Modular Arithmetic Basics in DSA Python - Build from Scratch

Modular Arithmetic Basics

📖 Scenario: Imagine you are organizing a game where players take turns in a circle. You want to find out which player's turn it is after a certain number of moves. This is a classic use of modular arithmetic.

🎯 Goal: You will create a small program that uses modular arithmetic to find the current player's turn number after a given number of moves.

📋 What You'll Learn

Create a variable for the total number of players.

Create a variable for the number of moves made.

Calculate the current player's turn using modular arithmetic.

Print the current player's turn number.

💡 Why This Matters

🌍 Real World

Modular arithmetic is used in scheduling, cryptography, computer graphics, and anywhere cycles or repeating patterns occur.

💼 Career

Understanding modular arithmetic is important for software developers, especially in game development, security, and algorithm design.

1

Create variables for players and moves

Create a variable called total_players and set it to 5. Then create a variable called moves_made and set it to 12.

DSA Python

# Create variables total_players and moves_made with values 5 and 12
# Your code here

Hint

Use simple assignment to create the variables with the exact values.

2

Calculate current player's turn using modular arithmetic

Create a variable called current_turn that stores the result of moves_made % total_players. This will give the remainder when moves_made is divided by total_players.

DSA Python

total_players = 5
moves_made = 12
# Calculate current_turn using modular arithmetic
# Your code here

Hint

Use the modulus operator % to find the remainder.

3

Adjust current turn for zero remainder

Since player numbers start at 1, create an if statement that checks if current_turn is 0. If it is, set current_turn to total_players.

DSA Python

total_players = 5
moves_made = 12
current_turn = moves_made % total_players
# Adjust current_turn if it is 0
# Your code here

Hint

Use an if statement to check and update current_turn.

4

Print the current player's turn

Print the value of current_turn using print(current_turn).

DSA Python

total_players = 5
moves_made = 12
current_turn = moves_made % total_players
if current_turn == 0:
    current_turn = total_players
# Print current_turn
# Your code here

Hint

Use the print function to display the current player's turn.

Practice

1. What is the result of 17 % 5 in modular arithmetic?

easy

A. 3

B. 2

C. 5

D. 12

Solution

1. Step 1: Understand the modulo operation

   The modulo operator (%) gives the remainder when the first number is divided by the second.

2. Step 2: Calculate 17 divided by 5

   17 divided by 5 is 3 with a remainder of 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   17 % 5 = 2 [OK]

Hint: Modulo gives remainder after division [OK]

Common Mistakes:

• Confusing modulo with division
• Using subtraction instead of modulo
• Mixing up dividend and divisor

2. Which of the following is the correct syntax to compute the remainder of 25 divided by 4 in Python?

easy

A. remainder = 25 % 4

B. remainder = 25 mod 4

C. remainder = 25 // 4

D. remainder = 25 / 4

Solution

1. Step 1: Recall Python modulo operator

   In Python, the modulo operator is the percent sign (%).

2. Step 2: Check each option

   remainder = 25 % 4 uses 25 % 4 which correctly computes the remainder. remainder = 25 mod 4 uses 'mod' which is not valid syntax. remainder = 25 // 4 uses floor division (//) which gives quotient, not remainder. remainder = 25 / 4 uses normal division (/), which gives a float result.

3. Final Answer:

   remainder = 25 % 4 -> Option A

4. Quick Check:

   Use % for modulo in Python [OK]

Hint: Use % symbol for modulo in Python [OK]

Common Mistakes:

• Using 'mod' keyword
• Confusing // with %
• Using / instead of %

3. What is the output of the following Python code?

for i in range(1, 6):
    print(i % 3, end=' ')

medium

A. 0 1 2 0 1

B. 1 2 3 1 2

C. 1 2 0 1 2

D. 1 2 0 2 1

Solution

1. Step 1: Understand the loop and modulo

   The loop runs i from 1 to 5. For each i, we compute i % 3.

2. Step 2: Calculate each modulo

   1 % 3 = 1, 2 % 3 = 2, 3 % 3 = 0, 4 % 3 = 1, 5 % 3 = 2.

3. Final Answer:

   1 2 0 1 2 -> Option C

4. Quick Check:

   Modulo cycles every 3 numbers [OK]

Hint: Modulo repeats remainder pattern every divisor [OK]

Common Mistakes:

• Starting loop at 0 instead of 1
• Miscomputing modulo for 3
• Confusing modulo with division

4. Find the error in the following code snippet that tries to compute n % 4 for n = 10:

n = 10
result = n %
print(result)

medium

A. Missing operand after % operator

B. Incorrect variable name

C. Using print without parentheses

D. No error, code runs fine

Solution

1. Step 1: Analyze the modulo expression

   The line 'result = n %' is incomplete because modulo requires two operands: dividend and divisor.

2. Step 2: Identify syntax error

   Without a number or variable after %, Python will raise a syntax error.

3. Final Answer:

   Missing operand after % operator -> Option A

4. Quick Check:

   Modulo needs two numbers: a % b [OK]

Hint: Modulo operator needs both numbers [OK]

Common Mistakes:

• Leaving out divisor after %
• Using print without () in Python 3
• Typos in variable names

5. You want to find the remainder when the sum of numbers from 1 to 100 is divided by 7. Which Python expression correctly computes this using modular arithmetic?

hard

A. sum(i for i in range(1, 101)) // 7

B. (sum(range(1, 101)) // 7) % 7

C. sum(i % 7 for i in range(1, 101))

D. sum(range(1, 101)) % 7

Solution

1. Step 1: Understand the problem

   We want the remainder of the sum of numbers 1 to 100 divided by 7.

2. Step 2: Evaluate each option

   sum(range(1, 101)) % 7 correctly sums all numbers then applies modulo 7. (sum(range(1, 101)) // 7) % 7 first does floor division to get quotient then % 7, which is incorrect. sum(i % 7 for i in range(1, 101)) sums remainders but does not apply modulo to the total sum, so it gives a wrong result. sum(i for i in range(1, 101)) // 7 uses floor division (//) which gives quotient, not remainder.

3. Final Answer:

   sum(range(1, 101)) % 7 -> Option D

4. Quick Check:

   Sum then modulo gives remainder [OK]

Hint: Sum first, then modulo for remainder [OK]

Common Mistakes:

• Applying modulo inside sum without final modulo
• Using floor division instead of modulo
• Using floor division before modulo