<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:
    def countSmaller(self, nums: List[int]) -> List[int]:
        n = len(nums)
        ans = [0] * n
        def mergesort(indexArray):
            if len(indexArray) <= 1:
                return indexArray
            mid = (0 + len(indexArray) - 1) // 2
            left = mergesort(indexArray[:mid+1])  # 2 , 2
            right = mergesort(indexArray[mid+1:])  # 2, 3
            # merge
            leftIndex = 0
            rightIndex = 0
            sortedIndexArray = []
            jumpsSoFar = 0
            while leftIndex < len(left) and rightIndex < len(right):
                if nums[left[leftIndex]] <= nums[right[rightIndex]]:
                    sortedIndexArray.append(left[leftIndex])
                    ans[left[leftIndex]] += jumpsSoFar
                    leftIndex += 1
                else:
                    sortedIndexArray.append(right[rightIndex])
                    jumpsSoFar += 1
                    rightIndex += 1
            if leftIndex < len(left):
                sortedIndexArray += left[leftIndex:]
                for index in left[leftIndex:]:
                    ans[index] += jumpsSoFar
            if rightIndex < len(right):
                sortedIndexArray += right[rightIndex:]
            # print("Sorted index array:", sortedIndexArray)
            return sortedIndexArray


        mergesort(list(range(n)))
        return ans
        
1648