# Recursive function homework
# There are many different correct recurive answers to these problems

# Problem 1: sumdigits(n)
def sumdigits(n):
    if n//10 == 0:
        return n
    return n%10 + sumdigits(n//10)

# Problem 2: biggest(L) -- there are many cleverer ways of doing this
def biggest(L):
    return biggest_sofar(L[0],L[1:])

def biggest_sofar(biggie,rest):
    if rest == []:
        return biggie
    if biggie > rest[0]:
        return biggest_sofar(biggie,rest[1:])
    return biggest_sofar(rest[0],rest[1:])

# Problem #3: ten2two(n)
def ten2two(n):
    if n < 2:
        return n
    return ten2two(n//2)*10 + n%2

# Problem #4: baseConvert(n, inbase, outbase)
def baseConvert(n,inbase,outbase):
    # first convert into base 10, then back out to the outbase
    baseten = convert_to_ten(n,inbase)
    return convert_from_ten(baseten,outbase)

def convert_from_ten(n,outbase):
    if n < outbase:
        return n
    return convert_from_ten(n//outbase,outbase)*10 + n%outbase

def convert_to_ten(n,inbase):
    if n < inbase:
        return n
    return n%10 + inbase * convert_to_ten(n//10,inbase)