Python Functions for Counting Eights and Coin Change

HW_SOURCE_FILE = __file__ def num_eights(pos): """Returns the number of times 8 appears as a digit of pos. >>> 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', 'AnnAssign', 'AugAssign', 'NamedExpr']) True """ if pos == 0: return 0 if pos%10 == 8: return num_eights(pos//10) + 1 else: return num_eights(pos//10) + 0 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', 'AnnAssign', 'AugAssign', 'NamedExpr']) True """ def wrapper(pingpong_val, direction, k, n): if k == n: return pingpong_val if k > 0: if num_eights(k) or k%8==0: return wrapper(pingpong_val - direction, -direction, k+1, n) return wrapper(pingpong_val + direction, direction, k+1, n) return wrapper(0, 1, 0, n) def get_larger_coin(coin): """Returns the next larger coin in order. >>> get_larger_coin(1) 5 >>> get_larger_coin(5) 10 >>> get_larger_coin(10) 25 >>> get_larger_coin(2) # Other values return None """ if coin == 1: return 5 elif coin == 5: return 10 elif coin == 10: return 25 def get_smaller_coin(coin): """Returns the next smaller coin in order. >>> get_smaller_coin(25) 10 >>> get_smaller_coin(10) 5 >>> get_smaller_coin(5) 1 >>> get_smaller_coin(2) # Other values return None """ if coin == 25: return 10 elif coin == 10: return 5 elif coin == 5: return 1 def count_coins(change): """Return the number of ways to make change 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 >>> count_coins(200) 1463 >>> from construct_check import check >>> # ban iteration >>> check(HW_SOURCE_FILE, 'count_coins', ['While', 'For']) True """ def start_small(change, coin): if change == coin or change == 0: return 1 elif change < 0 or coin > change: return 0 if coin == 25: return start_small(change - coin, coin) else: return start_small(change-coin, coin) + start_small(change, get_larger_coin(coin)) return start_small(change, 1) def start_big(change, coin): if change < 0 or coin == None: return 0 elif change == 0: return 1 if coin == 1: return start_big(change - coin, coin) else: return start_big(change-coin, coin) + start_big(change, get_smaller_coin(coin)) return start_big(change, 25)

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