Python Combinatory Algorithm - A Binomial Coefficient application with n mutable and k fixed to 2

Question

This question came from a real use case. I had a data frame with different columns each one containing data from a data source and I wanted to design a hypothesis test to prove or not if the data had the same mean. So I had to compute the Kolmogorov-Smirnov test for each couple of columns.

Now the problem can be generalized to any combinatory task.

It follows that I had to implement a Binomial Coefficient like

$$ \binom{n}{k} $$

Where n is the number of columns

and k is = 2

My question is: if exists a more efficient way to apply a function on permutated samples taken from a list? And how to do this permutation eg. Given a func and a list [a,b,c,d]

func(a,b)
func(a,c)
func(a,d)
func(b,c)
func(b,d)
func(c,d)

I created an algorithm to solve this issue, but I am wondering if there is a better way to do that in Python.

In my algorithm, I simply multiply each n element in an explanatory array with another element i of the same array, with n!=i, instead of computing the statistical test.

to_do=[1,2,3,4,5]
#done will store information on the elements already combined
done=[]
#j will store information on the results of the combination  
j=[]


#iterating over the to_do array
for n in to_do:

  #checking if we already computed the n element  
  if n not in done:
    print(n)
    #taking another i element from the array
    #where n!=i    
    for i in to_do: 
      print(i)
      #if the condition is satisfied       
      if i!=n:
        #combine the two elements        
        m=n*i

        #append the result on the "j" array 
        j.append(m)
    #updating the array with the "done" elements        
    done.append(n)    

print(len(done))
print(len(j))

Answer 1

If you just want the length of the list, your code can be reduced to one line:

result = len(to_do) * (len(to_do) - 1)

Also, you're comments are, at the very least, excessive. You should really only use comments to explain a design choice or a complicated equation/algorithm. Comments like #if the condition is satisfied just clutters your code.

As explained in a comment, actual computations need to be made. This can be done using itertools.permutations.

import itertools
from typing import List

def func(nums: List[int]) -> List[int]:

    return list(set(
        x * y for x, y in itertools.permutations(nums, 2)
    ))

While this doesn't avoid the extra computations, it's a short and sweet solution. And below is how you would use it:

to_do = [1, 2, 3, 4, 5]
func(to_do)

Answer 2

My question is: if exists a more efficient way to apply a function on permutated samples taken from a list? And how to do this permutation eg. Given a func and a list [a,b,c,d]

func(a,b)

func(a,c)

func(a,d)

func(b,c)

func(b,d)

func(c,d)

It seems that you are looking for combinations rather than permutations. In that case, use itertools.combinations:

from itertools import combinations

for x, y in combinations(['a', 'b', 'c', 'd'], 2):
    print(x, y)

It prints:

a b
a c
a d
b c
b d
c d

Using itertools.combinations in your example:

from itertools import combinations

todo = [1, 2, 3, 4, 5]
j = [x * y for x, y in combinations(todo, 2)]