<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.empty()) return {};
        vector<int> result(nums.size(), 0);
        vector<pair<int,int>> num_inds;
        for (int i = 0; i < nums.size(); i++) {
            num_inds.push_back({nums[i], i});
        }

        mergeSort(num_inds, 0, nums.size()-1, result);

        return result;
    }

    void mergeSort(vector<pair<int,int>>& num_inds, const int start, const int end, vector<int>& result) {
        if (start >= end) {
            return;
        }
        int mid = (end - start) / 2 + start;
        mergeSort(num_inds, start, mid, result);
        mergeSort(num_inds, mid+1, end, result);

        vector<pair<int,int>> temp;
        // int n = end - start + 1;
        int i = start, j  = mid + 1, j_len = end-j+1;
        while (i <= mid || j <= end) {
            if ( i > mid ||(j <= end && num_inds[j].first < num_inds[i].first)) {
                // j ok
                temp.push_back(num_inds[j]);
                j++;
            } else {
                int smaller_than_i = j - (mid+1);
                result[num_inds[i].second] += smaller_than_i;
                temp.push_back(num_inds[i]);
                i++;
            }


        }

        copy(temp.begin(), temp.end(), num_inds.begin() + start);
    } 


};
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