Modular Arithmetic Basics in DSA Javascript - Build from Scratch

Modular Arithmetic Basics

📖 Scenario: Imagine you are organizing a circular game where players take turns in a fixed order. After the last player, the turn goes back to the first player. This cycle repeats indefinitely.

🎯 Goal: You will create a small program to find the player number whose turn it is after a certain number of moves using modular arithmetic.

📋 What You'll Learn

Create a variable called totalPlayers with the exact value 5.

Create a variable called movesMade with the exact value 12.

Calculate the current player's turn using modular arithmetic and store it in a variable called currentPlayer.

Print the value of currentPlayer.

💡 Why This Matters

🌍 Real World

Games, scheduling, and circular queues often use modular arithmetic to cycle through options repeatedly.

💼 Career

Understanding modular arithmetic is important for programming tasks involving cycles, hashing, and time calculations.

1

Create the total number of players

Create a variable called totalPlayers and set it to 5.

DSA Javascript

// Your code here

Hint

Use const to create a variable named totalPlayers and assign it the number 5.

2

Create the number of moves made

Create a variable called movesMade and set it to 12.

DSA Javascript

const totalPlayers = 5;
// Your code here

Hint

Use const to create a variable named movesMade and assign it the number 12.

3

Calculate the current player's turn using modular arithmetic

Create a variable called currentPlayer and set it to the remainder of movesMade divided by totalPlayers. Use the modulus operator %.

DSA Javascript

const totalPlayers = 5;
const movesMade = 12;
// Your code here

Hint

Use % to find the remainder when movesMade is divided by totalPlayers.

4

Print the current player's turn

Print the value of currentPlayer using console.log(currentPlayer).

DSA Javascript

const totalPlayers = 5;
const movesMade = 12;
const currentPlayer = movesMade % totalPlayers;
// Your code here

Hint

Use console.log(currentPlayer) to display the current player's number.

Practice

1. What is the result of 7 % 3 in modular arithmetic?

easy

A. 2

B. 3

C. 1

D. 0

Solution

1. Step 1: Understand the modulus operation

   The modulus operator (%) gives the remainder after division of the first number by the second.

2. Step 2: Calculate 7 divided by 3

   7 divided by 3 is 2 with a remainder of 1.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   7 % 3 = 1 [OK]

Hint: Modulus gives remainder after division [OK]

Common Mistakes:

• Confusing modulus with division
• Using 3 instead of remainder
• Thinking modulus returns quotient

2. Which of the following is the correct syntax to compute the remainder of a divided by b in JavaScript?

easy

A. a % b

B. a mod b

C. mod(a, b)

D. a // b

Solution

1. Step 1: Recall JavaScript modulus syntax

   In JavaScript, the modulus operator is the percent sign (%) placed between two numbers or variables.

2. Step 2: Identify correct syntax

   Only a % b correctly computes the remainder of a divided by b.

3. Final Answer:

   a % b -> Option A

4. Quick Check:

   Use % for modulus in JavaScript [OK]

Hint: Use % operator for modulus in JavaScript [OK]

Common Mistakes:

• Using 'mod' keyword
• Using integer division operator //
• Calling a non-existent mod() function

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

const x = 15;
const y = 4;
console.log(x % y);

medium

A. 4

B. 3

C. 0

D. 1

Solution

1. Step 1: Calculate 15 divided by 4

   15 divided by 4 is 3 with a remainder of 3.

2. Step 2: Apply modulus operator

   The expression 15 % 4 returns the remainder, which is 3.

3. Final Answer:

   3 -> Option B

4. Quick Check:

   15 % 4 = 3 [OK]

Hint: Modulus returns remainder after division [OK]

Common Mistakes:

• Confusing remainder with quotient
• Expecting 4 instead of remainder
• Mistaking modulus for division

4. Find the error in the following code snippet that tries to compute the modulus of two numbers:

let a = 10;
let b = 3;
let result = a % b();
console.log(result);

medium

A. Missing semicolon after console.log

B. Modulus operator should be replaced with division

C. Variables a and b should be strings

D. Using parentheses after b causes an error

Solution

1. Step 1: Analyze the modulus expression

   The code uses a % b(), which treats b as a function call, but b is a number, not a function.

2. Step 2: Identify the error

   Parentheses after b cause a runtime error because numbers cannot be called like functions.

3. Final Answer:

   Using parentheses after b causes an error -> Option D

4. Quick Check:

   Variables are not functions, so no () after b [OK]

Hint: Don't add () after variables unless they are functions [OK]

Common Mistakes:

• Adding () after number variables
• Confusing modulus with division
• Ignoring runtime errors

5. You want to find the remainder when the sum of two numbers a = 123456789 and b = 987654321 is divided by 1000. Which expression correctly computes this using modular arithmetic properties?

hard

A. ((a % 1000) + (b % 1000)) % 1000

B. (a % 1000) + (b % 1000)

C. a + b % 1000

D. a % (b % 1000)

Solution

1. Step 1: Recall modular addition property

   The remainder of a sum modulo m equals the sum of remainders modulo m: (a + b) % m = ((a % m) + (b % m)) % m.

2. Step 2: Apply property to given numbers

   Compute (a % 1000) and (b % 1000), add them, then take modulo 1000 again to get correct remainder.

3. Final Answer:

   ((a % 1000) + (b % 1000)) % 1000 -> Option A

4. Quick Check:

   Use modular addition: ((a%m)+(b%m))%m [OK]

Hint: Add remainders then mod again for sum modulus [OK]

Common Mistakes:

• Skipping final modulus after addition
• Adding without modulus
• Using wrong modulus order