Complete guideline to be a PRO competitive programmer

Competitive Programming (CP) Math & Concepts Roadmap

This guide is designed for those who want to become top-level competitive programmers worldwide.

It includes all the mathematical concepts and core topics you need to master, along with suggested

resources.

Step 1: Basic Math for CP (Beginner Level)

Topics:

- Prime numbers, Divisibility rules

- GCD, LCM, Euclidean Algorithm

- Modular arithmetic (mod, inverse)

- Combinatorics basics: nCr, permutations

- Fast Exponentiation (Binary exponentiation)

Resources:

- CP-Algorithms: https://cp-algorithms.com

- Book: Competitive Programmer's Handbook - Antti Laaksonen (Chapters 2-4)

Step 2: Number Theory

Topics:

- Fermat's Little Theorem, Euler's Theorem

- Sieve of Eratosthenes

- Prime factorization techniques

- Chinese Remainder Theorem (CRT)

- Modular inverse techniques

Resources:

- CP-Algorithms Number Theory Section

- Book: A Path to Combinatorics for Undergraduates

- YouTube: William Lin math lectures

Step 3: Combinatorics & Probability

Topics:

- Factorials with mod

- Inclusion-Exclusion Principle- Pigeonhole Principle

- Catalan Numbers

- Burnside Lemma (Advanced)

Resources:

- Book: Art of Problem Solving Vol. 1 & 2

- Math StackExchange for problem-solving

Step 4: Geometry

Topics:

- 2D geometry basics (distance, area, angle)

- Cross and dot product

- Convex Hull algorithms

- Line/Circle intersections

- Pick's Theorem

Resources:

- Book: Computational Geometry - de Berg et al.

- CP-Algorithms Geometry Section

- Book: Challenge and Thrill of Pre-College Mathematics

Step 5: Advanced Math Topics

Topics:

- Linear Algebra (matrix exponentiation)

- Fast Fourier Transform (FFT), NTT

- Mobius Function, Euler Totient

- Game Theory (Grundy numbers)

Resources:

- Book: Concrete Mathematics by Knuth

- MIT OpenCourseWare (Discrete Math, Linear Algebra)

Optional: Olympiad Math Books (If Needed)

Topics:

- Art of Problem Solving Vol. 1 & 2

- Problem Solving Strategies - Arthur Engel

- Challenge and Thrill of Pre-College Mathematics (CTPCM)Resources:

- Use these books for deeper insight and creative problem solving.