# Question

Formatted question description: https://leetcode.ca/all/315.html

 315	Count of Smaller Numbers After Self

You are given an integer array nums and you have to return a new counts array.
The counts array has the property where counts[i] is the number of smaller elements to the right of nums[i].

Example:

Input: [5,2,6,1]
Output: [2,1,1,0]

Explanation:
To the right of 5 there are 2 smaller elements (2 and 1).
To the right of 2 there is only 1 smaller element (1).
To the right of 6 there is 1 smaller element (1).
To the right of 1 there is 0 smaller element.



# Algorithm

You can start traversing from the right, and keep putting the traversed numbers into another sort array, and store this sort array in ascending order, So, if you are looking for a few smaller numbers to the right of the current value, then you have to find the position where the current value should be placed in the sort array (In order to improve efficiency, use the binary search method to determine where the current value should be placed), that is, there are several smaller numbers on the right.

example:

nums: [5,2,6,1] When i = 3, nums[i] =1, sort[0]=nums[i];

0 1 2 3     <= sort[] index
1           <= sort[] value


When i = 2, nums[i] = 6, by using the dichotomy search in sort (currently only element 1), it is found that 6 should be inserted after 1, [1,6], ie index=1, sort[index] =nums[i]; So the number of numbers smaller than it on the right of the current value 6 is index=1

0 1 2 3
1 6


When i = 1, nums[i] = 2, by using the dichotomy search in sort (currently only elements 1, 6), it is found that 2 should be inserted after 1, [1,2,6], ie index=1, sort[index]=nums[i]; So the number of numbers smaller than it on the right side of the current value 2 is index=1

0 1 2 3
1 2 6


When i = 0 and nums[i] = 5, by using the dichotomy search in sort (currently only elements 1, 2, 6), it is found that 5 should be inserted after 2, [1,2,5,6], that is index=2, sort[index]=nums[i]; So the number of numbers smaller than it on the right of the current value of 5 is index=2

0 1 2 3
1 2 5 6


Then, the result is Output: [2,1,1,0].

Java