How to get sum of products of all combinations in

Question

I'm using Python and I'm given an array like a = [1, 2, 3, 4] and I want to find sum of all possible combination multiplications like:

For combinations of 1: 1 + 2 + 3 + 4

For combinations of 2:1*2 + 2*3 + 3*4 + 4*1.

For combination of 3: 1*2*3 + 1*3*4 + 2*3*4

For combinations of 4: 1*2*3*4

And finally sum of all these sums is my answer. I'm using numpy.prod() and numpy.sum(). But it's still too slow. Is there some better algorithm to find the sum quickly?

Answer 1

You can do with numpy and itertools:

from numpy import linspace, prod
from itertools import combinations

arr = np.array([1,2,3,4])

[sum([prod(x) for x in combinations(arr,int(i))]) for i in linspace(1,len(arr), len(arr))]
[10, 35, 50, 24]