Problem Set 1: Fundamentals

Homework for Module 1

Introduction

Try the exercises below to practice the concepts from this module. I recommend deactivating Gemini first (and any other AI helper) and attempting the exercises on your own. This approach will help you gain a deeper understanding of how Python works.

Mandatory exercises are highlighted in red boxes. These are the ones you must complete to get your participation points. Feel free to use AI help on other exercises, but remember, you will be asked to explain the code in class!

Each exercise includes one or more examples of how your solution should function. Keep in mind that a good Python program should work under any circumstances, or at the very least, provide an informative message when it fails. Always test your code in as many scenarios as you can imagine! For instance, if the exercise asks you to write a function that computes \(\sqrt{x}\), does your code handle decimal numbers? What if \(x\) is negative?

Numeric Variables

Currency Converter

Write a Python program that converts an amount in Euros to US Dollars. The user inputs the amount in Euros, and the program calculates the equivalent amount in US Dollars. Assume a fixed exchange rate of 1 Euro to 1.17 US Dollars.

Sample input: euros = 100
Expected result: 117.0

euros = 100
dollars = euros * 1.17
print(dollars)
Temperature Converter

Write a Python code that takes a temperature in Fahrenheit and converts it to Celsius. The formula is: \((F - 32) \cdot 5/9 = C\)

Sample input: fahrenheit = 270
Expected result: 132.22

fahrenheit = 270
celsius = (fahrenheit - 32) * 5 / 9
print(round(celsius, 2))
Polynomial Evaluation

Given the polynomial \[f(x) = a \cdot x^2+b \cdot x+c\]

with \[\begin{cases} a=1 \\ b=1 \\ c=-6 \end{cases}\]

Compute the values of \(f(-2)\), \(f(0)\), and \(f(2.1)\).

a, b, c = 1, 1, -6

x = -2
f = a * x**2 + b * x + c
print(f"f(-2) = {f}")

x = 0
f = a * x**2 + b * x + c
print(f"f(0) = {f}")

x = 2.1
f = a * x**2 + b * x + c
print(f"f(2.1) = {f}")

See how we are repeating the same code for different values of x? In the following sessions we will learn how to define a function to avoid this repetition and make our code more efficient.

Polynomial Evaluation II

Given another polynomial \[g(x) = \frac{a}{x}\]

with \(a\) defined above.

  1. Compute the values of \(g(-2)\) and \(g(2.1)\).
  2. What happens when you try to compute \(g(0)\)?
a = 1

x = -2
g = a / x
print(f"g(-2) = {g}")

x = 2.1
g = a / x
print(f"g(2.1) = {g}")

x = 0
# g = a / x  # This will raise a ZeroDivisionError
print("g(0) = Division by zero!")
Polynomial Operation

Let us define a third polynomial using the two previous: \[h(x) = \frac{f(x)}{g(x)}\]

Compute the values of \(h(-2)\), \(h(0)\), and \(h(2.1)\). Are you able to compute all three cases?

Simplified Polynomial Operation

What if we simplify the polynomial of the previous exercise? \[h(x) = \frac{f(x)}{g(x)} = \frac{a \cdot x^2+b \cdot x+c}{a/x} = x^3 + \frac{b}{a} \cdot x^2 + \frac{c}{a} \cdot x\]

Can you now compute all three cases? Do we get the same values?

Basketball Scoring

During a game of basketball, a team scored:

  • 21 two-point field goals
  • 12 three-point field goals, of which 4 occurred in the final minute and are worth double (6 points each)
  • 17 free throws (1 point each)

Tasks: 1. Compute the total number of points scored. 2. Decompose the total into runs (groups) of 7 points: determine how many full runs fit and find how many points are left.

two_pointers = 21 * 2
three_pointers = (12 - 4) * 3 + 4 * 6
free_throws = 17 * 1

total = two_pointers + three_pointers + free_throws
print(f"Total points: {total}")

full_runs = total // 7
remaining = total % 7
print(f"Full runs of 7: {full_runs}, Remaining: {remaining}")
Currency Converter (Advanced)

Write a Python program that converts an amount in Euros to US Dollars with two decimal places precision. The user inputs the amount in Euros, and the program calculates the equivalent amount in US Dollars, outputting a message like "(...) Euros is approximately (...) US Dollars". Assume a fixed exchange rate of 1 Euro to 1.17 US Dollars.

Sample input: euros = 100
Expected result: "100 Euros is approximately 117.00 US Dollars"

euros = 100
dollars = euros * 1.17
print(f"{euros} Euros is approximately {dollars:.2f} US Dollars")
Car Fuel and Speed

A car’s baseline fuel consumption at \(v_0=90 \text{ km/h}\) is \(C_0=6.5\) L/100 km. On the highway, the model \[C(v)=C_0\left(\frac{v}{v_0}\right)^{2}\] estimates the consumption (in L/100 km) at speed \(v\) due to aerodynamic drag.

Tasks: 1. Compute \(C(120)\) for \(v=120 \text{ km/h}\). 2. For a \(250\) km trip at \(120 \text{ km/h}\), compute the total liters used. 3. If fuel costs €1.79 per liter, compute the trip’s fuel cost.

v0 = 90
C0 = 6.5
v = 120
distance = 250
cost_per_liter = 1.79

# Task 1
C_120 = C0 * (v / v0)**2
print(f"Consumption at 120 km/h: {C_120:.2f} L/100km")

# Task 2
liters_used = (distance / 100) * C_120
print(f"Total liters used: {liters_used:.2f} L")

# Task 3
total_cost = liters_used * cost_per_liter
print(f"Trip cost: €{total_cost:.2f}")
Trigonometric Angle Formatter

Create a Python program that takes an angle in degrees and formats it in degrees with minutes and seconds.

Sample input: degrees = 30.4
Expected result: "30 deg 24 min 0 sec"

Printing Numbers

Without running the code, determine the output of each cell.

x = 4

print(x)
y = 2 * 2

print(y)

Both cells print 4.

String Variables

Substring Extraction

Write a Python code to get a substring with the odd index characters.

Sample input 1: s = "abcdefg"
Expected result 1: "bdf"

Sample input 2: s = "0123456789"
Expected result 2: "13579"

s = "abcdefg"
result = s[1::2]
print(result)
Substring Extraction (Advanced)

Write a Python code to get a substring with the even index characters, and make them uppercase.

Sample input: s = "abcdefg"
Expected result: "ACEG"

s = "abcdefg"
result = s[::2].upper()
print(result)
Substring Combination

Write a Python code that gets a string s made of the first 3 and last 2 characters of a given string.

Sample input 1: s = "This is a string"
Expected result 1: "Thing"

Sample input 2: s = "dragon"
Expected result 2: "draon"

s = "This is a string"
result = s[:3] + s[-2:]
print(result)
Substring Combination (Advanced)

Write a Python code that gets a string s made of the first 3 and last 2 characters of a given string, ignoring leading and trailing white spaces.

Sample input 1: s = " This is a string "
Expected result 1: "Thing"

Sample input 2: s = " This has many spaces! "
Expected result 2: "This!"

s = "   This is a string  "
s = s.strip()
result = s[:3] + s[-2:]
print(result)
String Swap

Write a Python code to get a single string from two given strings (u, v), separated by a space and swap the first two characters of each string.

Sample input 1: u = "abc", v = "xyz"
Expected result 1: "xyc abz"

Sample input 2: u = "horse", v = "fly"
Expected result 2: "horsy fle"

u = "abc"
v = "xyz"
result = v[:2] + u[2:] + " " + u[:2] + v[2:]
print(result)
Series Information

Write a Python code that, given a string in the following format: "SeriesName S02E05", where S02 represents the season and E05 represents the episode, returns the information in the following format:

Sample input: "Wendnesday S01E03"
Expected result:

Series: Wendnesday
    Season: 01
    Episode: 03
s = "Wendnesday S01E03"
parts = s.split()
series_name = parts[0]
season = parts[1][1:3]
episode = parts[1][4:6]

print(f"Series: {series_name}")
print(f"    Season: {season}")
print(f"    Episode: {episode}")
Character Replacement

Write a Python code to get a string from a given string where all occurrences of its first char have been changed to "$", except the first character itself.

Sample input 1: s = "excellent"
Expected result 1: "exc$ll$nt"

Sample input 2: s = "crocodile"
Expected result 2: "cro$odile"

Substring Detection

Write a Python code that finds the first occurrence of the substring "cat" and outputs it. It must work both for lowercase and uppercase.

Sample input 1: s = "Catch that fly!"
Expected result 1: "Cat"

Sample input 2: s = "I love cats. Cats are the best."
Expected result 2: "cat"

Adjacent String Literals

Without running the code, what will it print?

message = "Pi is" "3.14"

print(message)
Pi is3.14

Python joins adjacent string literals. No space is added automatically.

Printing Quotation Marks

Write one print() statement that produces this message:

The cow says "Moooo"
print('The cow says "Moooo"')

You could also escape the inner double quotation marks.

Valid Print Statements

Which statements fail? There may be more than one.

# A
print("The number 3.14 is close to pi")
# B
print(f"The number {3.1415.2f} is close to pi")
# C
number = 3.1415
print(f"The number {number:.2f} is close to pi")
# D
number = 3.1415
print("The number", number, "is close to pi")
# E
number = 3.1415
print("The number" + number + "is close to pi")
# F
number = "3.14"
print("The number", number, "is close to pi")

Statements B and E fail.

  • B uses invalid f-string formatting. A valid expression is {3.1415:.2f}.
  • E tries to concatenate strings and a float with +.
  • A, C, D, and F run successfully.
Values Stored in f-Strings

Predict the output of each cell.

pet = "dog"
message = f"I have a {pet}"

print(message)
pet = "dog"
message = f"I have a {pet}"
pet = "cat"

print(message)
x = 1
y = 3 * x
x = 2
y = 2 * x

print(y)

The outputs are:

I have a dog
I have a dog
4

The f-string is evaluated when message is created. Changing pet later does not update the existing string.

Flow Control

Odd/Even Checker

Create a code that checks if an integer is even or odd. The output should be a message like "(number) is an odd/even number".

Sample input: num = 267
Expected result: "267 is an odd number"

num = 267
if num % 2 == 0:
    print(f"{num} is an even number")
else:
    print(f"{num} is an odd number")
Divisible Checker

Create a code that checks if a number a is divisible by another b. The output should be a message like "(a) is divisible by (b)".

Sample input: a = 10, b = 7
Expected result: "10 is not divisible by 7"

a = 10
b = 7
if a % b == 0:
    print(f"{a} is divisible by {b}")
else:
    print(f"{a} is not divisible by {b}")
Leap Year Checker

Write a Python program that checks whether a given year is a leap year or not. We input a year, and the program determines if it’s a leap year based on the leap year rules (divisible by 4, but not divisible by 100 unless divisible by 400).

Sample input: year = 2023
Expected result: "2023 is not a leap year."

year = 2023
if (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):
    print(f"{year} is a leap year.")
else:
    print(f"{year} is not a leap year.")
Vowel Checker

Create a code that checks if a character is a vowel or a consonant. The output should be a message like "(letter) is a vowel/consonant".

Sample input: s = "o"
Expected result: "o is a vowel"

s = "o"
vowels = "aeiouAEIOU"
if s in vowels:
    print(f"{s} is a vowel")
else:
    print(f"{s} is a consonant")
Grade Calculator

Develop a code that takes a numeric variable representing a student’s score (between 0 and 100) and uses if/else statements to calculate the corresponding letter grade (A, B, C, D, or F) based on standard grading criteria:

  • F: Grade between 0 and 60
  • D: Grade between 61 and 70
  • C: Grade between 71 and 80
  • B: Grade between 81 and 90
  • A: Grade between 91 and 100

The output should be a message like "Student's grade: (grade)". If the input score is out of the range (i.e. below 0 or above 100), it should instead return a message "Invalid score (out of range)".

Sample input: score = 89
Expected result: "Student's grade: B"

score = 89
if score < 0 or score > 100:
    print("Invalid score (out of range)")
elif score <= 60:
    print("Student's grade: F")
elif score <= 70:
    print("Student's grade: D")
elif score <= 80:
    print("Student's grade: C")
elif score <= 90:
    print("Student's grade: B")
else:
    print("Student's grade: A")
Parcheesi Move

Write a Python program to play Parcheesi. Your opponent has one pawn 4 squares away and another 2 squares away, and you still have pawns at home. It is your turn, and the program will simulate your actions. Your program input will be the number you rolled on the die.

Rules: - If the roll is 5, print: "You must move a pawn out of home" (this has priority over any other move). - If the roll is 2 or 4, print: "You capture an opponent's pawn and count 20". - Otherwise, print: "Move the pawn x positions", where x is the number rolled on the die.

Sample input: die = 3
Expected result: "Move the pawn 3 positions"

die = 3
if die == 5:
    print("You must move a pawn out of home")
elif die == 2 or die == 4:
    print("You capture an opponent's pawn and count 20")
else:
    print(f"Move the pawn {die} positions")
Password Validator

Write a Python program that checks if a password is valid.

Rules: - If the password has fewer than 10 characters, print: "Password too short". - If the password starts with "admin", print: "Password not allowed: starts with 'admin'". - If the password does not end with one of the special characters !?#$, print: "Password does not end with a special character". - Otherwise, print: "Password correct".

Sample input: password = "goodpassword?"
Expected result: "Password correct"

password = "goodpassword?"
if len(password) < 10:
    print("Password too short")
elif password.startswith("admin"):
    print("Password not allowed: starts with 'admin'")
elif password[-1] not in "!?#$":
    print("Password does not end with a special character")
else:
    print("Password correct")
String Palindrome Checker

Create a code that checks if a string is a palindrome (reads the same forwards and backward).

Sample input: s = "tacocat"
Expected result: "The string is a palindrome"

s = "tacocat"
if s == s[::-1]:
    print("The string is a palindrome")
else:
    print("The string is not a palindrome")
Angle Quadrant Checker

Write a code that takes an angle (in degrees) and determines in which quadrant of the Cartesian coordinate system it lies, even for angles outside the typical range.

In the Cartesian coordinate system:

  • Quadrant I: Angle between 0 and 90 degrees
  • Quadrant II: Angle between 90 and 180 degrees
  • Quadrant III: Angle between 180 and 270 degrees
  • Quadrant IV: Angle between 270 and 360 degrees

The code should provide an output message in the form "The angle (angle) degrees is in quadrant (quadrant)".

Sample input: angle = 56
Expected result: "The angle 56 degrees is in quadrant I"

Fraction Formatter

Develop a Python program that takes two integers, the numerator and denominator of a fraction, and formats it as a proper fraction or mixed number. For example, if the input is 3 and 2, the output should be formatted as "1 + 1/2".

Sample input: numerator = 7, denominator = 4
Expected result: "1 + 3/4"

Quadratic Equation Solver

Write a Python code that takes three numeric variables (coefficients a, b, and c) representing a quadratic equation \(a \cdot x^2 + b \cdot x + c = 0\). Use if/else statements to determine and display the roots (real or complex) of the equation. The code should provide one of the following output messages based on the result:

  • "Roots are real and different: (root 1) and (root 2)"
  • "Root is real and equal: (root)"
  • "Roots are complex: (real 1) + (img 1)i and (real 2) + (img 2)i"

In all cases, ensure that the displayed numbers have a maximum of two decimal places.

Sample input: a = 1, b = 4, c = 2
Expected result: "Roots are real and different: -0.59 and -3.41"

Pythagorean Triple Checker

Write a program that checks whether a given set of three numbers forms a Pythagorean triple (\(a^2+b^2=c^2\)). Provide appropriate messages based on the check.

Sample input: a = 4, b = 3, c = 5
Expected result: "(a=4, b=3, c=5) forms a Pythagorean triple"

Unreachable Branches

Which branches can never run, assuming apples, bananas, and friends are positive?

apples = 10
bananas = 5
friends = 15

if apples + bananas >= friends:
    print("We have enough fruit for our friends!")
elif apples >= friends:
    print("We have enough apples for our friends!")
elif bananas >= friends:
    print("We have enough bananas for our friends!")
else:
    print("We do not have enough fruit for our friends!")

The two elif branches can never run. If either the apples or bananas are enough on their own, their combined total is also enough, so the first condition already succeeds.

Updating a Variable in a Conditional

What is the final value of x?

x = 5
condition = x**2 < 10

if condition:
    x = x + 1
else:
    x = x + 3

x = x / 2

print(x)

The final value is 4.0. The condition is false, so x becomes 8 before being divided by 2.

Comparing Different Types

What happens when this code runs?

years = "5"

if years > 0:
    print(f"I am {years} years old")

Python raises a TypeError because it cannot compare a string with an integer using >.

years = "5"

if int(years) > 0:
    print(f"I am {years} years old")
Assignment or Comparison?

Explain why this code fails and correct it.

a = 10
b = 2

if a % b = 0:
    print(f"{a} is divisible by {b}")

The condition needs the comparison operator ==. A single equals sign performs assignment and is invalid in this position.

a = 10
b = 2

if a % b == 0:
    print(f"{a} is divisible by {b}")

Looping

Multiplication Table

Write a Python program that gets an integer and then generates and displays the multiplication table for that number from 1 to 10. For example, if the user enters 5, the program should display:

Multiplication Table for 5:
5 x 1 = 5
5 x 2 = 10
...
5 x 10 = 50
num = 5
print(f"Multiplication Table for {num}:")
for i in range(1, 11):
    print(f"{num} x {i} = {num * i}")
Factorial Calculator

Write a Python program that gets a positive integer and then calculates its factorial. Ensure that the input is a positive integer, and provide feedback if it’s not.

Sample input: num = 4
Expected result: 24

num = 4
factorial = 1
for i in range(1, num + 1):
    factorial *= i
print(factorial)
Multiples of a Number

Write a Python program that finds and displays all the multiples of a given number within a specified range. The user inputs the number and the range, and the program lists the multiples. The output should be a string with all the terms separated by commas.

Sample input: num = 7, limit = 50
Expected result: "7, 14, 21, 28, 35, 42, 49"

Warning: We are talking about “range”, but do not name the variable range! Why? Because range is a built-in function. If you assign range = 50, then you lose the handy range function.

num = 7
limit = 50
multiples = []
for i in range(num, limit, num):
    multiples.append(str(i))
print(", ".join(multiples))
Sum of Digits

Write a Python program that takes a positive integer as input and then calculates and displays the sum of its digits. Ensure that the input is a positive integer, and provide feedback if it’s not.

Sample input 1: num = 517
Expected result 1: 13

Sample input 2: num = 1002
Expected result 2: 3

Tip: Use modules and remainders! The remainder of \(517 / 10\) is 7 (we have its last digit!), and the quotient is 51. Now we can compute the remainder of \(51 / 10\), which will be 1 (we have the second digit!). And so on.

num = 517
digit_sum = 0
while num > 0:
    digit_sum += num % 10
    num //= 10
print(digit_sum)
Fibonacci Sequence

Write a Python program that generates the Fibonacci sequence up to a specified number of terms. The input should be the number of terms we want to see in the sequence. The output should be a string with all the terms separated by commas.

Sample input: num = 5
Expected result: "0, 1, 1, 2, 3"

num = 5
a, b = 0, 1
sequence = [str(a)]
for _ in range(num - 1):
    sequence.append(str(b))
    a, b = b, a + b
print(", ".join(sequence))
Palindrome Checker (Advanced)

Enhance the palindrome checker program to ignore spaces, punctuation, and letter casing.

Sample input: s = "Was it a car or a cat I saw?"
Expected result: "The string is a palindrome"

Guessing a Number

I’m sure you’ve played many times the game of guessing a number someone has thought of to make a decision.

Let’s write a program to simulate this game. The user will enter numbers until they guess correctly. If the attempt is greater than the chosen number, the program should display “My number is smaller”, and if it is smaller: “My number is greater”. If the user guesses correctly, the program ends and tells them they have won.

number = 42  # The secret number
while True:
    guess = int(input("Guess the number: "))
    if guess == number:
        print("You have won!")
        break
    elif guess > number:
        print("My number is smaller")
    else:
        print("My number is greater")
Reversed Number

Write a program that takes a number as input and outputs the reversed number.

Sample input: num = 1435
Expected result: 5341

Prime Number Checker

Write a Python program that takes an integer and determines whether it’s a prime number. The output should be a message indicating whether the entered number is prime or not.

Sample input: num = 7
Expected result: "7 is a prime number"

Perfect Number Checker

Develop a program that checks whether a given number is a perfect number (a positive integer that is equal to the sum of its proper divisors, excluding itself). The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.

Sample input: num = 100
Expected result: "100 is not a perfect number"

Iterating Over a List

Without running the code, write its output.

for value in [1, 2, 3]:
    print(value)
1
2
3
Understanding range()

Without running the code, write its output.

for value in range(1, 3):
    print(value)
1
2

The stopping value 3 is excluded.

Range with a Step

Without running the code, write its output.

for c in range(1, 4, 2):
    print(c)

print("Next!")
1
3
Next!
Reusing a Previous Loop Variable

Assume the previous exercise has already run, so c has the value 3. Without running the code, write its output.

for d in ["apple", "banana", "chocolate"]:
    print(c)
    print("Next!")
3
Next!
3
Next!
3
Next!

The loop changes d, but the code prints the existing value of c from the previous exercise.

Conditional Output Inside a Loop

Without running the code, write its output.

n = 0

for d in ["apple", "banana", "chocolate"]:
    n = n + 1

    if n != 1:
        print(d)

    print("Next!")
Next!
banana
Next!
chocolate
Next!

The food is not printed during the first iteration, but "Next!" is printed during every iteration.

Sum with for and while

Use a for loop to calculate the sum of the positive integers below 10. Then solve the same problem with a while loop.

Expected result: 45.

Using for:

result = 0

for number in range(1, 10):
    result += number

print(result)

Using while:

result = 0
number = 1

while number < 10:
    result += number
    number += 1

print(result)
Two Multiplication Tables

Use loops to generate the multiplication tables of 2 and 4, from multiplier 1 through 10.

lines = []

for number in (2, 4):
    lines.append(f"Multiplication table of {number}")

    for multiplier in range(1, 11):
        product = number * multiplier
        lines.append(f"{number} x {multiplier} = {product}")

print("\n".join(lines))
Factorial with for and while

Use a for loop to calculate 5!. Then solve the same problem with a while loop.

Expected result: 120.

Using for:

result = 1

for number in range(2, 6):
    result *= number

print(result)

Using while:

result = 1
number = 2

while number <= 5:
    result *= number
    number += 1

print(result)
Build a Sentence with Loops

Use a for loop to combine the words below into one sentence. Then solve the same problem with a while loop.

words = ["Hello", "my", "name", "is", "Daniel"]

Expected result: "Hello my name is Daniel".

Using for:

words = ["Hello", "my", "name", "is", "Daniel"]
sentence = ""

for word in words:
    sentence = sentence + " " + word

print(sentence.strip())

Using while:

words = ["Hello", "my", "name", "is", "Daniel"]
sentence = ""
index = 0

while index < len(words):
    sentence = sentence + " " + words[index]
    index += 1

print(sentence.strip())
Repair the Multiples Program

Explain why the code fails, then correct it.

number = 7
limit = 50
message = ""

for value in range(1, limit + 1):
    if value % number == 0:
        message = message + value + ", "

print(message)

Expected result: "7, 14, 21, 28, 35, 42, 49".

The code tries to concatenate an integer to a string. Convert each multiple with str().

number = 7
limit = 50
message = ""

for value in range(1, limit + 1):
    if value % number == 0:
        message = message + str(value) + ", "

message = message[:-2]

print(message)
Repair the Fibonacci Program

The program below should generate five Fibonacci terms. Find and correct every error.

number_of_terms = 5
first = 0
second = 1
terms_computed = 2
message = "0, 1"

while terms_computed < number_of_terms:
    next_value = first + second
    message = message + ", " + next_value
    terms_computed = +1

print(message)

Expected result: "0, 1, 1, 2, 3".

The original code concatenates a number to a string, resets the counter to 1, and never updates the two previous Fibonacci values.

number_of_terms = 5
first = 0
second = 1
terms_computed = 2
message = "0, 1"

while terms_computed < number_of_terms:
    next_value = first + second
    message = message + ", " + str(next_value)
    first = second
    second = next_value
    terms_computed += 1

print(message)

Functions

Input/Output Functions

Sum

Write a Python program that asks the user to input two numbers, using the input() function. The program then sums both values and prints a message with the result.

Sample input: 3, 6
Expected result: "The sum is 9"

num1 = int(input("Enter first number: "))
num2 = int(input("Enter second number: "))
print(f"The sum is {num1 + num2}")
Number of Characters

Write a Python program that asks the user to input any sentence, using the input() function. The program then prints the number of characters in that string.

Sample input: "How long is this sentence?"
Expected result: "The sentence has 26 characters"

sentence = input("Enter a sentence: ")
print(f"The sentence has {len(sentence)} characters")
Rounding Floating-Point Numbers

Write a Python program that prompts the user to input a floating-point number using the input() function. The program should then round the number to three decimal places and display a message.

Sample input: 2.71828
Expected result: "I have rounded your number to 2.718"

number = float(input("Enter a number: "))
rounded = round(number, 3)
print(f"I have rounded your number to {rounded}")
Rounding Numbers (Advanced)

Update the program from the previous exercise. Now:

  • If the input is an integer, display a message: "Your number is an integer."
  • If the input number is approximately equal to \(\pi\) (\(\sim 3.142\)), the program should display a special message: "Your number is pi!"

Sample input 2: 42
Expected result 2: "Your number is an integer"

Sample input 3: 3.14159265359
Expected result 3: "Your number is pi!"

pi = 3.14159265359

number = float(input("Enter a number: "))
if number == int(number):
    print("Your number is an integer")
elif abs(number - pi) < 0.001:
    print("Your number is pi!")
else:
    rounded = round(number, 3)
    print(f"I have rounded your number to {rounded}")

User-Defined Functions

Multiplication

Write a Python function multiply(x, y) that takes two numbers as arguments and returns their multiplication.

Sample input: multiply(3, 6)
Expected result: 18

def multiply(x, y):
    return x * y

print(multiply(3, 6))
Area of Rectangle

Define a function rectangle_area(length, width) that calculates the area of a rectangle based on its length and width.

Sample input: rectangle_area(3, 6)
Expected result: 18

def rectangle_area(length, width):
    return length * width

print(rectangle_area(3, 6))
Area of Circle

Define a function circle_area(radius) that calculates the area of a circle based on its radius.

Sample input: circle_area(1.1)
Expected result: 3.80

pi = 3.14159265359

def circle_area(radius):
    return round(pi * radius**2, 2)

print(circle_area(1.1))
Print Strings

Define a function say_hello(surname, name) that accepts the user’s last and first name and prints them in reverse order with a space between them.

Sample input: say_hello("Simpson", "Homer")
Expected result: "Hello Homer Simpson"

def say_hello(surname, name):
    return f"Hello {name} {surname}"

print(say_hello("Simpson", "Homer"))
Fahrenheit to Celsius

Create a function fahrenheit_to_celsius(fahrenheit) that converts temperature from Fahrenheit to Celsius.

Sample input: fahrenheit_to_celsius(270)
Expected result: 132.22

def fahrenheit_to_celsius(fahrenheit):
    celsius = (fahrenheit - 32) * 5 / 9
    return round(celsius, 2)

print(fahrenheit_to_celsius(270))
Even/Odd Checker

Define a function that checks if a number is even or odd and returns a corresponding message.

Sample input: even_or_odd(5)
Expected result: "5 is an odd number"

def even_or_odd(num):
    if num % 2 == 0:
        return f"{num} is an even number"
    else:
        return f"{num} is an odd number"

print(even_or_odd(5))
Factorial

Write a function factorial(x) that calculates the factorial of a given number. If the input is zero or negative, the output should be 0.

Sample input: factorial(5)
Expected result: 120

def factorial(x):
    if x <= 0:
        return 0
    result = 1
    for i in range(1, x + 1):
        result *= i
    return result

print(factorial(5))
Vowel Count

Define a function count_vowels(string) that counts the number of vowels in a given string.

Sample input: count_vowels("I wish you an awesome day!")
Expected result: 10

def count_vowels(string):
    vowels = "aeiouAEIOU"
    count = 0
    for char in string:
        if char in vowels:
            count += 1
    return count

print(count_vowels("I wish you an awesome day!"))
Prime Number Checker

Write a Python function is_prime(num) that takes an integer num and uses a for loop to determine whether it’s a prime number. The output should be a boolean True / False.

Sample input: is_prime(7)
Expected result: True

def is_prime(num):
    if num < 2:
        return False
    for i in range(2, int(num**0.5) + 1):
        if num % i == 0:
            return False
    return True

print(is_prime(7))
Largest Prime Factor

Develop a function largest_prime_factor(num) that calculates and displays the largest prime factor of a given number num. Tip: this function can use is_prime(num) to get prime numbers.

Sample input: largest_prime_factor(18)
Expected result: 3

Common Divisors

Write a Python function common_divisors(num1, num2) that takes two numbers and prints the common divisors of those numbers. A divisor is a number that divides another number without leaving a remainder.

Sample input: common_divisors(12, 4)
Expected result: "1, 2, 4"

def common_divisors(num1, num2):
    divisors = []
    for i in range(1, min(num1, num2) + 1):
        if num1 % i == 0 and num2 % i == 0:
            divisors.append(str(i))
    return ", ".join(divisors)

print(common_divisors(12, 4))
Greatest Common Divisor

Modify the previous function to return only the GCD (Greatest Common Divisor). The greatest common divisor of two or more integers is the largest positive integer that divides each of the numbers exactly.

Sample input 1: common_divisors(18, 24)
Expected result 1: 6

Sample input 2: common_divisors(6, 12)
Expected result 2: 6

def common_divisors(num1, num2):
    gcd = 1
    for i in range(1, min(num1, num2) + 1):
        if num1 % i == 0 and num2 % i == 0:
            gcd = i
    return gcd

print(common_divisors(18, 24))
Sum of Divisors

Write a Python function sum_of_divisors(num) that calculates the sum of all positive divisors of a given positive integer num. A divisor is a number that divides another number without leaving a remainder.

Sample input 1: sum_of_divisors(12)
Expected result 1: 28

Sample input 2: sum_of_divisors(16)
Expected result 2: 31

Amicable Numbers

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

Write a Python function are_amicable(num1, num2) that checks whether two given positive integers num1 and num2 are amicable numbers.

Sample input 1: are_amicable(220, 284)
Expected result 1: True

Sample input 2: are_amicable(1184, 1210)
Expected result 2: True

Digital Root

The digital root of a number is found by summing all its digits repeatedly until a single-digit result is obtained. For instance, the digital root of 89 is 8 because: \(8 + 9 = 17 \rightarrow 1 + 7 = 8\).

Write a Python function digital_root(num) that calculates the digital root of a given positive integer num using recursion.

Your function should follow these steps: 1. Compute the sum of the digits of the given number. 2. If the result is a single digit, output it. 3. If the result has multiple digits, call the digital_root() function recursively using the new result.

Sample input 1: digital_root(89)
Expected result 1: 8

Sample input 2: digital_root(9875)
Expected result 2: 2

Number of Collatz Steps

Consider the Collatz sequence, which is defined as follows:

  1. Start with a positive integer \(n\).
  2. If \(n\) is even, divide it by 2.
  3. If \(n\) is odd, multiply it by 3 and add 1.
  4. Repeat these steps until \(n\) becomes 1.

Write a Python function collatz_steps(num) that calculates the number of steps it takes for the Collatz sequence to reach 1 starting from a positive integer num.

For example, if you start with \(n = 6\), the sequence is: \(6 \rightarrow 3 \rightarrow 10 \rightarrow 5 \rightarrow 16 \rightarrow 8 \rightarrow 4 \rightarrow 2 \rightarrow 1\). It took 8 steps to reach 1, so collatz_steps(6) should return 8.

Sample input 1: collatz_steps(6)
Expected result 1: 8

Sample input 2: collatz_steps(27)
Expected result 2: 111

Functions with Keyword Arguments

Area of Circle (Advanced)

Define a function circle_area(radius, is_diameter=False) that calculates the area of a circle based on its radius. If the keyword argument is_diameter is input as True, then the function considers that radius is instead the diameter.

Sample input 1: circle_area(1.1)
Expected result 1: 3.80

Sample input 2: circle_area(2.2, is_diameter=True)
Expected result 2: 3.80

pi = 3.14159265359

def circle_area(radius, is_diameter=False):
    if is_diameter:
        radius = radius / 2
    return round(pi * radius**2, 2)

print(circle_area(1.1))
print(circle_area(2.2, is_diameter=True))
Estimate Capital

Write a Python function capital_increase(capital, years=15, rate=2) that accepts a user’s initial capital and calculates the resulting capital after a certain amount of years, with a compound interest of rate% yearly. Both years and rate are keyword arguments.

Sample input 1: capital_increase(100000)
Expected result 1: 134586.83

Sample input 2: capital_increase(100000, years=10, rate=1)
Expected result 2: 110462.21

def capital_increase(capital, years=15, rate=2):
    final_capital = capital * ((1 + rate/100)**years)
    return round(final_capital, 2)

print(capital_increase(100000))
print(capital_increase(100000, years=10, rate=1))
Time Difference between Days

Define a function time_difference(day1, hour1, min1, day2, hour2, min2) that calculates the time difference in days, hours, and minutes between two given dates that belong to the same month.

Sample input 1: time_difference(5, 12, 35, 7, 17, 10)
Expected result 1: "2 days, 4 hours, 35 minutes"

def time_difference(day1, hour1, min1, day2, hour2, min2):
    total_min1 = day1 * 24 * 60 + hour1 * 60 + min1
    total_min2 = day2 * 24 * 60 + hour2 * 60 + min2
    diff_min = total_min2 - total_min1
    
    days = diff_min // (24 * 60)
    hours = (diff_min % (24 * 60)) // 60
    minutes = diff_min % 60
    
    return f"{days} days, {hours} hours, {minutes} minutes"

print(time_difference(5, 12, 35, 7, 17, 10))
Happy Numbers

A happy number is a number that, when you repeatedly replace it with the sum of the square of its digits, eventually reaches the number 1. For instance, 19 is a happy number because: \(1^2 + 9^2 = 82 \rightarrow 8^2 + 2^2 = 68 \rightarrow 6^2 + 8^2 = 100 \rightarrow 1^2 + 0^2 + 0^2 = 1\).

Write a Python function is_happy_number(num, max_iter=100) that checks whether a given positive integer num is a happy number or not.

Note that unhappy numbers will never end the loop, so you should set some stopping criteria! I recommend allowing a maximum of 100 iterations through the keyword argument max_iter, and output that the number is unhappy if you reach that limit.

Sample input 1: is_happy_number(19)
Expected result 1: True

Sample input 2: is_happy_number(19, max_iter=3)
Expected result 2: False

Function Behavior

Defining Without Calling

Without running the code, what output does this cell produce?

def yell(text="hello"):
    print(text.upper() + "!")

The cell produces no output. It defines yell() but never calls it.

yell()

The added call prints HELLO!.

Default Arguments and range()

Without running the code, write its output.

def powers_of_number(number, limit=4):
    for exponent in range(1, limit):
        print(f"{number}^{exponent} = {number**exponent}")


powers_of_number(2)
2^1 = 2
2^2 = 4
2^3 = 8

The stopping value 4 is excluded from the range.

Initialise Before a Password Loop

Explain why the program fails and correct it.

password = "coconut"

while user_input != password:
    user_input = input("Enter a password: ")

print("Access granted!")

The condition uses user_input before that variable exists.

password = "coconut"
user_input = input("Enter a password: ")

while user_input != password:
    user_input = input("Enter a password: ")

print("Access granted!")
Repair the Natural-Number Sum

Find and correct every error.

number = input("Enter a positive integer: ")

while number > 0:
    result += number
    number -= 1

print(result)

input() returns a string, and result has not been initialised.

number = int(input("Enter a positive integer: "))
result = 0

while number > 0:
    result += number
    number -= 1

print(result)
Repair the Naming Errors

Each block contains a naming error. Explain and correct all three.

def rectangle_area(length, width):
    return len * width


print(rectangle_area(10, 20))
def rectangle_area(length, width):
    return length * width


rectangle_area = rectangle_area(20, 40)
area_2 = rectangle_area(10, 20)

print(area_2)
print = "Hello world"

print(8)

The first block uses the built-in function len instead of the parameter length.

def rectangle_area(length, width):
    return length * width


print(rectangle_area(10, 20))

The second block replaces the function name with a number. Store the result under another name.

def rectangle_area(length, width):
    return length * width


area_1 = rectangle_area(20, 40)
area_2 = rectangle_area(10, 20)

print(area_2)

The third block replaces the name of the built-in print() function. Use a descriptive variable name instead.

message = "Hello world"

print(message)
Unreachable Code After return

Explain why the diameter correction never runs, then repair the function.

def circle_area(radius, is_diameter=False):
    return 3.1415 * radius**2

    if is_diameter:
        radius = radius / 2
        return 3.1415 * radius**2

The first return ends the function before Python reaches the conditional.

def circle_area(radius, is_diameter=False):
    if is_diameter:
        radius = radius / 2

    return 3.1415 * radius**2
print(circle_area(10, is_diameter=True))

Scope

Nested Function Parameters

Do these two versions return different values? Predict each output.

def add(a, b):
    result = a + b

    def multiply(a, b):
        return a * b

    return multiply(a, b), result


product, total = add(2, 3)

print(f"{product}\n{total}")
def add(a, b):
    result = a + b

    def multiply(c, d):
        return c * d

    return multiply(a, b), result


product, total = add(2, 3)

print(f"{product}\n{total}")

Both versions print:

6
5

Parameter names are local to their function. Renaming the nested parameters from a, b to c, d does not change the calculation.

Shadowing print()

What happens when this code runs? How can you restore the built-in print() function?

print = 7

print(print)

Python raises a TypeError because the name print now refers to the integer 7.

del print

print("The built-in function is available again")

Restarting the Python session also removes the accidental assignment.

Immutable Arguments

What is the value of variable after the function call?

def modify_variable(value):
    value += 5


variable = 10
modify_variable(variable)

print(variable)

The output is 10. Integers are immutable, and the parameter value is local to the function.

Local Variable Shadowing

Predict the two outputs.

def factorial(number):
    x = number
    result = 1

    while x > 1:
        result *= x
        x -= 1

    return result


x = 10
factorial_result = factorial(x)
print(factorial_result)
print(x)

The outputs are 3628800 and 10. The x created inside factorial() is local and does not replace the outer x.

Number-System Conversions

Decimal to Binary

Write a function named decimal_to_binary(decimal) that converts a non-negative integer to a binary string without using bin().

Sample input: decimal_to_binary(10)
Expected result: "1010"

def decimal_to_binary(decimal):
    if not isinstance(decimal, int) or decimal < 0:
        raise ValueError("decimal must be a non-negative integer")

    if decimal == 0:
        return "0"

    binary = ""

    while decimal > 0:
        remainder = decimal % 2
        binary = str(remainder) + binary
        decimal //= 2

    return binary
Binary to Decimal

Write a function named binary_to_decimal(binary) that converts a binary string to an integer without using int(binary, 2).

Sample input: binary_to_decimal("1010")
Expected result: 10

def binary_to_decimal(binary):
    if not binary or any(digit not in "01" for digit in binary):
        raise ValueError("binary must contain only 0 and 1")

    decimal = 0

    for digit in binary:
        decimal = decimal * 2 + int(digit)

    return decimal

Generator Functions

Custom Range Generator

Implement a generator function custom_range(stop, start=0, step=1) that generates numbers within a custom range specified by the user, just like range does. For obvious reasons, your function cannot use the original range function (but should work the same way!).

Sample input 1: [number for number in custom_range(6)]
Expected result 1: [0, 1, 2, 3, 4, 5]

Sample input 2: [n for n in custom_range(-4, start=1, step=-2)]
Expected result 2: [1, -1, -3]

def custom_range(stop, start=0, step=1):
    current = start
    while (step > 0 and current < stop) or (step < 0 and current > stop):
        yield current
        current += step

print([number for number in custom_range(6)])
print([n for n in custom_range(-4, start=1, step=-2)])
Powers of Two

Define a generator function powers_of_two(num) that generates the powers of 2 up to a certain limit.

Sample input: [number for number in powers_of_two(100)]
Expected result: [2, 4, 8, 16, 32, 64]

def powers_of_two(num):
    power = 1
    result = 2
    while result <= num:
        yield result
        power += 1
        result = 2 ** power

print([number for number in powers_of_two(100)])
Fibonacci Generator

Write a Python generator function fibonacci(num) that generates Fibonacci numbers up to a specified number.

Sample input: [number for number in fibonacci(5)]
Expected result: [0, 1, 1, 2, 3]

def fibonacci(num):
    a, b = 0, 1
    count = 0
    while count < num:
        yield a
        a, b = b, a + b
        count += 1

print([number for number in fibonacci(5)])
Clock Generator

Create a generator function clock(limit) that simulates a digital clock.

Rules: - The generator should yield the current time in the format "HH:MM:SS". - It must start at "00:00:00" and increment by one second each step. - After "23:59:59", the cycle should continue again from "00:00:00". - The generator must stop when the chosen limit of steps has been reached.

Sample usage: [time for time in clock(4)]
Expected result: ["00:00:00", "00:00:01", "00:00:02", "00:00:03"]

def clock(limit):
    hour, minute, second = 0, 0, 0
    for _ in range(limit):
        yield f"{hour:02d}:{minute:02d}:{second:02d}"
        second += 1
        if second == 60:
            second = 0
            minute += 1
            if minute == 60:
                minute = 0
                hour += 1
                if hour == 24:
                    hour = 0

print([time for time in clock(4)])
Prime Number Generator

Create a generator function prime_numbers(num) that yields prime numbers within a specified range.

Sample input: [number for number in prime_numbers(9)]
Expected result: [2, 3, 5, 7]

def prime_numbers(num):
    def is_prime(n):
        if n < 2:
            return False
        for i in range(2, int(n**0.5) + 1):
            if n % i == 0:
                return False
        return True
    
    for i in range(2, num):
        if is_prime(i):
            yield i

print([number for number in prime_numbers(9)])

Want to Practice More?

If you want to practice for the quiz and exams, go to the exam repository.