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

Solution: Currency Converter

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

Solution

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 $f(2.1)$.

Solution: Polynomial Evaluation

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.

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

Solution: Polynomial Evaluation II

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.

Solution: Basketball Scoring

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"

Solution: Currency Converter

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.

Solution: Car Fuel and Speed

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"

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"

Solution: Substring Extraction

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"

Solution

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"

Solution

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!"

Solution

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"

Solution

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

Solution

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"

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"

Solution

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"

Solution

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."

Solution

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"

Solution

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"

Solution

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"

Solution

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"

Solution

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"

Solution

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"

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

Solution

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

Solution

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.

Solution

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.

Solution

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"

Solution

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.

Solution

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"

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"

Solution

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"

Solution

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"

Solution

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!"

Solution

import math

number = float(input("Enter a number: "))
if number == int(number):
    print("Your number is an integer")
elif abs(number - math.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

Solution

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

Solution

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

Solution

import math

def circle_area(radius):
    return round(math.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"

Solution

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

Solution

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"

Solution

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

Solution

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

Solution

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

Solution

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"

Solution

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

Solution

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:

Start with a positive integer $n$.
If $n$ is even, divide it by 2.
If $n$ is odd, multiply it by 3 and add 1.
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

Solution

import math

def circle_area(radius, is_diameter=False):
    if is_diameter:
        radius = radius / 2
    return round(math.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

Solution

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"

Solution

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

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]

Solution

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]

Solution

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]

Solution

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"]

Solution

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]

Solution

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?

You can find more exercises and solutions in the review section.

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

--- title: "Problem Set 1: Fundamentals" subtitle: "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 ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution: Currency Converter ```{python} #| eval: false euros = 100 dollars = euros * 1.17 print(dollars) ``` ::: ::: {.callout-note} ## 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` ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false fahrenheit = 270 celsius = (fahrenheit - 32) * 5 / 9 print(round(celsius, 2)) ``` ::: ::: ::: {.callout-note} ## 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 $f(2.1)$. ::: ::: {.callout-tip collapse="true"} ## Solution: Polynomial Evaluation ```{python} #| eval: false 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. ::: ::: {.callout-note} ## Polynomial Evaluation II Given another polynomial $$g(x) = \frac{a}{x}$$ with $a$ defined above. a) Compute the values of $g(-2)$ and $g(2.1)$. b) What happens when you try to compute $g(0)$? ::: ::: {.callout-tip collapse="true"} ## Solution: Polynomial Evaluation II ```{python} #| eval: false 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!") ``` ::: ::: {.callout-warning} ## 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? ::: ::: {.callout-warning} ## 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? ::: ::: {.callout-note} ## 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. ::: ::: {.callout-tip collapse="true"} ## Solution: Basketball Scoring ```{python} #| eval: false 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}") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution: Currency Converter ```{python} #| eval: false euros = 100 dollars = euros * 1.17 print(f"{euros} Euros is approximately {dollars:.2f} US Dollars") ``` ::: ::: {.callout-note} ## 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. ::: ::: {.callout-tip collapse="true"} ## Solution: Car Fuel and Speed ```{python} #| eval: false 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}") ``` ::: ::: {.callout-warning} ## 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"` ::: --- # String Variables ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution: Substring Extraction ```{python} #| eval: false s = "abcdefg" result = s[1::2] print(result) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false s = "abcdefg" result = s[::2].upper() print(result) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false s = "This is a string" result = s[:3] + s[-2:] print(result) ``` ::: ::: {.callout-note} ## 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!"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false s = " This is a string " s = s.strip() result = s[:3] + s[-2:] print(result) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false u = "abc" v = "xyz" result = v[:2] + u[2:] + " " + u[:2] + v[2:] print(result) ``` ::: ::: {.callout-note} ## 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 ``` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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}") ``` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-warning} ## 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"` ::: *** # Flow Control ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num = 267 if num % 2 == 0: print(f"{num} is an even number") else: print(f"{num} is an odd number") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false a = 10 b = 7 if a % b == 0: print(f"{a} is divisible by {b}") else: print(f"{a} is not divisible by {b}") ``` ::: ::: {.callout-note} ## 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."` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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.") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false s = "o" vowels = "aeiouAEIOU" if s in vowels: print(f"{s} is a vowel") else: print(f"{s} is a consonant") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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") ``` ::: ::: {.callout-note} ## 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 `!?#$`, print: `"Password does not end with a special character"`. - Otherwise, print: `"Password correct"`. *Sample input:* `password = "goodpassword?"` *Expected result:* `"Password correct"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false password = "goodpassword?" if len(password) < 10: print("Password too short") elif password.startswith("admin"): print("Password not allowed: starts with 'admin'") elif password[-1] not in "!?#$": print("Password does not end with a special character") else: print("Password correct") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false s = "tacocat" if s == s[::-1]: print("The string is a palindrome") else: print("The string is not a palindrome") ``` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-warning} ## 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"` ::: --- # Looping ::: {.callout-note} ## 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 ``` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num = 5 print(f"Multiplication Table for {num}:") for i in range(1, 11): print(f"{num} x {i} = {num * i}") ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num = 4 factorial = 1 for i in range(1, num + 1): factorial *= i print(factorial) ``` ::: ::: {.callout-note} ## 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. ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num = 7 limit = 50 multiples = [] for i in range(num, limit, num): multiples.append(str(i)) print(", ".join(multiples)) ``` ::: ::: {.callout-note} ## 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. ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num = 517 digit_sum = 0 while num > 0: digit_sum += num % 10 num //= 10 print(digit_sum) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-note} ## 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. ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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") ``` ::: ::: {.callout-warning} ## Reversed Number Write a program that takes a number as input and outputs the reversed number. *Sample input:* `num = 1435` *Expected result:* `5341` ::: ::: {.callout-warning} ## 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"` ::: ::: {.callout-warning} ## 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"` ::: --- # Functions ## Input/Output Functions ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false num1 = int(input("Enter first number: ")) num2 = int(input("Enter second number: ")) print(f"The sum is {num1 + num2}") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false sentence = input("Enter a sentence: ") print(f"The sentence has {len(sentence)} characters") ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false number = float(input("Enter a number: ")) rounded = round(number, 3) print(f"I have rounded your number to {rounded}") ``` ::: ::: {.callout-note} ## 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!"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false import math number = float(input("Enter a number: ")) if number == int(number): print("Your number is an integer") elif abs(number - math.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 ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false def multiply(x, y): return x * y print(multiply(3, 6)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false def rectangle_area(length, width): return length * width print(rectangle_area(3, 6)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false import math def circle_area(radius): return round(math.pi * radius**2, 2) print(circle_area(1.1)) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false def say_hello(surname, name): return f"Hello {name} {surname}" print(say_hello("Simpson", "Homer")) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false def fahrenheit_to_celsius(fahrenheit): celsius = (fahrenheit - 32) * 5 / 9 return round(celsius, 2) print(fahrenheit_to_celsius(270)) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false def factorial(x): if x <= 0: return 0 result = 1 for i in range(1, x + 1): result *= i return result print(factorial(5)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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!")) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-warning} ## 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` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-warning} ## 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` ::: ::: {.callout-warning} ## 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` ::: ::: {.callout-warning} ## 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` ::: ::: {.callout-warning} ## 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 ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false import math def circle_area(radius, is_diameter=False): if is_diameter: radius = radius / 2 return round(math.pi * radius**2, 2) print(circle_area(1.1)) print(circle_area(2.2, is_diameter=True)) ``` ::: ::: {.callout-note} ## 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` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-note} ## 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"` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)) ``` ::: ::: {.callout-warning} ## 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` ::: --- # Generator Functions ::: {.callout-note} ## 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]` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)]) ``` ::: ::: {.callout-note} ## 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]` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)]) ``` ::: ::: {.callout-note} ## 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]` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)]) ``` ::: ::: {.callout-note} ## 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"]` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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)]) ``` ::: ::: {.callout-note} ## 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]` ::: ::: {.callout-tip collapse="true"} ## Solution ```{python} #| eval: false 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? You can find more exercises and solutions in the [review section](review_fundamentals.qmd). If you want to practice for the quiz and exams, go to the [exam repository](exams.md). ---