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))

• superb rain: Unclear. What exactly is the input, what exactly is the output? Do you just want itertools.permutations(to_do, 2)?
• Andrea Ciufo: The input is the array ´to_do´ and then each element of the array is multiplied with another one and this operation should be done for each element.
• Andrea Ciufo: I read the documentation, how can I avoid to repeat an operation when I have to permutate like in the documentation a list of 4 elements [ABCD] and I need only AB and not BA (or viceversa). I tried to fix this issue with the done array in my code
• superb rain: Well your own code does both AB and BA. Are you saying your code isn't correct and thus your question is off-topic?

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)

• Andrea Ciufo: Thank you the point about the comment is very useful, the output as I commented above is to multiply each element of the list with another one and this should be done for all the elements, except for the multiplication of the element ´i´ with itself.
• Ben A: @AndreaCiufo Please see my edited answer.
• Andrea Ciufo: what does it mean -> List[int] it's the first time that I see it in the function signature?
• Ben A: @AndreaCiufo It means that the function returns a list of integers. Take a look at the python docs regarding type hints

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)]