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Find the sum of maximum difference possible from all subset of a given array in Python

Suppose we have an array A of n values (elements may not be distinct). We have to find the sum of maximum difference possible from all subsets of given array. Now consider max(s) denotes the maximum value in any subset, and min(s) denotes the minimum value in the set. We have to find the sum of max(s)-min(s) for all possible subsets.

So, if the input is like A = [1, 3, 4], then the output will be 9.

To solve this, we will follow these steps −

  • n := size of A

  • sort the list A

  • sum_min := 0, sum_max := 0

  • for i in range 0 to n, do

    • sum_max := 2 * sum_max + A[n-1-i]

    • sum_max := sum_max mod N

    • sum_min := 2 * sum_min + A[i]

    • sum_min := sum_min mod N

  • return(sum_max - sum_min + N) mod N

Example

Let us see the following implementation to get better understanding −

N = 1000000007
def get_max_min_diff(A):
   n = len(A)
   A.sort()
   sum_min = 0
   sum_max = 0
   for i in range(0,n):
      sum_max = 2 * sum_max + A[n-1-i]
      sum_max %= N
      sum_min = 2 * sum_min + A[i]
      sum_min %= N
   return (sum_max - sum_min + N) % N
A = [1, 3, 4]
print(get_max_min_diff(A))

Input

[1, 3, 4]

Output

9