<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:
    class Pair:
        def __init__(self, val, id):
            # 记录数组的元素值
            self.val = val
            # 记录元素在数组中的原始索引
            self.id = id
    temp = []
    ct = []
    def countSmaller(self, nums: List[int]) -> List[int]:
        
        self.temp = [self.Pair(0,0)]*len(nums)
        self.ct = [0] * len(nums)
        arr = []
        for i in range(len(nums)):
            arr.append(self.Pair(nums[i], i))
        self.sort(arr,0,len(nums)-1)
        return self.ct
        
        
    def sort(self, arr,lo,hi):
        if lo==hi:
            return 
        mid = lo + (hi-lo)//2
        self.sort(arr,lo,mid)
        self.sort(arr,mid+1,hi)
        self.merge(arr, lo,mid, hi)


    def merge(self,arr,lo, mid, hi):
        for ind in range(lo,hi+1):
            self.temp[ind] = arr[ind]
      
        i,j = lo,mid+1
        for p in range(lo,hi+1):
            if i == mid +1:
                arr[p] = self.temp[j]
                j+= 1
            elif j == hi +1:
                arr[p] = self.temp[i]
                i+= 1
                self.ct[arr[p].id] += j-mid-1
            elif self.temp[i].val > self.temp[j].val:
                arr[p] = self.temp[j]
                j += 1
            else:
                arr[p] = self.temp[i]
                self.ct[arr[p].id] += j-mid-1
                i+= 1
                

        
        
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