hw02.py

HW_SOURCE_FILE = __file__


def num_eights(x):
    """Returns the number of times 8 appears as a digit of x.

    >>> num_eights(3)
    0
    >>> num_eights(8)
    1
    >>> num_eights(88888888)
    8
    >>> num_eights(2638)
    1
    >>> num_eights(86380)
    2
    >>> num_eights(12345)
    0
    >>> from construct_check import check
    >>> # ban all assignment statements
    >>> check(HW_SOURCE_FILE, 'num_eights',
    ...       ['Assign', 'AugAssign'])
    True
    """
    "*** YOUR CODE HERE ***"
    if not x:
        return 0
    if x % 10 == 8:
        return 1 + num_eights(x // 10)
    else:
        return num_eights(x // 10)


def pingpong(n):
    """Return the nth element of the ping-pong sequence.

    >>> pingpong(8)
    8
    >>> pingpong(10)
    6
    >>> pingpong(15)
    1
    >>> pingpong(21)
    -1
    >>> pingpong(22)
    -2
    >>> pingpong(30)
    -2
    >>> pingpong(68)
    0
    >>> pingpong(69)
    -1
    >>> pingpong(80)
    0
    >>> pingpong(81)
    1
    >>> pingpong(82)
    0
    >>> pingpong(100)
    -6
    >>> from construct_check import check
    >>> # ban assignment statements
    >>> check(HW_SOURCE_FILE, 'pingpong', ['Assign', 'AugAssign'])
    True
    """
    "*** YOUR CODE HERE ***"

    # while version
    # index, sign, value = 1, 1, 1
    # while index < n:
    #     value += sign * 1
    #     index += 1
    #     if index % 8 == 0 or num_eights(index):
    #         sign *= -1
    # return value

    # HINT: Write a helper function that has a parameter for each variable that changes values in the body of the while loop.
    def helper(index, sign, value):
        if index == n:
            return value
        if index % 8 == 0 or num_eights(index):
            return helper(index + 1, -sign, value - sign)
        else:
            return helper(index + 1, sign, value + sign)

    return helper(1, 1, 1)


def missing_digits(n):
    """Given a number a that is in sorted, increasing order,
    return the number of missing digits in n. A missing digit is
    a number between the first and last digit of a that is not in n.
    >>> missing_digits(1248) # 3, 5, 6, 7
    4
    >>> missing_digits(1122) # No missing numbers
    0
    >>> missing_digits(123456) # No missing numbers
    0
    >>> missing_digits(3558) # 4, 6, 7
    3
    >>> missing_digits(35578) # 4, 6
    2
    >>> missing_digits(12456) # 3
    1
    >>> missing_digits(16789) # 2, 3, 4, 5
    4
    >>> missing_digits(19) # 2, 3, 4, 5, 6, 7, 8
    7
    >>> missing_digits(4) # No missing numbers between 4 and 4
    0
    >>> from construct_check import check
    >>> # ban while or for loops
    >>> check(HW_SOURCE_FILE, 'missing_digits', ['While', 'For'])
    True
    """
    "*** YOUR CODE HERE ***"
    if n < 10:
        return 0

    if n % 10 - (n // 10) % 10 > 0:
        return n % 10 - (n // 10) % 10 - 1 + missing_digits(n // 10)

    return missing_digits(n // 10)


def next_largest_coin(coin):
    """Return the next coin.
    >>> next_largest_coin(1)
    5
    >>> next_largest_coin(5)
    10
    >>> next_largest_coin(10)
    25
    >>> next_largest_coin(2) # Other values return None
    """
    if coin == 1:
        return 5
    elif coin == 5:
        return 10
    elif coin == 10:
        return 25


def count_coins(total):
    """Return the number of ways to make change for total using coins of value of 1, 5, 10, 25.
    >>> count_coins(15)
    6
    >>> count_coins(10)
    4
    >>> count_coins(20)
    9
    >>> count_coins(100) # How many ways to make change for a dollar?
    242
    >>> from construct_check import check
    >>> # ban iteration
    >>> check(HW_SOURCE_FILE, 'count_coins', ['While', 'For'])
    True
    """
    "*** YOUR CODE HERE ***"

    def helper(coin, cur):
        if coin == None or cur + coin > total:
            return 0

        if cur + coin == total:
            return 1

        return helper(coin, cur + coin) + helper(next_largest_coin(coin), cur)

    return helper(1, 0)


from operator import sub, mul


def make_anonymous_factorial():
    """Return the value of an expression that computes factorial.

    >>> make_anonymous_factorial()(5)
    120
    >>> from construct_check import check
    >>> # ban any assignments or recursion
    >>> check(HW_SOURCE_FILE, 'make_anonymous_factorial', ['Assign', 'AugAssign', 'FunctionDef', 'Recursion'])
    True
    """
    return (lambda func: lambda n: func(func, n))(
        lambda a, n: mul(n, a(a, sub(n, 1))) if n > 1 else 1
    )