Computer Science Notes

COMS 261 - Fall 2026

Week 1 Notes

Mon, Aug 24

Today we introduced Python and the Thonny IDE (Integrated Development Environment).

We learned how to use the Python Shell and how to write Python scripts. We also covered the following:

• Operators (like +, -, *, /, **)
• Types (like int, float, and str)
• Variables
• Comments

1. Try out each of the operations +, -, *, /, ** in the shell.

2. Why doesn’t the following command calculate $\sqrt{5}$? How could you fix it?

   5 ** 1 / 2

We talked about how operators follow an order of operations, and if operators have the same level of precedence, then they are computed left to right. We also talked about how some operators don’t work for all types. For example, the + operator concatenates strings, but the * operator is not defined for strings.

3. Write a script to calculate the volume of a sphere.

    # A script to calculate the volume of a sphere.
   
    PI = 3.14159 
    radius = 4
    volume = 4 / 3 * PI * radius ** 3
    print("The volume of the sphere is:", volume)

Additional practice

1. Which of the following Python commands work? Try them in the shell to find out.

   • n = 4
   • 4 = n
   • x = y = 1

2. Write a program which uses two variables miles and gals and prints out the miles per gallon for a car on a tank of gas. Your output should look something like

   You got 37.5 miles per gallon.

   (depending on the values of your variables).

Wed, Aug 26

Variable Name Rules

• Variable names can only contain numbers, letters, and the underscore character _.
• A variable name cannot start with a number.
• You cannot use any of the 35 special Python keywords as a variable name.

It is recommended to only use lower case letters only in most variable names (except when you want to indicate that the variable is constant and won’t ever change, in which case ALL_CAPS is recommended). If a variable name has multiple words, then separate the words with an underscore character, like: surface_area.

Functions

We talked about the following built-in functions.

• print
• int, float, str (type conversion functions)
• type
• abs, round
• help

1. How many spaces can you put between a function and its arugment(s)? How many should you have?

We finished by talking about how to import functions from modules. We imported the math module which contains familiar math functions like sin(), cos(), and sqrt(). You can use the command dir(math) to list all of functions in the math module.

2. Write a program to calculate the roots of a quadratic polynomial $a x^2 + bx + c$ using the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$$

Additional practice

1. Write a program to calculate miles per gallon and print the output rounded to 1 decimal place.

2. How could you tell if the sine and cosine function expect the input in degrees or radians? Test your idea in the shell and see what the default is.

3. What happens if you type math.sin without an input?

4. What happens if you enter help(math.sin)?

5. What does the degrees() function do?

6. How could you calculate $\sqrt{\pi}$ (i.e., the square root of pi) using the math library?

Thu, Aug 27

Today we talked about some of the isses that came up in the quadratic formula programs from yesterday.

Statements versus Expressions

The first error we looked at was this incorrect line of code:

(x1 = (-b + math.sqrt(b ** 2 - 4 * a * c)) / (2 * a))

To explain this error, we talked about the difference between statements and expressions in Python.

• A statement is a piece of code that executes a command.
  
• An expression is a piece of code that has a value.

Every expression is a statement, but not vice versa. In Python, every valid line of code is a statement.

# Example statements
import math
a = 5.0
b = 3 + a
print("Hello")

# Example expressions
1+1
5.0
(-b + math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)

Notice that statements can include expressions. A special kind of statement is an assignment statement where you assign a value to a variable. Every assignment statement has the form:

variable_name = # some expression

You can always wrap an expression in parentheses, and it will still be an expression with the same value. But, the reason the line of code (x1 = (-b + math.sqrt(b ** 2 - 4 * a * c)) / (2 * a)) is not correct is that an assignment statement is not an expression, and cannot be wrapped in parentheses.

Breaking Up Code

It is a good idea to break code into small reusable pieces. We compared some different implementations of the quadratic formula from last time to see how we could make the code easier to read, and also easier to fix if something goes wrong.

Conditional Statements (If-Then-Else Statements)

We finished by introducing if-then-else statements in Python. We ran into the problem that our quadratic formula program sometimes gives and error message if you try to take the square root of a negative number. To fix this, we added an if-then statement to check that the number inside the square root is not negative before trying to calculate the two roots.

import math

a = 1
b = 2 
c = 3

if (b**2 - 4*a*c >= 0):
    x1 = (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)
    x2 = (-b - math.sqrt(b**2 - 4*a*c)) / (2*a)
    print("The roots are", x1, "and", x2)
else:
    print("There are no roots.")

We finished with this challenge problem:

1. Write a program that uses if-then-else statements to print the largest of three numbers, $a$, $b$, and $c$. You can assume that all three numbers are different (no repeat values).

Fri, Aug 28

Algorithms and Flow Charts

Yesterday, we used a lot of different approaches to find the maximum of three distinct numbers. As we saw, it can get challenging to keep track of the logic. Engineers often use a flow chart to keep track of the steps in an algorithm.

Here is one possible flow chart for an algorithm to find the largest of three numbers:

Binary Numbers

Computers store numbers & data in binary. We talked about how to write whole numbers in base-2.

1. Convert $(110)_2$ to base-10.

2. Convert $(10101)_2$ to base-10.

3. Convert $(0.1)_2$ to base-10.

4. Convert $(10.11)_2$ to base-10.

After that we talked about how to convert base-10 integers to base-2. That is a little bit harder, so we introduced the algorithm below which can be described using a flow chart:

5. Use the algorithm above to convert 13 to base-2.

After we introduced binary numbers, we talked about bits and how many integers can be stored using $n$ bits.

6. How many 4-bit numbers are there?

The maximum number of rupees (money) you could have in the original Zelda game was 255 because the data was stored using 8 bits.

Unlike a lot of programming languages, Python allows arbitrarily large integers. This avoids integer overflow errors, but it can be slower for large integers.

Floating Point Numbers

We also talked about how computers store floating point numbers. Most modern programming languages (including Python) store floating point numbers using the IEEE 754 standard.

Because there are only a limited number of bits to store floating point numbers, there is a limit to how large and how accurate they can get.

• Limited accuracy. Only accurate to about 15 decimal places (in scientific notation).
• Limited size. Maximum 64-bit float is $\approx 10^{308}$.

7. Compare the output you get when you type 2**1024 versus 2.0**1024 in the Python shell.

8. Compare the output for 2.0**(-1024) versus 2**(-1070). Notice that you lose precision with small floating point numbers, but you don’t get an error the way you do with large floats.

9. Why do you get an incorrect answer when you enter 0.1+0.1+0.1?

We finished with this workshop:

• Workshop: Binary numbers

Week 2 Notes

Mon, Aug 31

Defining Functions

To create your own functions in Python, use the def keyword to define them:

def hello():
    print("Hello!")

Every function is a function object. So function is a type just like int, float, and str. When you refer to a function object in Python, there is a difference between the name of the function (which is hello in the previous example) and the way you call the function to get it to run by typing hello(). Here is another function example.

def print_twice(string): # The first line is called the **header**
    print(string) # All of the other lines are called the **body of the function**
    print(string) # The code in the body must be indented

# Code that is not indented is not part of the function.  
print_twice("Hello!")

This function has a parameter which is the variable called string in the parentheses. We you call this function, you need to include an argument which is a value for the parameter.

>>> print_twice("Hello")
Hello
Hello
>>> print_twice(5)
5
5

In this example, “Hello” and 5 are arguments. The variable called string in the function is a parameter. Weirdly, when we pass the argument 5 to the function, then the parameter called string stores the value 5 which is an integer not a string! But that is okay, because Python knows how to print integers.

When you create a function, you should always include a docstring that briefly explains what the functions does. A docstring is a comment that is written using triple quotes instead of the hash symbol. Here is an example.

def hypot(a, b):
    """Calculates the hypoteneuse of a right triangle with legs a and b."""
    c = math.sqrt(a ** 2 + b ** 2)
    print(c)

The advantage of a docstring over a regular comment is that it can take up multiple lines. Python style guides recommend using docstrings even for one line descriptions of functions, since you might need to add more explanation later.

Functions can have as many parameters as needed. Try to make your own functions to do the following.

1. Calculate the area of a circle based on its radius.

Return Values

Some functions return values and some functions don’t. For example, math.sqrt(4) returns the value 2.0, so it can be used as an expression. But the function print("Hello") does not return a value.

2. What are the values of the variables x and y below?

   x = print(4)
   y = abs(-5)

To create a function that returns a value, use the return keyword.

3. Change the circle_area function to return the area of a circle instead of printing the area.

Additional Practice

1. Write a multiply_by_2 function that returns twice its input.

Wed, Sep 2

Today we talked some more about functions. We introduced local variables and global variables. Compare these two programs.

def circle_area(radius):
    PI = 3.14
    area = PI * radius ** 2
    return area

radius = 5
PI = 3.14 
area = PI * radius ** 2    

Any variable created in a function body is local, which means it can only be used inside the function. You won’t have access to local variables outside the function. Variables defined in a program that aren’t parameters or defined in the body of a function are global and can be accessed anywhere in a program. But if you try to change the value of a global variable inside of a function, it creates a new local variable inside the function instead!

Important: Avoid using global variables, except for constants.

Here is a function that calls another function in its body:

def cylinder_volume(radius, height):
    """Returns the volume of a cylinder."""
    return circle_area(radius) * height

1. Write a Python program with the following functions:
   • A function called sales_tax that returns the sales tax (5.3% in Virginia) for an item.
     
   • A function called print_receipt that prints three things: The base price of the item, the sales tax, and the total price.
   Both functions should input the price of an item.

We finished by introducing recursive functions which are functions that call themselves. In order to make a recursive function that doesn’t get stuck looping forever, you need to use an if-then statement with an escape condition. For example:

def countdown(n):
    """Print the numbers from n down to 1."""
    if n > 0:
        print(n)
        countdown(n - 1)

2. What happens if you call countdown with a negative number as the argument? Why does that happen?

3. What happens if you call countdown with a large value like 1000?

Additional Practice

1. Write a recursive function to make triangles of different sizes like this:

   **        ***        ****         *****
   *         **         ***          ****
             *          **           ***
                        *            ** 
                                     *

Thu, Sep 3

Today we introduced for-loops. We started with two example functions to demonstrate how they work.

def box(n):
    """Prints an n-by-n square made of * symbols."""
    for i in range(n):
        print("*" * i)

def countup(n):
    """Print the first n positive numbers."""
    for i in range(1,n+1):
        print(i)

These examples use the range function. (Try asking ChatGPT or Claude to explain the Python range function).

Python is zero-indexed which means that by default it starts counting at zero.

1. Write a function to print the positive odd numbers below n. 

2. Write a function to print the first n perfect squares (i.e., 1, 4, 9, 16, etc.)

3. Write a function to print a triangle with n rows like this:

    *
    **
    ***
    ****

We finished by talking about accumulator variables in loops. I showed this example.

def add_odd_numbers(n):
    """Returns the sum of the odd numbers less than n."""
    total = 0 # total is an accumulator variable
    for odd in range(1, n, 2):
        total = total + odd
    return total

Additional Practice

1. Write a function to print an upside down triangle with n rows:

    ****
    ***
    **
    *

2. Write a function to print a hollow n-by-n square, like this example when n is 4:

    ****
    *  *
    *  *
    ****

3. Write a function that uses a for-loop with an accumulator variable to multiply the numbers 1, 2, …, n. In other words, write a function to compute the factorial of n. 

4. Write a function called sum_of_squares that adds up all of first n positive perfect squares.

Fri, Sep 4

Today we played with turtle graphics using the turtle module in Python.

1. Use the commands forward(100) and left(90) to draw a rectangle.

2. Write a function to draw a rectangle of any length and width.

3. Write a function to draw an equilateral triangle.

Here is an example using a for-loop to make a polygon with any number of sides.

from turtle import *

def polygon(side_length, n):
    """Draw a polygon with n sides."""
    for i in range(n):
        forward(side_length)
        left(360 / n)

Use for-loops to implement these examples:

4. Use the circle(radius) function to draw a picture like this one.

   

5. Write a function to draw a bullseye with n rings, like this:

   

   Hint: To get circles with the same center, you need to move the turtle from the center the edge of the circle without drawing a line. Use the penup() function before moving to avoid drawing. Then use pendown() to resume drawing when you move.

Week 3 Notes

Wed, Sep 9

Today we introduced while-loops. A while-loop is an alternative to a for-loop that is often useful when you don’t know how many steps you need to repeat. We started with these examples:

Example 1: Counter

count = 0
while count < 100:
    count = count + 1
    print(count)

1. How could you re-write this program with a for-loop? Which is easier?

Example 2: Password checker

password = input("Enter the password. ")

while password != "banana":
    print("That's not the correct password.")
    password = input("Enter the password. ")

print("Welcome, you entered the correct password!")

In-Class Exercises.

1. Write a while-loop to print the odd numbers between 0 and n. 

2. Use the flow chart below to write a guessing_game program. It should have a while-loop that runs until the user inputs the correct number. If the user guesses the wrong number, tell them if they are too high or too low before their next guess. Hint: Be sure to convert the user input from a string to an integer using the int function.

   

Additional Practice

1. Change the following function so that it uses a while-loop instead of a for-loop:

   def countdown(n):
       """Count down from an integer n, printing each number.  When you get to zero, print 'Go!'"""
       for i in range(n, 0, -1):
           print(i)
       print("Go!")

    def countdown(n):
        """Count down from an integer n, printing each number.  When you get to zero, print 'Go!'"""
        while n > 0:
            print(n)
            n = n - 1
        print("Go!")

2. Write a while-loop to repeat a string until the total length is more than $n$. You’ll need to use the len function which returns the length of a string.

Thu, Sep 10

Today we talked about while-loops again. We started with Heron’s algorithm for finding square roots.

1. What happens when you compute square_root(10) with this function? Why doesn’t it work?

   def square_root(a):
       """Uses Heron's algorithm to find the square root of a."""
       x = a
       while x**2 != a:
           x = (x + a/x) / 2
       return x

We talked about why it is a bad idea to use != and == with floating point numbers. We also talked about the difference between a single equal sign = which is the Python assignment operator versus a double equal sign == which is a Python comparison operator. Python has 6 comparison operators: (==, !=, >, <, >=, and <=).

Here is a better way to write the square root function. Notice the accuracy parameter has a default value.

def square_root(a, accuracy = 10 ** (-12)):
    """Uses Heron's algorithm to find the square root of a."""
    x = a
    while abs(x**2 - a) > accuracy:
        x = (x + a/x) / 2
    return x

Next we looked at an example with an accumulator variable.

"""Keeps track of the running total of numbers entered by the user."""
print("Enter integers to add. Enter the word done when you are finished.")
total = 0
while True:
    user_input = input("> ")
    if user_input == "done":
        break
    else:
        total = total + int(user_input)
        print("The current total is:", total)

2. Re-write this program using a loop without a break statement.

3. Re-write this program as a function that returns the final total when the user enters “quit”. Note: the return keyword also breaks out of loops.

Additional Practice

1. Write a factorial function using a loop. Recall that the factorial function inputs a positive integer $n$ and returns the product of 1 * 2 * 3 * ... * n.

2. Write a program to add the fractions $\dfrac{1}{n}$ for $n = 1, 2, 3, \ldots$ up to 100. Would it be better to use a while-loop or a for-loop?

3. Write a program to add the fractions $\dfrac{1}{n}$ until the total is greater than 100. Would it be better to use a while-loop or a for-loop?

Fri, Sep 11

Today we talked about Python operators. We introduced the modulus (%) and floor division (//) operators with these examples:

1. 23 // 5

2. 23 % 5

3. -100 // 12

4. -100 % 12

5. What day of the week will it be exactly one month from now on October 11 (without looking at a calendar)?

We also reviewed how the Boolean operators and, or, and not work.

6. Evaluate the expression (True and False) or not True

Then we did this workshop in class.

• Workshop: Python operators

Additional Practice

1. Write a Python function days that inputs a number of minutes, and then prints how long that is in days and hours and leftover minutes. For example, days(3015) should print 2 days, 2 hours, and 15 minutes.

Week 4 Notes

Mon, Sep 14

We started today by talking about how to trace a loop or a program. We did this example in class:

n = 365
total = 0
while n > 0:
    digit = n % 10
    total = total + digit
    n = n // 10
print(total)

To trace a program, make a table with a column for every variable in the program. Follow the program line by line, and update the values of the variables in the columns as you go.

• Workshop: Tracing loops

After that, we did these programming exercises involving modular arithmetic.

1. Write a program to make change using the fewest coins possible for any amount of money less than $1.00. For example, 63¢ could be 2 quarters, 1 dime, and 3 pennies.

Additional Practice

1. For any integer $n > 1$, the Collatz sequence is obtained by following this rule:

   • If $n$ is even, then the next number is $n$ divided by 2.
   • If $n$ is odd, then the next number is $3n+1$.
   • Stop when you get to 1.

   Write a function with a while-loop to print the Collatz sequence for any positive integer $n$. The Collatz conjecture is a famous unsolved math problem which predicts that you will eventually reach 1 no matter which $n$ you start with.

2. Write a function called collatz_length that returns the length of a Collatz sequence starting at $n$ instead of printing the sequence.

3. Use the collatz_length function to find longest Collatz sequence for the numbers from 2 to 999.

4. Which number between 2 and 999 has the longest Collatz sequence?

Wed, Sep 16

We began by reviewing the coins problem from last time. Then we did these exercises in class.

1. Write a function to print all positive integer divisors of $n$. For example, divisors(12) should print the numbers 1, 2, 3, 4, 6, 12.

2. Write a program to solve Brahmagupta’s Egg Problem (from the 7th century):

   An old woman goes to market and a horse steps on her basket and crushes her eggs. The rider offers to pay for the damages and asks her how many eggs were in the basket. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had?

Additional Practice

1. Write a function that returns how many divisors $n$ has. For example, count_divisors(12) should return 6.

2. How could you use the count_divisors function to print all of the prime numbers below 1000? Recall that a number is prime if its only divisors are 1 and itself.

3. A year is a leap year if it is divisible by 4 but not by 100, unless it is divisible by 400 in which case it is a leap year. For example, 1900 was not a leap year, but 2000 was. Write a function called is_leap_year that determines whether a given year is a leap year or not. It should return a Boolean value (True or False).

Thu, Sep 17

We started by talking about Boolean valued functions. We did the example of determining whether a year is a leap year from the additional practice problems yesterday. We ended up writing two versions of the is_leap_year function, one using if-then statements (including the else-if keyword elif):

def is_leap_year(year):
    """Returns True if year is a leap year, otherwise returns False."""
    if year % 4 == 0 and year % 100 != 0:
        return True
    elif year % 400 == 0:
        return True
    else:
        return False

Since the conditions we are checking are already Boolean expressions, we can skip if-then statements entirely and just return the value of a single Boolean expression:

def is_leap_year(year):
    """Returns True if year is a leap year, otherwise returns False."""
    return (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):

You can decide for yourself which version of the is_leap_year function you prefer. We finished our discussion of Boolean valued functions with the following exercise.

1. Use the is_leap_year function in a loop to print the next 20 years, with an asterisk to mark leap years.

After that, we talked about Python strings.

Selecting characters from a string

# Some example strings
fruit = "banana"
alphabet = "abcdefghijklmnopqrstuvwxyz"
string = "The quick brown fox"

Each character in a string has an index. For example, the indices of string are shown below.

1. What is the value of alphabet[3]? What is alphabet[0]?

2. How could you get the last character in alphabet?

3. What error message do you get if you ask for alphabet[26]?

4. What happens if you ask for the character at a non-integer index, like fruit[1.5]?

You can also access characters in a string using negative index values. These count from the end of the string backwards.

1. What is alphabet[-2]?

The length function

To get the length of a string, use the Python function len.

1. What is len(alphabet)?

2. What is len("6")?

3. What is len("")?

Slicing strings

You can get a substring by slicing the string using this pattern: string[start:stop].

1. How would you select the word "brown" from the string string = "The quick brown fox"?

You can use positive or negative index values when you slice a string. If you want to slice all the way to the end, you can leave the end blank:

2. What is alphabet[-3:]?

Looping through strings

You can loop through the characters of a string using a for-loop:

string = "hello"
for char in string:
    print(char)

1. Write a function called count_char. It should input a string and a character, and return the number of times that character appears in the string. For example

   count_char("banana", "a") # should return 3.  

Additional Practice

1. Write a loop to print all consecutive substrings of a given length. For example,

   print_substrings("banana", 4) # should print "bana", "anan", and "nana"  

   Hint: Unlike the count_char function, it is not a good idea to loop through the characters in the string. Instead, loop through the index numbers for the starting positions of substrings you want to print.

2. Write a function called count_substrings that inputs a string and substring, and counts how often that substring appears in the string. For example

   count_substring("banana", "an") # should return 2. 

Fri, Sep 18

Today we talked about string methods. A method is a special kind of function that belongs to the object you are using it on. To call a string method, you use the following syntax.

Python has lots of string methods, but today we talked about some of the most important examples.

1. The count method. Try the command "banana".count("a"). What does the count method do? Does it work if the additional argument is a substring like "an" instead of a single character?

2. The find method. Returns the index where the first example of a substring can be found in a larger string. If the larger string does not contain the substring, then it returns $-1$.

   • What is "banana".find("na")?
   • What about "banana".find("x")?
   • What happens if a substring or character occurs more than once, like "banana".find("a")?

3. The upper and lower methods. Try these commands: "Banana".upper() and "Banana".lower().

4. The replace method. What does the replace method do? Try these examples to see: "banana".replace("a", "b")

We did these practice problems:

1. Write a function called count_vowels that returns how many vowels (a, e, i, o, u) there are in a string. It helps to use the .lower() method to avoid having to check for upper case vowels too.

This example let us talk about method chaining when you call methods like this: x.method1().method2().

Additional Practice

1. Use method chaining to remove punctuation and make every letter lower case for this string: "hELLo, WOrlD!".

2. Use method chaining to write an expression that converts a string to lower case and replaces spaces with dashes. So it should convert "Week 4 Notes" to "week-4-notes".

Week 5 Notes

Mon, Sep 21

Today we introduced lists in Python. Lists are a type of object the can store more than one value. We introduced how to define a list using square brackets (including an empty list).

# Example lists
fruits = ["apple", "banana", "cherry"]
squares = [1, 4, 9, 16, 25, 36]
mixed = [4, True, "ten", 3.14] # Unlike Java arrays, lists can contain more than one type. 

Basic list operations

• Selecting elements
• Slicing
• Length function (len)
• Adding lists
• Multiplying by an integer
• Looping through elements

Looping through lists

There are two different ways to loop through the elements in a list.

# Looping through each element in a list
fruits = ["apple", "berry", "cherry"]
for fruit in fruits:
    print("I like " + fruit + " pie")

# Looping through each index in a list
fruits = ["apple", "berry", "cherry"]
for i in range(len(fruits)):
    print("I like " + fruits[i] + " pie")

Practice

1. Write a function called multiply that multiplies all of the numbers in a list together and returns the result. Use a loop with an accumulator variable to accumulate the product as you go.

2. Write a function called print_lengths that inputs a list of strings, and then prints out the length of each string.

We finished with this example, which requires us to use an empty list as an accumulator variable, and then add new elements to the list as we go. To add an element to a list, use the .append method.

3. Write a function called return_lengths that inputs a list of strings, and then returns a new list that contains the length of each string in the original list. For example:

   return_lengths(["apple", "berry", "cherry"]) # Should return [5, 5, 6]

Additional Practice

1. Write a function that returns the index of the first even number in a list, or $-1$ if there are no even numbers in the list. Hint: to get the index, you won’t be able to loop directly through the elements in the list like you did in the other exercises. Instead, you’ll need to loop through the index values from 0 up to, but not including the length of the list.

Wed, Sep 23

We started talking about the in operator in Python. We did this exercise in class:

1. Write a function print_common_elements(list1, list2) which prints any elements that appear in both list1 and list2. Hint: You only need to use a single loop combined with a single if-then statement involving the in operator.

After that we talked about reasons why you would want to loop through the indices of a string or list instead of the elements themselves. We talked about how to solve these two problems:

2. Write a function to print all continuous length 3 substrings of a string.

3. Write a function to return the index of the first even element in a list of numbers (or -1 if there are no even elements).

Practice

1. Write a function called repeat_pair that returns True if a string has two consecutive characters that are the same (otherwise return False).

2. What happens if you use your function on a list instead of a string. Does it still work?

Thu, Sep 24

We did a workshop in class.

• Workshop: Sequence types

Additional Practice

1. What is "Test this"[-1]?

2. Can you slice from a range? Try it out: what is range(10)[2:5]?

3. Can you add two ranges together? What is range(4) + range(5)?

Fri, Sep 25

Today we introduced 2-dimensional lists. We started with this example. Suppose I have a grid with data like the following:

I could store each student’s data in a Python list.

student_data = [
    ["Alice Adams", 90, 85, 80],
    ["Bob Brown", 80, 90, 87],
    ["Charlie Clark", 60, 75, 72],
    ["Daisy Davis", 78, 69, 75],
    ["Edward Evans", 81, 90, 97]
]

1. What is the value of student_data[1]?

2. What is the value of student_data[-1][3]?

3. How would you select the midterm grade for the 4th student?

4. Write a for-loop to print every entry in the last column.

5. Suppose that the final grade for the course above is 20% homework, 30% midterm exam, and 50% final exam. Write a loop that prints each student’s name and their final grade.

Two-dimensional lists are convenient for storing the data in many board games.

6. Create a 2-dimensional list called board that stores the data from this tic-tac-toe board.

7. How would you add an "X" to the top right corner of the tic-tac-toe board?

You can also use double indexing for other data structures, like lists of strings:

8. Suppose we have a list:

   lst = ["How", "are", "you", "today?"]

   What is lst[3][2]?

9. Here is an example with triple indexing:

   triple = [
       ["One", "list"],
       ["Two", "lists"],
       ["One", "more", "list"]
   ]

   What is the value of triple[-1][1][0]?

Additional Practice

1. Write a function called row_sums that inputs a 2-dimensional list of numbers, and returns a list with the sum of the numbers in each row. For example:

   row_sum([[1, 2], [3, 4], [5, 6]]) # should return [3, 7, 11]

2. Write a function called column_sums that inputs a 2-dimensional list of numbers, and returns a list with the sum of the numbers in each column. You can assume that every row has the same number of elements. For example:

   column_sum([[1, 2], [3, 4], [5, 6]]) # should return [9, 12]

Week 6 Notes

Mon, Sep 28

Today we talked about how to trace a recursive function. We started with this example:

def fib(n):
    """Computes the n-th Fibonacci number"""
    if n <= 1:
        return n
    return fib(n-1) + fib(n-2)  

print(fib(5))

We made a table showing how the variable n and the return value change as the function recursively evaluates fib(5).

After that example, we did this:

• Workshop: Tracing recursive functions

Additional Practice

1. Write a recursive function is_palindrome to check if a string is a palindrome (a word that is spelled the same forward and backward like “racecar”). Hint: Use string[0] and string[-1] to check if the first and last letters are the same. Then use string[1:-1] to get the middle part of the string. A string of length one or zero is automatically a palindrome.

2. Write a recursive function to add up all of the numbers in a list.

Wed, Sep 30

We started by going over example 2 on the workshop from last time. Then we traced another recursive function example.

def split_string(string):
    """Returns a list of substrings separated by commas."""
    if "," in string:
        location = string.find(",")
        return [string[:location]] + split_string(string[location+1:])
    return [string]

print(split_string("1,cat,2,dog"))

We made a table to keep track of the variables in the loop, and what gets returned (both the expression and its eventual value).

In Python it is usually recommended to use loops rather than recursion, when possible.

1. Re-write the split_string function above without using recursion. Use a while-loop instead.

Additional Practice

1. One way to calculate the remainder of a (positive) number modulo 7 is to subtract 7 repeatedly until you get something smaller than 7. For example, 30 → 23 → 16 → 9 → 2. Write a recursive function called mod7 that implements this strategy.

2. Write a recursive function mod(m, n) that computes m % n for any integers (assuming that n is not zero) without using the modulo operator (%) or division.

Week 7 Notes

Week 8 Notes

Week 9 Notes

Week 10 Notes

Week 11 Notes

Week 12 Notes

Week 13 Notes

Week 14 Notes

Week 15 Notes