Discussion 1: Control, Environment Diagrams

This is an online worksheet that you can work on during discussions. Your work is not graded and you do not need to submit anything.

Control structures

Control structures direct the flow of a program using logical statements. For example, conditionals (if-elif-else) allow a program to skip sections of code, and iteration (while), allows a program to repeat a section.

Conditional statements

Conditional statements let programs execute different lines of code depending on certain conditions. Let’s review the if-elif-else syntax:

  • The elif and else clauses are optional, and you can have any number of elif clauses.
  • A conditional expression is an expression that evaluates to either a truthy value (True, a non-zero integer, etc.) or a falsy value (False, 0, None, "", [], etc.).
  • Only the first if/elif expression that evaluates to a truthy value will have its corresponding indented suite be executed.
  • If none of the conditional expressions evaluate to a true value, then the else suite is executed. There can only be one else clause in a conditional statement.

Here's the general form:

if <conditional expression>:
    <suite of statements>
elif <conditional expression>:
    <suite of statements>
    <suite of statements>

Boolean Operators

Python also includes the boolean operators and, or, and not. These operators are used to combine and manipulate boolean values.

  • not returns the opposite boolean value of the following expression, and will always return either True or False.
  • and evaluates expressions in order and stops evaluating (short-circuits) once it reaches the first falsy value, and then returns it. If all values evaluate to a truthy value, the last value is returned.
  • or evalutes expressions in order and short-circuits at the first truthy value and returns it. If all values evaluate to a falsy value, the last value is returned.

For example:

>>> not None
>>> not True
>>> -1 and 0 and 1
>>> False or 9999 or 1/0

Q1: Case Conundrum

In this question, we will explore the difference between if and elif.

What is the result of evaluating the following code?

def special_case():
    x = 10
    if x > 0:
        x += 2
    elif x < 13:
        x += 3
    elif x % 2 == 1:
        x += 4
    return x


What is the result of evaluating this piece of code?

def just_in_case():
    x = 10
    if x > 0:
        x += 2
    if x < 13:
        x += 3
    if x % 2 == 1:
        x += 4
    return x

How about this piece of code?
def case_in_point():
    x = 10
    if x > 0:
        return x + 2
    if x < 13:
        return x + 3
    if x % 2 == 1:
        return x + 4
    return x


Which of these code snippets result in the same output, and why? Based on your findings, when do you think using a series of if statements has the same effect as using both if and elif cases?

Q2: Jacket Weather?

Alfonso will only wear a jacket outside if it is below 60 degrees or it is raining.

Write a function that takes in the current temperature and a boolean value telling if it is raining. This function should return True if Alfonso will wear a jacket and False otherwise.

Try solving this problem using an if statement.

Note: Since we'll either return True or False based on a single condition, whose truthiness value will also be either True or False. Knowing this, try to write this function using a single line.

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While loops

To repeat the same statements multiple times in a program, we can use iteration. In Python, one way we can do this is with a while loop.

while <conditional clause>:
    <statements body>

As long as <conditional clause> evaluates to a true value, <statements body> will continue to be executed. The conditional clause gets evaluated each time the body finishes executing.

Q3: Square So Slow

What is the result of evaluating the following code?

def square(x):
    return x * x

def so_slow(num):
    x = num
    while x > 0:
        x = x + 1
    return x / 0


Hint: What happens to x over time?

Q4: Is Prime?

Write a function that returns True if a positive integer n is a prime number and False otherwise.

A prime number n is a number that is not divisible by any numbers other than 1 and n itself. For example, 13 is prime, since it is only divisible by 1 and 13, but 14 is not, since it is divisible by 1, 2, 7, and 14.

Hint: Use the % operator: x % y returns the remainder of x when divided by y.

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Q5: Fizzbuzz

Implement the fizzbuzz sequence, which prints out a single statement for each number from 1 to n. For a number i,

  • If i is divisible by both 3 and 5, then we print "fizzbuzz".
  • If i is divisible by 3 only, then we print "fizz".
  • If i is divisible by 5 only, then we print "buzz".
  • Otherwise, we print the number i by itself.

Implement fizzbuzz(n) here:

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Q6: Unique Digits

Write a function that returns the number of unique digits in a positive integer.

Hints: You can use // and % to separate a positive integer into its one's digit and the rest of its digits.

You may find it helpful to first define a function has_digit(n, k), which determines whether a number n has digit k.

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Environment Diagrams

An environment diagram is a model we use to keep track of all the variables that have been defined and the values they are bound to. We will be using this tool throughout the course to understand complex programs involving several different assignments and function calls.

One key idea in environment diagrams is the frame. A frame helps us keep track of what variables have been defined in the current execution environment, and what values they hold. The frame we start off with when executing a program from scratch is what we call the Global frame. Later, we'll get into how new frames are created and how they may depend on their parent frame.

Here's a short program and its corresponding diagram (only visible on the online version of this worksheet):

Remember that programs are mainly just a set of statements or instructions— so drawing diagrams that represent these programs also involves following sets of instructions! Let’s dive in...

Assignment Statements

Assignment statements, such as x = 3, define variables in programs. To execute one in an environment diagram, record the variable name and the value:

  1. Evaluate the expression on the right side of the = sign.
  2. Write the variable name and the expression’s value in the current frame.

Q7: Assignment Diagram

Use these rules to draw an environment diagram for the assignment statements below:

x = 11 % 4
y = x
x **= 2
Global frame

def Statements

A def statement creates ("defines") a function object and binds it to a name. To diagram def statements, record the function name and bind the function object to the name. It’s also important to write the parent frame of the function, which is where the function is defined.

A very important note: Assignments for def statements use pointers to functions, which can have different behavior than primitive assignments (such as variables bound to numbers).

  1. Draw the function object to the right-hand-side of the frames, denoting the intrinsic name of the function, its parameters, and the parent frame (e.g. func square(x) [parent = Global].
  2. Write the function name in the current frame and draw an arrow from the name to the function object.

Q8: def Diagram

Use these rules for defining functions and the rules for assignment statements to draw a diagram for the code below.

def double(x):
    return x * 2

def triple(x):
    return x * 3

hat = double
double = triple
Global frame