<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 Node:
    def __init__(self, val):
        self.val = val
        self.left_cnt = 0
        self.cnt = 0
        self.left = None
        self.right = None
        
class Solution:
    def countSmaller(self, nums: List[int]) -> List[int]:
        """
        [5,2,6,2,1]
        [1, 2, 5, 6]
        [0, 1, 2, 1, 3] -> [3, 1, 2, 1, 0]
        
                2 (l=1,c=2)
            /       \
           1(l=0,c=1) 5 (l=3,c=0)
                        \
                         6 (l=2,c=1)
        
        """
        nums_uqi = sorted(list(set(nums)))
        def createNode(left, right):
            if left > right:
                return None
            mid = (left + right) // 2
            root = Node(nums_uqi[mid])
            root.left = createNode(left, mid - 1)
            root.right = createNode(mid + 1, right)
            return root
        
        root = createNode(0, len(nums_uqi) - 1)
        
        print(nums_uqi, root.val)
        
        res = []
        for num in reversed(nums):
            left_cnt = 0
            node = root
            while node.val != num:
                if node.val > num: 
                    node.left_cnt += 1
                    node = node.left
                else:
                    left_cnt += node.cnt + node.left_cnt
                    node = node.right
                    
            node.cnt += 1
            res.append(node.left_cnt + left_cnt)
        return reversed(res)
         
        
#         res = []
#         for i in range(len(nums))[::-1]:
#             cnt = 0
#             for j in range(i+1, len(nums))[::-1]:
#                 if nums[i] > nums[j]:
#                     cnt += 1
#             res.append(cnt)
            
#         return reversed(res)
739