Modular Arithmetic Basics in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the remainder of 17 divided by 5.

DSA C++

int result = 17 [1] 5;

Drag options to blanks, or click blank then click option'

A*

B%

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using division operator / instead of modulo.

Using multiplication or addition operators.

The modulo operator % gives the remainder of division. Here, 17 % 5 equals 2.

2fill in blank

medium

Complete the code to compute (a + b) modulo m correctly.

DSA C++

int modSum = (a [1] b) % m;

Drag options to blanks, or click blank then click option'

A-

B/

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Taking modulo before adding.

To add two numbers under modulo, add them first then take modulo. So use + operator inside parentheses.

3fill in blank

hard

Fix the error in the code to compute (a * b) modulo m without overflow.

DSA C++

long long modProduct = ((long long)a [1] b) % m;

Drag options to blanks, or click blank then click option'

A*

B-

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication.

Not casting to long long causing overflow.

To multiply two integers safely without overflow, cast one to long long and use the multiplication operator *.

4fill in blank

hard

Fill both blanks to compute (a - b) modulo m correctly, ensuring the result is non-negative.

DSA C++

int modDiff = ((a [1] b) [2] m) % m;

Drag options to blanks, or click blank then click option'

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Not adding m after subtraction causing negative modulo.

Using multiplication or division instead of addition.

Subtract b from a, then add m before taking modulo to avoid negative results.

5fill in blank

hard

Fill all three blanks to create a map of numbers to their squares modulo m for numbers 1 to 5.

DSA C++

std::map<int, int> squares;
for (int [1] = 1; [1] <= 5; ++[1]) {
  squares[[1]] = ([2] [3] [2]) % m;
}

Drag options to blanks, or click blank then click option'

Ai

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong variable names.

Using addition instead of multiplication for square.

Use i as the key and value base, multiply i * i then take modulo m.

Practice

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

easy

A. 5

B. 3

C. 2

D. 0

Solution

1. Step 1: Understand the modulo operation

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

2. Step 2: Calculate 17 % 5

   Dividing 17 by 5 gives 3 with a remainder of 2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   17 divided by 5 leaves remainder 2 [OK]

Hint: Modulo gives remainder after division [OK]

Common Mistakes:

• Confusing modulo with division
• Using 5 instead of remainder
• Ignoring remainder sign

2. Which of the following is the correct syntax to compute the modulo of two integers a and b in C++?

easy

A. a // b

B. a mod b

C. mod(a, b)

D. a % b

Solution

1. Step 1: Recall C++ modulo operator syntax

   In C++, the modulo operator is represented by the percent sign (%).

2. Step 2: Identify correct syntax

   Among the options, only a % b is valid C++ syntax for modulo.

3. Final Answer:

   a % b -> Option D

4. Quick Check:

   C++ uses % for modulo [OK]

Hint: Use % operator for modulo in C++ [OK]

Common Mistakes:

• Using 'mod' keyword
• Using '//' which is floor division in some languages
• Using function call syntax incorrectly

3. What is the output of the following C++ code?

int a = 14;
int b = 4;
int c = (a + b) % 5;
std::cout << c << std::endl;

medium

A. 3

B. 4

C. 2

D. 1

Solution

1. Step 1: Calculate sum inside parentheses

   a + b = 14 + 4 = 18.

2. Step 2: Calculate modulo 5 of the sum

   18 % 5 = 3 because 5 * 3 = 15 and remainder is 3.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   (14 + 4) % 5 = 18 % 5 = 3 [OK]

Hint: Add first, then modulo [OK]

Common Mistakes:

• Modulo before addition
• Wrong remainder calculation
• Confusing output with sum

4. Identify the error in the following C++ code snippet that tries to compute modulo:

int x = 10;
int y = 0;
int z = x % y;
std::cout << z << std::endl;

medium

A. Syntax error in modulo operator

B. Division by zero error

C. Variable z not declared

D. No error, code runs fine

Solution

1. Step 1: Check modulo divisor value

   The divisor y is 0, which is invalid for modulo operation.

2. Step 2: Understand runtime behavior

   Modulo by zero causes a runtime error (division by zero).

3. Final Answer:

   Division by zero error -> Option B

4. Quick Check:

   Modulo divisor cannot be zero [OK]

Hint: Modulo divisor must not be zero [OK]

Common Mistakes:

• Ignoring zero divisor
• Assuming modulo by zero returns zero
• Confusing syntax error with runtime error

5. Given the expression (a * b) % m, which of the following is a correct way to compute it without causing integer overflow in C++ when a and b can be very large?

hard

A. Use ((a % m) * (b % m)) % m

B. Use (a % m) * (b % m)

C. Use ((long long)a * b) % m

D. Use (a * b) % m directly

Solution

1. Step 1: Understand integer overflow risk

   Multiplying large int values a and b directly can cause undefined behavior due to overflow before % m.

2. Step 2: Safe computation using modulo properties

   Using ((a % m) * (b % m)) % m ensures intermediate values stay within range and prevents overflow.

3. Step 3: Why others fail

   ((long long)a * b) % m may still overflow if b is large and not casted. (a % m) * (b % m) misses final modulo. (a * b) % m overflows.

4. Final Answer:

   ((a % m) * (b % m)) % m -> Option A

5. Quick Check:

   Modulo before multiply and after prevents overflow [OK]

Hint: Apply modulo before and after multiplication to avoid overflow [OK]

Common Mistakes:

• Modulo before multiply without final modulo
• Missing final modulo
• Direct multiplication without modulo