<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) {
        int n = nums.size();
        vector<int> result(n,0);
        vector<int> indices(n,0);
        for(int i=0;i<n;i++){
            indices[i] = i;
        }
        mergeSort(nums,0,n-1,result,indices);
        for(auto it: indices){
            cout<<it<<" "; 
        }
        return result;
    }
    void mergeSort(vector<int> &nums, int left,int right,vector<int> &result, vector<int> &indices){
        if(left>=right){
            return ;
        }
        int mid = (left+right)/2;
        mergeSort(nums,left,mid,result,indices);
        mergeSort(nums,mid+1,right,result,indices);
        merge(nums,left,right,result,indices);
        return ;
    }
    void merge(vector<int> &nums,int left,int right,vector<int> &result,vector<int> &indices){
        int mid = (left+right)/2;
        int i = left;
        int j = mid+1;
        vector<int> helper;
        while(i<=mid && j<=right){
            if(nums[indices[i]]<=nums[indices[j]]){
                result[indices[i]] +=j-(mid+1);
                helper.push_back(indices[i]);
                i++;
            }
            else{
                helper.push_back(indices[j]);
                j++;
            }
        }
        while(i<=mid){
            result[indices[i]] += j - (mid+1);
            helper.push_back(indices[i]);
            i++;
        }
        while(j<=right){
            helper.push_back(indices[j]);
            j++;
        }
        for(int k = left;k<=right;k++){
            indices[k] = helper[k-left];
        }
    }
};
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