Python Challenge

Question

I am doing the coin-change problem. I have finished the problem, that it prints out how many coins I need to make the least amount of change possible, but how do I change my program so that it also prints those coins??

Here is a sample I/O:

input: coin_change(48, [1, 5, 10, 25, 50])

output: [6, [25, 10, 10, 1, 1, 1]]

input: coin_change(48, [1, 7, 24, 42])

output: [2, [24, 24]]

Currently my code only returns the 6.

By the way, this must be done with recursion only. No loops are allowed.

Code:

def change(C, V):
    def min_coins(i, aC):
        if aC == 0:
            return 0
        elif i == -1 or aC < 0:
            return float('inf')
        else:
            return min(min_coins(i-1, aC), 1 + min_coins(i, aC-V[i]))
    return min_coins(len(V)-1, C)

The code below is what I tried, but it does NOT work for the second input

def giveChange(C, V, res = None):
    res=[] if res is None else res
    if len(V)==0:
        return len(res),res
    maxx=max(V)
    print maxx
    V.remove(maxx)
    ans=C//maxx
    if ans==0 and maxx<C :
        print maxx
        res +=[maxx]*ans
        return  len(res),res
    else:
        res += [maxx]*ans
        return  giveChange(C % maxx,V,res)

Answer 1

Might not use maxx=max(V)

An optimal solution may comprise of small coins, for example 48=24+24, which has two coins, lesser than 48=25+10+10+1+1+1. In that case, though 25>24, you have to use more tiny coins to make a 48.

Thus if your input is (48, [1, 7, 24, 42]), you will be trapped in the second situation and get a 48 = 42+1+1+1+1+1+1. You can combine your second posted codes with your first one, add a list as parameter for storing the changes and use the same recursion design.

Answer 2

Your first code will work with a few changes. Instead of returning just count, a function can return a list or even (count, [coins]) tuple. you may also want to sort V.