Python code - I'm stuck - recursion

Question

I need some help because I think I'm lost. I've search before in this site and of course I've Google it, but believe me that if it was so simple to me, I haven't ask it at all, so please be kind to me. I'm new to python and coding isn't that easy to me.

Anyway, take a look at my code:

def coin_problem(price, cash_coins):
    if (price < 0):
        return []
    if (price == 0):
        return [[]]

    options = []

    for a_coin in cash_coins:
        coins_minus_coin = cash_coins[:]
        coins_minus_coin.remove(a_coin)
        sub_coin_problem = coin_problem (price - a_coin, cash_coins)
        for coin in sub_coin_problem:
            coin.append(a_coin)
        options.extend(sub_coin_problem)

    return options

print coin_problem(4, [1, 2])

As you can see, I've tried to deal with the famous coin problem by recursion (and as I wrote before, I know many have already asked about this, I read their questions and the answers but I still couldn't understand the fully solutions).

This code was made by me, all of it. And now I'm stuck and confused. When the value of "price" is 4 and the value of "cash_coins" is [1,2] instead of returning something like this:

[1,1,1,1]
[2,2]
[2,1,1]

I get something more like:

[[1, 1, 1, 1], [2, 1, 1], [1, 2, 1], [1, 1, 2], [2, 2]]

the combination of "2" and the double "1" repeats 3 times instead of "1". I don't know what should I do in order to fix the problem or to improve my code so it will work better.

Answer 1

When you want to add a single item to a list, use append . When you want to combine two lists together, use extend .

Answer 2

Tips:

    coins_minus_coin = cash_coins[:]
    coins_minus_coin.remove(coin)

You never use this variable.

    for i in sub_coins:
        i.append(coin)
    cash_coins_options.append(sub_coins)

You never use i either. I'd guess you meant:

    for i in sub_coins:
        i.append(coin)
        cash_coins_options.append(i)

That solves the problem of stange results, but your solution will still only find [] . Why? Your recursion can only stop on a return [] ; it can't handle another fundamental case when you can tell the price using a single coin. Try adding at the top this simple condition:

# actually I changed my mind-
# I assume you're learning so try this one yourself :-)

This will cause your function to behave much better:

>>> print coin_problem(4, [1,2])
[[2, 1, 1], [1, 2, 1], [2, 2]]

which manages to produce correct answers (even though it duplicates some of them).