<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 {
    void merge(vector<int>& nums, int l, int mid, int h, vector<int>& result, vector<int>& idx){
        if(l >= h)
            return;
        vector<int>temp;
        int i = l;
        int j = mid + 1;
        int cnt = 0;
        while(i <= mid && j <= h){
            if(nums[idx[i]] > nums[idx[j]]){
                cnt++;
                temp.push_back(idx[j++]);
            }
            else{
                result[idx[i]] += cnt;
                temp.push_back(idx[i++]);
            }
        }   
        while(i <= mid){
            result[idx[i]] += cnt;
            temp.push_back(idx[i]);
            i++;
        }
        while(j <= h){
            temp.push_back(idx[j]);
            j++;
        }
        for(int i = l;i <= h;i++)
            idx[i] = temp[i - l];  
    }
    void mergeSort(vector<int>& nums, int l, int h, vector<int>& result, vector<int>& idx){
        if(l >= h)
            return;
        int mid = (l + h) >> 1;
        mergeSort(nums, l, mid, result, idx);
        mergeSort(nums, mid + 1,h, result, idx);
        merge(nums, l, mid, h, result, idx);
    }
public:
    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        vector<int> result(n, 0);
        vector<int> idx(n);
        for(int i = 0;i < n;i++)
            idx[i] = i;
        mergeSort(nums, 0, n - 1, result, idx);    
        return result;    
    }
};
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