homework01

CS61A homeWord 答案：

Question 1

Fill in the blanks in the following function definition for adding a to the absolute value of b, without calling abs.

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
"""
　　if b < 0:
　　　　f = sub
　　else:
　　　　f = add
　　return f(a, b)

Question 2

Write a function that takes three positive numbers and returns the sum of the squares of the two largest numbers. Use only a single line for the body of the function.

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

>>> two_of_three(1, 2, 3)
13
>>> two_of_three(5, 3, 1)
34
>>> two_of_three(10, 2, 8)
164
>>> two_of_three(5, 5, 5)
50
"""
　　return a * a + b * b + c * c - min(a, b, c) * min(a, b, c)

Question 3

Write a function that takes an integer n that is greater than 1 and returns the largest integer that is smaller than n and evenly divides n.

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
"""
"*** YOUR CODE HERE ***"
　　for i in range(1, n):
　　　　if n % i == 0:
　　　　　　maxFactor = i
　　return maxFactor

 

Question 4

Let's write a function that does the same thing as an if 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():
"""
>>> with_if_statement()
1
"""
if c():
　　return t()
else:
　　return f()

def with_if_function():
　　return if_function(c(), t(), f())

def c():
"*** YOUR CODE HERE ***"
　　return True

def t():
"*** YOUR CODE HERE ***"
　　return 1

def f():
"*** YOUR CODE HERE ***"
　　return 1

 

Question 5

Douglas Hofstadter's Pulitzer-prize-winning book, Gödel, Escher, Bach, poses the following mathematical puzzle.

1. Pick a positive integer n as the start.
2. If n is even, divide it by 2.
3. If n is odd, multiply it by 3 and add 1.
4. Continue this process until n is 1.

The number n will travel up and down but eventually end at 1 (at least for all numbers that have ever been tried -- nobody has ever proved that the sequence will terminate). Analogously, a hailstone travels up and down in the atmosphere before eventually landing on earth.

This sequence of values of n is often called a Hailstone sequence, Write a function that takes a single argument with formal parameter name n, prints out the hailstone sequence starting at n, and returns the number of steps in the sequence:

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
"""
"*** YOUR CODE HERE ***"
　　count = 1
　　while n != 1:
　　if n % 2 == 0:
　　　　print(n)
　　　　n = n // 2
　　　　count += 1
　　else:
　　　　print(n)
　　　　n = n * 3 + 1
　　　　count += 1
　　　　print(n)
　　return count