<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:
    struct viPair {
    int val;
    int originalIdx;
    viPair(int v, int idx) : val(v), originalIdx(idx) {}
};

    vector<int> countSmaller(vector<int>& nums) {
        int n = nums.size();
        
        if (!n) return vector<int>();
        vector<viPair> newNums;
        for (int i = 0; i < n; i++) {
            newNums.emplace_back(nums[i],i);
        }
        
        vector<int> res(n, 0);
        mergeSort(newNums, 0, n-1, res);
        return res;
    }
    
    void mergeSort(vector<viPair>& nums, int start, int end, vector<int>& result) {
        if (start >= end) return;
        int mid = (start + end) / 2;
        mergeSort(nums, start, mid, result);
        mergeSort(nums, mid+1, end, result);
        
        int leftPos = start;
        int rightPos = mid+1;
        deque<viPair> merged;
        int smallerThanLeft = 0;
        
        while (leftPos <= mid && rightPos <= end) {
            if (nums[leftPos].val > nums[rightPos].val) {
                smallerThanLeft++;
                merged.push_back(nums[rightPos]);
                rightPos++;
            } else {
                result[nums[leftPos].originalIdx] += smallerThanLeft;
                merged.push_back(nums[leftPos]);
                leftPos++;
            }
        }
        
        while (leftPos <= mid) {
            result[nums[leftPos].originalIdx] += smallerThanLeft;
            merged.push_back(nums[leftPos]);
            leftPos++;
        }
        
        while (rightPos <= end) {
            merged.push_back(nums[rightPos]);
            rightPos++;
        }
        
        int pos = start;
        for (auto& m: merged)
            nums[pos++] = m;
    }
    
};
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