Algorithm to find a list of numbers that sum up to a certain number

Question

I'm learning python and I have a problem with this task

I have a list of numbers 0<=n<=(end), and I want to find all combinations of lists with 6 elements whose elements sum up to a certain number S

I'll use the list created by the function to check some conditions which I think would be another kind of task. Right now, I'm looking for an effective way to do the task above! I tried to use Brute-force, but I guess the time complexity gets exponential!

Pseudocode or suggestion of a known algorithm would also be nice for me! I just a piece of advice, thank you.

For example,

def f(end, S):
   #definition of the function

input f(14, 14)
output [14, 0, 0, 0, 0, 0] [0, 14, 0, 0, 0, 0] ...(and so on)... [0, 0, 3, 0, 7, 4] [0, 0, 3, 0, 6, 5] (and so on)...

---

Below is information about the condition I mentioned above, still my main question is about the task above! So you can just ignore the below part

I have three different functions that return a String(the only possible outputs are A, B, C or (none). eg) f1(list) --> 'A' f2(list) --> 'B' f3(list) --> 'C'

I will put the list created by the function I asked for into those functions and find out which cases of lists lead the three functions to return a String different from each other, while they all do not return (none)(f1, f2, f3 should return A or B or C). I will make a loop for each list and find out which of them meets this condition.

Answer 1

You can do -

def f(Num, List):
    n = Num 
    l = List 
    for i in range(len(List)):
        if len(List) > 0 and len(List) != 1:
            x= List.pop(0)
            y= List.pop(0)
            if x + y == Num:
                print(str(x) + " and " + str(y) + " are a sum of " + str(Num))  
        else:
            # print("the list has no more values")
            exit(0)

f(10, [5, 5, 8, 2, 3, 4, 3]) # 3, 4, 3 will not be checked

the reason why 3,4,3 will not be checked is because the program does not support the sums of more then 2 numbers, imagine if you give this list [4, 4, 2] and want to find 10 as its sum, the program will not do anything and just quit, because it does not support 3 or more numbers.