CS61A FALL2020 Homework1

Summary

• 函数调用
• 非纯函数
• //运算符，结果为整数

Q2: A Plus Abs B

from operator import add, sub

def a_plus_abs_b(a, b):
    """Return a+abs(b), but without calling abs.

    >>> a_plus_abs_b(2, 3)
    5
    >>> a_plus_abs_b(2, -3)
    5
    >>> # a check that you didn't change the return statement!
    >>> import inspect, re
    >>> re.findall(r'^\s*(return .*)', inspect.getsource(a_plus_abs_b), re.M)
    ['return f(a, b)']
    """
    if b < 0:
        f = sub
    else:
        f = add
    return f(a, b)

• return表明f为一个函数

Q3: Two of Three

def two_of_three(x, y, z):
    """Return a*a + b*b, where a and b are the two smallest members of the
    positive numbers x, y, and z.

    >>> two_of_three(1, 2, 3)
    5
    >>> two_of_three(5, 3, 1)
    10
    >>> two_of_three(10, 2, 8)
    68
    >>> two_of_three(5, 5, 5)
    50
    >>> # check that your code consists of nothing but an expression (this docstring)
    >>> # a return statement
    >>> import inspect, ast
    >>> [type(x).__name__ for x in ast.parse(inspect.getsource(two_of_three)).body[0].body]
    ['Expr', 'Return']
    """
    return x**2+y**2+z**2-max(x,y,z)**2

Q4: Largest Factor
我的解答：

def largest_factor(n):
    """Return the largest factor of n that is smaller than n.

    >>> largest_factor(15) # factors are 1, 3, 5
    5
    >>> largest_factor(80) # factors are 1, 2, 4, 5, 8, 10, 16, 20, 40
    40
    >>> largest_factor(13) # factor is 1 since 13 is prime
    1
    """
    list = []
    k=1
    while k<n:
      if n%k == 0:
        list.append(k)
      k += 1
    return list[-1]

参考作业提示视频后：

    k = n-1  #要找到比n小的最大除数→从n-1开始
    while n%k != 0:
      k -= 1       #对于每个比n小的数，看是否能被整除
    return k

改进

    half_n = n // 2
    largestfactor = half_n
    while n % largestfactor != 0:
        largestfactor = largestfactor -1
    return largestfactor

参考答案

    factor = n - 1
    while factor > 0:
        if n % factor == 0:
            return factor
        factor -= 1

Q5：If Function vs Statement

def if_function(condition, true_result, false_result):
    """Return true_result if condition is a true value, and
    false_result otherwise.

    >>> if_function(True, 2, 3)
    2
    >>> if_function(False, 2, 3)
    3
    >>> if_function(3==2, 3+2, 3-2)
    1
    >>> if_function(3>2, 3+2, 3-2)
    5
    """
    if condition:
        return true_result
    else:
        return false_result


def with_if_statement():
    """
    >>> result = with_if_statement()
    47
    >>> print(result)
    None
    """
    if cond():    # 调用cond()函数
        return true_func()     #如果条件为真，则只会调用true_func()，false_func()将永远不会被调用
    else:
        return false_func()    #如果条件为假，则只会调用false_func()，true_func()将永远不会被调用

def with_if_function():
    """
    >>> result = with_if_function()
    42
    47
    >>> print(result)
    None
    """
    return if_function(cond(), true_func(), false_func()) #将cond()函数、true_func()函数、false_func()函数的结果传递给if_function()，所有三个函数被调用，它们的结果被返回到一个函数，作为if_function的参数

def cond():
    return False

def true_func():
    print(42)

def false_func():
    print(47)

• 理解with_if_statement()和with_if_function()的中的调用函数区别，在代码中进行了注释。
• 考虑非纯函数的副作用（side effect），导致with_if_statement()和with_if_function()的结果不同且print(result)为None

Q6: Hailstone

def hailstone(n):
    """Print the hailstone sequence starting at n and return its
    length.

    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1
    >>> a
    7
    """
    k = 1
    while n != 1:
      print(n)
      if n%2 == 0:
        n = n//2
      else:
        n = n*3+1
      k += 1
    print(n)
    return k

• 注意到

    >>> a = hailstone(10)
    10
    5
    16
    8
    4
    2
    1

• hailstone()非纯函数，a = hailstone(10)调用了hailstone()函数，显示的是hailstone()函数调用这一过程，调用完后其返回的值储存在a中。
• 注意使用//去掉小数