Fall 2020 Berkeley cs61a hw02答案
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 x == 8:
return 1
elif x != 8 and x < 10:
return 0
return num_eights(x//10) + 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 ***"
def helper(index, ppn, dir):
if n == 1:
return 1
elif index != n:
if num_eights(index) > 0 or index % 8 == 0:
return helper(index+1, ppn-dir, -dir)
else:
return helper(index+1, ppn+dir, dir)
else:
return ppn
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
elif n % 10 - n // 10 % 10 - 1 == -1:
return missing_digits(n // 10)
else:
return n % 10 - n // 10 % 10 - 1 + 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 max_num(x):
if x <= 1:
return 0
else:
i = x
while not next_largest_coin(i):
i = i - 1
if next_largest_coin(i) > x:
return i
if next_largest_coin(i) <= x:
return next_largest_coin(i)
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 using_num(m , n):
if m == 1 or m == 0:
return 1
elif m < 0:
return 0
elif n <= 0:
return 0
elif n == 1:
return 1
else:
with_max = using_num(m - max_num(n), max_num(n))
without_max = using_num(m, max_num(n-1))
return without_max + with_max
return using_num(total, max_num(total))
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 'YOUR_EXPRESSION_HERE'
