Use Cases of Modular arithmetic in Competitive Programming

Modular arithmetic is commanly used in competitive programming and coding contests that require us to calculate the mod of something. It is typically used in combinatorial and probability tasks, where you are asked to calculate a huge number, then told to output it modulo 10^9 + 7. Below are the more use cases of modular arithmetic in CP.

1. Modular arithmetic in Combinatorial Tasks:

In combinatorial tasks, you are often asked to calculate a huge number, then told to output it modulo 10^9 + 7. This is because the number can be so large that it cannot be stored in a variable of any data type. By taking the mod of the number, we reduce its size to a manageable level.

2. Modular arithmetic in Polynomial Arithmetic:

Modular arithmetic is used in polynomial arithmetic to perform addition, subtraction, and multiplication of polynomials under a modulus

3. Modular arithmetic in Hashing Algorithms:

Many hashing algorithms use modular arithmetic to ensure that the hash values they produce fit into a certain range.

4. Modular arithmetic in Probability Tasks:

In probability tasks, you might need to calculate the probability of an event occurring. The probability can be a huge number, and you are often asked to output it modulo 10^9 + 7.

5. Modular arithmetic in Solving Linear Congruence:

Modular arithmetic can be used to solve linear congruence, which are equations of the form ax ≡ b (mod m). These types of problems often appear in number theory and cryptography.

In mathematics, modular arithmetic refers to the arithmetic of integers that wraps around when a certain value is reached, called the modulus. This becomes particularly crucial when handling large numbers in competitive programming. This article “Modular Arithmetic for Competitive Programming” will explore modular arithmetic, its operations, the underlying concepts, and practical applications. By understanding and implementing modular arithmetic, programmers can effectively manage and manipulate large integers, enhancing their skills in competitive programming.