L10 Hw03 1

def next_smaller_dollar(bill):
    """Returns the next smaller bill in order."""
    if bill == 100:
        return 50
    if bill == 50:
        return 20
    if bill == 20:
        return 10
    elif bill == 10:
        return 5
    elif bill == 5:
        return 1
def next_larger_dollar(bill):
    """Returns the next larger bill in order."""
    if bill == 1:
        return 5
    elif bill == 5:
        return 10
    elif bill == 10:
        return 20
    elif bill == 20:
        return 50
    elif bill == 50:
        return 100
def count_dollars(total):
    """Return the number of ways to make change.

    >>> count_dollars(15)  # 15 $1 bills, 10 $1 & 1 $5 bills, ... 1 $5 & 1 $10 bills
    6
    >>> count_dollars(10)  # 10 $1 bills, 5 $1 & 1 $5 bills, 2 $5 bills, 10 $1 bills
    4
    >>> count_dollars(20)  # 20 $1 bills, 15 $1 & $5 bills, ... 1 $20 bill
    10
    >>> count_dollars(45)  # How many ways to make change for 45 dollars?
    44
    >>> count_dollars(100) # How many ways to make change for 100 dollars?
    344
    >>> count_dollars(200) # How many ways to make change for 200 dollars?
    3274
    >>> from construct_check import check
    >>> # ban iteration
    >>> check(HW_SOURCE_FILE, 'count_dollars', ['While', 'For'])
    True
    """
    def helper(n,bill):
        if bill==None:
            return 0
        if bill==1:
            return 1
        if bill>n:
            return helper(n,next_smaller_dollar(bill))
        else:
            with_max = helper(n-bill,bill)
            without_max = helper(n,next_smaller_dollar(bill))
            return with_max + without_max
    return helper(total,100)

print(count_dollars(100))

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