempIndices[k] = indices[left];
            counts[indices[left]] += (right - mid - 1);
            left++;
            k++;
        }

        while (right <= r) {
            temp[k] = arr[right];
            tempIndices[k] = indices[right];
            right++;
            k++;
        }

        for (int i = l; i <= r; i++) {
            arr[i] = temp[i - l];
            indices[i] = tempIndices[i - l];
        }
    }

    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector<int> counts(n, 0);
        vector<int> indices(n, 0);
        for (int i = 0; i < n; i++) {
            indices[i] = i;
        }
        mergesort(nums, 0, n - 1, counts, indices);
        return counts;
    }
};

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