Program to find sum of absolute differences in a sorted array in Python

Suppose we have an array nums and that is sorted in non-decreasing order. We have to make an array called result with the same length as nums such that result[i] is the summation of absolute differences between nums[i] and all the other elements in the array.

So, if the input is like nums = [5,7,12], then the output will be [9, 7, 12] because

• |5-5| + |5-7| + |5-12| = 0+2+7 = 9
• |7-5| + |7-7| + |7-12| = 2+0+5 = 7
• |5-12| + |7-12| + |12-12| = 7+5+0 = 12

To solve this, we will follow these steps −

• res := a new list
• s:= 0
• n := size of nums
• for i in range 1 to n - 1, do
  • s := s + nums[i] - nums[0]
• insert s at the end of res
• for i in range 1 to n - 1, do
  • diff := nums[i] - nums[i-1]
  • s := s + diff*i
  • s := s - diff *(n-i)
• insert s at the end of res
• return res

Example

Let us see the following implementation to get better understanding −

def solve(nums):
   res = []
   s=0
   n = len(nums)
   for i in range(1,n):
      s+=nums[i]-nums[0]
   res.append(s)
   for i in range(1,n):
      diff = nums[i]-nums[i-1]
      s += diff*i
      s -= diff *(n-i)
      res.append(s)
   return res

nums = [5,7,12]
print(solve(nums))

Input

[5,7,12]

Output

[9, 7, 12]