<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:
    // vector<int> countSmaller(vector<int>& nums) {
    //     if (nums.size() == 1)
    //         return {0};

    //     int n = nums.size();
    //     vector<int> ans;

    //     brute force
    //     for (int i = 0; i < n; i++) {
    //         int count=0;
    //         for (int j = i + 1; j < n; j++) {
    //             if(nums[j] < nums[i])
    //                 count++;
    //         }
    //         ans.push_back(count);
    //     }
        
    //     return ans;
    // }
    void mergeCountSmaller(vector<int>& indices, int left, int right, vector<int>& counts, vector<int>& nums) {
        if (right - left <= 1) return;

        int mid = (left + right) / 2;
        mergeCountSmaller(indices, left, mid, counts, nums);
        mergeCountSmaller(indices, mid, right, counts, nums);

        vector<int> temp(right - left);
        int i = left, j = mid, k = 0, rightCount = 0;

        while (i < mid && j < right) {
            if (nums[indices[j]] < nums[indices[i]]) {
                temp[k++] = indices[j++];
                rightCount++;
            } else {
                counts[indices[i]] += rightCount;
                temp[k++] = indices[i++];
            }
        }

        while (i < mid) {
            counts[indices[i]] += rightCount;
            temp[k++] = indices[i++];
        }

        while (j < right) {
            temp[k++] = indices[j++];
        }

        for (int i = left; i < right; i++) {
            indices[i] = temp[i - left];
        }
    }

    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;
        }

        mergeCountSmaller(indices, 0, n, counts, nums);

        return counts;
    }
};
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