“ACM算法编程模板：最大公约数、最小公倍数、素数相关及中国剩余定理”

ACM algorithm programming code template is a comprehensive guide for programmers to effectively solve mathematical problems. It covers a wide range of topics such as the greatest common divisor, least common multiple, prime numbers, and modular arithmetic. One of the key algorithms mentioned in the template is the Euclidean algorithm for finding the greatest common divisor in O(n) time complexity. This algorithm is useful for finding the largest number that divides two given numbers without a remainder. Another important algorithm is the Stein algorithm, which calculates the greatest common divisor in O(log(max(a,b))) time complexity. This algorithm is more efficient than the Euclidean algorithm for large numbers. The template also includes information on finding the least common multiple of two numbers. The least common multiple is the smallest number that is divisible by both given numbers. This can be calculated using various methods such as prime factorization and the Euclidean algorithm. In terms of prime numbers, the template covers basic prime number checking algorithms and sieving methods. Prime numbers are numbers that are only divisible by 1 and themselves. The template also introduces the Miller-Rabin primality test method, which is used to efficiently determine if a given number is prime. The template also discusses modular arithmetic and its properties, including the Chinese Remainder Theorem. Modular arithmetic involves performing arithmetic operations with respect to a modulus. This is useful in cryptography and computer science for calculations involving large numbers. Overall, the ACM algorithm programming code template provides a detailed overview of essential mathematical algorithms and techniques for solving complex problems. It is a valuable resource for programmers and mathematicians looking to improve their problem-solving skills and efficiency.