1. Instructions

In this lab, you have two tasks:

• Think about what python would display if the code described in section 3 were input to a python interpreter. You don't have to submit your answers. See section 3 for more details.
• Complete the required problems described in section 4 and submit your code with Ok, as instructed in lab00. The starter code for these problems is provided in lab01.py, which is distributed as part of the homework materials.

Submission: As instructed above, you need to submit your work with Ok by python ok --submit. You may submit more than once before the deadline, and your score of this assignment will be the highest one of all your submissions.

Readings: You might find the following references to the textbook useful:

• Section 1.2
• Section 1.3
• Section 1.4
• Section 1.5

2. Review

Consult this section if you need a refresher on the material for this lab. It's okay to skip directly to the next section and refer back here should you get stuck.

2.1 Functions

If we want to execute a series of statements over and over, we can abstract them away into a function to avoid repeating code.

For example, let's say we want to know the results of multiplying the numbers 1-3 by 3 and then adding 2 to it. Here's one way to do it:

>>> 1 * 3 + 2
5
>>> 2 * 3 + 2
8
>>> 3 * 3 + 2
11

If we wanted to do this with a larger set of numbers, that'd be a lot of repeated code! Let's write a function to capture this operation given any input number.

def foo(x):
    return x * 3 + 2

This function, called foo, takes in a single argument and will return the result of multiplying that argument by 3 and adding 2.

Now we can call this function whenever we want this operation to be done:

>>> foo(1)
5
>>> foo(2)
8
>>> foo(1000)
3002

Applying a function to some arguments is done with a call expression.

2.1.1 Call expressions

A call expression applies a function, which may or may not accept arguments. The call expression evaluates to the function's return value.

The syntax of a function call:

  add   (    2   ,    3   )
   |         |        |
operator  operand  operand

Every call expression requires a set of parentheses delimiting its comma-separated operands.

To evaluate a function call:

1. Evaluate the operator, and then the operands (from left to right).
2. Apply the operator to the operands (the values of the operands).

If an operand is a nested call expression, then these two steps are applied to that inner operand first in order to evaluate the outer operand.

2.1.2 return and print

Most functions that you define will contain a return statement. The return statement will give the result of some computation back to the caller of the function and exit the function. For example, the function square below takes in a number x and returns its square.

def square(x):
    """
    >>> square(4)
    16
    """
    return x * x

When Python executes a return statement, the function terminates immediately. If Python reaches the end of the function body without executing a return statement, it will automatically return None.

In contrast, the print function is used to display values in the Terminal. This can lead to some confusion between print and return because calling a function in the Python interpreter will print out the function's return value.

However, unlike a return statement, when Python evaluates a print expression, the function does not terminate immediately.

def what_prints():
    print('Hello World!')
    return 'Exiting this function.'
    print('61A is awesome!')

>>> what_prints()
Hello World!
'Exiting this function.'

Notice also that print will display text without the quotes, but return will preserve the quotes.

2.2 Control

2.2.1 Boolean Operators

Python supports three boolean operators: and, or, and not:

>>> a = 4
>>> a < 2 and a > 0
False
>>> a < 2 or a > 0
True
>>> not (a > 0)
False

• and evaluates to True only if both operands evaluate to True. If at least one operand is False, then and evaluates to False.
• or evaluates to True if at least one operand evaluates to True. If both operands are False, then or evaluates to False.
• not evaluates to True if its operand evaluates to False. It evaluates to False if its operand evaluates to True.

What do you think the following expression evaluates to? Try it out in the Python interpreter.

>>> True and not False or not True and False

It is difficult to read complex expressions, like the one above, and understand how a program will behave. Using parentheses can make your code easier to understand. Python interprets that expression in the following way:

>>> (True and (not False)) or ((not True) and False)

This is because boolean operators, like arithmetic operators, have an order of operation:

• not has the highest priority
• and
• or has the lowest priority

Truthy and Falsey Values: It turns out and and or work on more than just booleans (True, False). Python values such as 0, None, '' (the empty string), and [] (the empty list) are considered false values. All other values are considered true values.

2.2.2 Short Circuiting

What do you think will happen if we type the following into Python?

1 / 0

Try it out in Python! You should see a ZeroDivisionError. But what about this expression?

True or 1 / 0

It evaluates to True because Python's and and or operators short-circuit. That is, they don't necessarily evaluate every operand.

Short-circuiting happens when the operator reaches an operand that allows them to make a conclusion about the expression. For example, and will short-circuit as soon as it reaches the first false value because it then knows that not all the values are true.

If and and or do not short-circuit, they just return the last value; another way to remember this is that and and or always return the last thing they evaluate, whether they short circuit or not. Keep in mind that and and or don't always return booleans when using values other than True and False.

2.2.3 If Statements

You can review the syntax of if statements in Section 1.5.4 of Composing Programs.

Tip: We sometimes see code that looks like this:

if x > 3:
    return True
else:
    return False

This can be written more concisely as return x > 3. If your code looks like the code above, see if you can rewrite it more clearly!

2.2.4 While Loops

You can review the syntax of while loops in Section 1.5.5 of Composing Programs.

2.3 Error Messages

By now, you've probably seen a couple of error messages. They might look intimidating, but error messages are very helpful for debugging code. The following are some common types of errors:

Using these descriptions of error messages, you should be able to get a better idea of what went wrong with your code. If you run into error messages, try to identify the problem before asking for help. You can often Google unfamiliar error messages to see if others have made similar mistakes to help you debug.

For example:

>>> square(3, 3)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: square() takes 1 positional argument but 2 were given

Note:

• The last line of an error message tells us the type of the error. In the example above, we have a TypeError.
• The error message tells us what we did wrong -- we gave square 2 arguments when it can only take in 1 argument. In general, the last line is the most helpful.
• The second to last line of the error message tells us on which line the error occurred. This helps us track down the error. In the example above, TypeError occurred at line 1.

3. What Would Python Display?

In this section, you need to think about what python would display if the code below were input to a python interpreter.

You don't have to submit your answers, which means the questions in this section don't count for your final score. However, they are great practice for future assignments, projects, and exams. Attempting these questions is valuable in helping cement your knowledge of course concepts.

To check the correctness of your answer, you can start a python interpreter, input the code into it, and compare the output displayed in the terminal with yours. Note that, it is possible for the interpreter to output nothing or raise an error.

Question 1: Control

>>> def xk(c, d):
...     if c == 4:
...         return 6
...     elif d >= 4:
...         return 6 + 7 + c
...     else:
...         return 25
>>> xk(10, 10)
______

>>> xk(10, 6)
______

>>> xk(4, 6)
______

>>> xk(0, 0)
______

>>> def how_big(x):
...     if x > 10:
...         print('huge')
...     elif x > 5:
...         return 'big'
...     elif x > 0:
...         print('small')
...     else:
...         print("nothin'")
>>> how_big(7)
______

>>> how_big(12)
______

>>> how_big(1)
______

>>> how_big(-1)
______

>>> n = 3
>>> while n >= 0:
...     n -= 1
...     print(n)
______

Hint: Make sure your while loop conditions eventually evaluate to a false value, or they'll never stop! Type Ctrl-C will stop infinite loops in the interpreter.

>>> positive = 28
>>> while positive:
...     print("positive?")
...     positive -= 3
______

>>> positive = -9
>>> negative = -12
>>> while negative:
...     if positive:
...         print(negative)
...     positive += 3
...     negative += 3
______

Question 2: Veritasiness

>>> True and 13
______

>>> False or 0
______

>>> not 10
______

>>> not None
______

>>> True and 1 / 0 and False
______

>>> True or 1 / 0 or False
______

>>> True and 0
______

>>> False or 1
______

>>> 1 and 3 and 6 and 10 and 15
______

>>> 0 or False or 2 or 1 / 0
______

>>> not 0
______

>>> (1 + 1) and 1
______

>>> 1/0 or True
______

>>> (True or False) and False
______

Question 3: What If?

>>> def ab(c, d):
...     if c > 5:
...         print(c)
...     elif c > 7:
...         print(d)
...     print('foo')
>>> ab(10, 20)
______

>>> def bake(cake, make):
...     if cake == 0:
...         cake = cake + 1
...         print(cake)
...     if cake == 1:
...         print(make)
...     else:
...         return cake
...     return make
>>> bake(0, 29)
______

>>> bake(1, "mashed potatoes")
______

4. Required Problems

In this section, you are required to complete the problems below and submit your code with Ok to get your answer scored.

Remember, you can use Ok to test your code:

$ python ok

and submit your work when you are done:

$ python ok --submit

Problem 1: Fix the Bug (100pts)

The following snippet of code doesn't work! Figure out what is wrong and fix the bugs.

def both_odd(a, b):
    """Returns True if both a and b are odd numbers.

    >>> both_odd(-1, 1)
    True
    >>> both_odd(2, 1)
    False
    """
    return a and b % 2 == 1 # You can replace this line!

Test your implementation with python ok -q both_odd.

Problem 2: Factorial (100pts)

Write a function that takes a positive integer \( n \) and returns its factorial.

Factorial of a positive integer \( n \) is defined as

\[ n! = \prod_{i=1}^n i = 1 \times 2 \times 3 \times \dots \times n. \]

def factorial(n):
    """Return the factorial of a positive integer n.

    >>> factorial(3)
    6
    >>> factorial(5)
    120
    """
    pass  # YOUR CODE HERE

pass的作用：正如冯老师在课上所说，pass是一条“空指令”，表示什么都不做。

通常，当我们定义一个函数，但没有想好函数怎么实现的时候，我们就会填入一个pass来保持程序结构的正确性。大家在完成lab和后续作业的时候，应该先把这一行pass语句删除，然后再编写自己的代码，请不要在提交的代码中包含pass。

Test your implementation with python ok -q factorial.

Problem 3: Is Triangle? (100pts)

Write a function that takes three integers (may be nonpositive) and returns True if the three integers can form the three sides of a triangle, otherwise returns False.

def is_triangle(a, b, c):
    """Given three integers (may be nonpositive), judge whether the three
    integers can form the three sides of a triangle.

    >>> is_triangle(2, 1, 3)
    False
    >>> is_triangle(5, -3, 4)
    False
    >>> is_triangle(2, 2, 2)
    True
    """
    pass  # YOUR CODE HERE

Test your implementation with python ok -q is_triangle.

Problem 4: Number of Six (100pts)

Write a function that takes a positive integer \( n \) and returns the number of \( 6 \) in each digit of it. (Using floor division and modulo might be helpful here!)

def number_of_six(n):
    """Return the number of 6 in each digit of a positive integer n.

    >>> number_of_six(666)
    3
    >>> number_of_six(123456)
    1
    """
    pass  # YOUR CODE HERE

Test your implementation with python ok -q number_of_six.

Problem 5: Max Digit (100pts)

Write a function that takes in a non-negative integer and return its max digit. (Using floor division and modulo might be helpful here!)

def max_digit(x):
    """Return the max digit of x.

    >>> max_digit(10)
    1
    >>> max_digit(4224)
    4
    >>> max_digit(1234567890)
    9
    >>> # make sure that you are using return rather than print
    >>> a = max_digit(123)
    >>> a
    3
    """
    pass  # YOUR CODE HERE

Test your implementation with python ok -q max_digit.

Test your code for lab01 with python ok, and submit with python ok --submit.

If you want to submit manually, you can upload lab01.py to OJ website.