Program to count average of all special values for all permutations of a list of items in Python

Suppose we have a list of elements we can calculate the value of S by the following algorithm.

while size of L > 1 is non-zero, do    a := L[0]    b := L[1]    remove L[1]    L[0] := a + b + a*b return L[0] mod (10^9 + 7)

Here we shall have to find the average of all S values that are calculated from all possible combinations of L.

So, if the input is like L = [5,3,4], then the output will be 199, because for all permutation of L, the value of S is 119, so their average is also 119.

To solve this, we will follow these steps −

• m := 10^9+7
• li := a list of x+1 for all x in L
• prod := 1
• for each i in li, do
  • prod := prod * i
  • prod := prod mod m
• return (prod-1) mod m

Example

Let us see the following implementation to get better understanding −

def solve(L):     m = 10**9+7     li = [x+1 for x in L]     prod = 1     for i in li:         prod *= i         prod %= m     return (prod-1) % m L = [5,3,4] print(solve(L)) 

Input

[5,3,4]

Output

119