9 mod 5

14 mod 12

9 + 5

12 mod 5

The Remainder

The Congruence

The Dividend

The Modulus

5

4

3.57

3

Both operators give the same result.

/ gives the remainder, % gives the quotient.

/ gives a floating-point result, % gives an integer.

/ gives the quotient, % gives the remainder.

8 + 4

(8 + 4) / 10

(8 % 10) + 4

(8 + 4) % 10

$(a + b) \% n = ((a \% n) + (b \% n)) \% n$

$(a + b) \% n = (a \% n) + (b \% n)$

$(a + b) \% n = (a + n) \% (b + n)$

$(a + b) \% n = a \% n + b$

It makes the code run faster.

It is the only way to perform addition in C++.

It helps prevent integer overflow when a and b are very large numbers.

It simplifies debugging by making numbers smaller.

Take the absolute value: abs(-5)

Add the modulus: (-5 % 12) + 12

Multiply by -1: (-5 % 12) * -1

It is not possible to normalize this result.

1

3

150

21

Sort the elements in the table.

Check if the table is full.

Map a large key value to a smaller, valid array index.

Encrypt the data being stored.

'C'

The operation is invalid because it goes past 'Z'.

'B'

'Z'

It produces a negative result.

It can cause a division-by-zero error.

It is much slower than applying the modulus at each step.

The intermediate product a * b might cause an integer overflow, leading to an incorrect final result.

False

True

1

45

5

0

int sub(int a, int b, int m) {
  int res = (a % m - b % m);
  if (res < 0) res += m;
  return res;
}

int sub(int a, int b, int m) {
  return (a % m) - (b % m);
}

int sub(int a, int b, int m) {
  return abs(a - b) % m;
}

int sub(int a, int b, int m) {
  return (a - b) % m;
}