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I am trying to write a function has input:

given_num=6, n=3

How to return a result of all possible combinations as list with n elements and sum = given_num nested in a list:

[[0,0,6],[0,1,5],[0,2,4],[0,3,3],[0,4,2],[0,5,1],[0,6,0],
[1,0,5],[1,1,4],[1,2,3],[1,3,2],[1, 4,1],[1,5,0],
...
[6,0,0]]

solved, and the possible combination is calculated as

factorial(given_num+n-1)/(factorial(given_num) * factorial(n-1))

Here a try using itertools product :

from itertools import product

given_num = 6
n = 3
all_comb = product(range(given_num+1), repeat=n)
final_lst = [i for i in all_comb if sum(i) == given_num]
print(final_lst)

Find all combinations of a set of lists with itertools.product, The same effect can be achieved in Python by combining map() and count() to So, if the input iterable is sorted, the combination tuples will be produced in  Elite Programming Professionals Ready to Teach Online. Anytime, Anywhere.

from itertools import product
import numpy as np

tuples = []
given_num = 6
n = 3

for numbers in product(np.arange(given_num+1), repeat=n):

    if sum(numbers) == given_num:
        tuples.append(numbers)

print(tuples)

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In case you want to have some fun with recursive functions

def summands(num, N):
    if N==1:
        return [[num]]
    else:
        return [[i] + j for i in range(num+1) for j in summands(num - i, N-1)]

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Comments
  • did you try anything? What was the problem with it?
  • Possible duplicate of Generate all possible outcomes of k balls in n bins (sum of multinomial / categorical outcomes)
  • @Georgy , thx for the link, the generator solution is time saving for a large given_num or n, considering I am working on a optimization problem.