All possible change combinations

Question

I'm trying to output a list of lists with all possible combinations of change given an amount and coins. For example - given the amount 6 and the coins = [1,5,10] I would get:

[[1,1,1,1,1,1],
[1,5],
[5,1]]

I wrote something that prints the correct solution but I cannot figure out how to get the function to output the solutions in a list of lists format

def possible_change(n,p=[],coins = [1,5,10]):
    if n == 0:
        print(p)
        return p
    else:
        for c in coins:
            if n - c >= 0:
                possible_change(n-c,p+[c],coins=coins)

possible_change(6,coins=[1,5,10])

How to I get the function to return the actual lists?

Answer 1

Instead of those print statements, simply populate a global list.

sols = []
def possible_change(n,p=[],coins = [1,5,10]):
    if n == 0:
        global sols
        sols.append(p)
    else:
        for c in coins:
            if n - c >= 0:
                possible_change(n-c,p+[c],coins=coins)    

possible_change(6,coins=[1,5,10])
print(sols)

[[1, 1, 1, 1, 1, 1], [1, 5], [5, 1]]

Answer 2

You can try to add a total list to the function and return it if the n - c is less then 0 or if the for loop for c in coins: is end

def possible_change(n,p=[],coins = [1,5,10], total=[]):
    if n == 0:
        total.append(p)
    else:
        for c in coins:
            if n - c >= 0:
                print("c {}".format(c))
                possible_change(n-c,p+[c],coins=coins)
            else:
                return total
    return total

print(possible_change(6,coins=[1,5,10]))

Result

[[1, 1, 1, 1, 1, 1], [1, 5], [5, 1]]