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    Competitive programming involves solving algorithmic problems under constraints, requiring mastery of various techniques, algorithms, and data structures. Below is an overview of essential methods and concepts widely used in competitive programming:

    Number Theory

    Number theory provides tools for solving problems involving integers, primes, and modular arithmetic. Key techniques include binary exponentiation, modular arithmetic, Sieve of Eratosthenes, and Chinese Remainder Theorem.

    Bit Manipulation

    Bit manipulation enables efficient handling of binary data. Techniques like bitwise operations, bit masking, and bitset are crucial for optimizing performance in problems involving binary representations.

    Combinatorics

    Combinatorics focuses on counting and arranging elements. Important concepts include permutations, combinations, Catalan numbers, and the Inclusion-Exclusion Principle.

    Advanced Mathematics

    Advanced mathematical techniques like geometry, matrix exponentiation, and the Pigeonhole Principle are essential for solving complex problems involving mathematical reasoning.

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