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649a145234
* Update sieve_of_eratosthenes.cpp * Update doc --------- Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com>
123 lines
4.1 KiB
C++
123 lines
4.1 KiB
C++
/**
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* @file
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* @brief Prime Numbers using [Sieve of
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* Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
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* @details
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* Sieve of Eratosthenes is an algorithm that finds all the primes
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* between 2 and N.
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*
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* Time Complexity : \f$O(N \cdot\log \log N)\f$
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* <br/>Space Complexity : \f$O(N)\f$
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*
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* @see primes_up_to_billion.cpp prime_numbers.cpp
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*/
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#include <cassert> /// for assert
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#include <iostream> /// for IO operations
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#include <vector> /// for std::vector
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/**
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* @namespace math
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* @brief Mathematical algorithms
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*/
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namespace math {
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/**
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* @namespace sieve_of_eratosthenes
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* @brief Functions for finding Prime Numbers using Sieve of Eratosthenes
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*/
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namespace sieve_of_eratosthenes {
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/**
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* @brief Function to sieve out the primes
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* @details
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* This function finds all the primes between 2 and N using the Sieve of
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* Eratosthenes algorithm. It starts by assuming all numbers (except zero and
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* one) are prime and then iteratively marks the multiples of each prime as
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* non-prime.
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*
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* Contains a common optimization to start eliminating multiples of
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* a prime p starting from p * p since all of the lower multiples
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* have been already eliminated.
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* @param N number till which primes are to be found
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* @return is_prime a vector of `N + 1` booleans identifying if `i`^th number is
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* a prime or not
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*/
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std::vector<bool> sieve(uint32_t N) {
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std::vector<bool> is_prime(N + 1, true); // Initialize all as prime numbers
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is_prime[0] = is_prime[1] = false; // 0 and 1 are not prime numbers
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for (uint32_t i = 2; i * i <= N; i++) {
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if (is_prime[i]) {
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for (uint32_t j = i * i; j <= N; j += i) {
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is_prime[j] = false;
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}
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}
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}
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return is_prime;
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}
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/**
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* @brief Function to print the prime numbers
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* @param N number till which primes are to be found
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* @param is_prime a vector of `N + 1` booleans identifying if `i`^th number is
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* a prime or not
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*/
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void print(uint32_t N, const std::vector<bool> &is_prime) {
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for (uint32_t i = 2; i <= N; i++) {
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if (is_prime[i]) {
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std::cout << i << ' ';
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}
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}
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std::cout << std::endl;
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}
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} // namespace sieve_of_eratosthenes
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} // namespace math
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/**
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* @brief Self-test implementations
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* @return void
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*/
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static void tests() {
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std::vector<bool> is_prime_1 =
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math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(10));
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std::vector<bool> is_prime_2 =
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math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(20));
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std::vector<bool> is_prime_3 =
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math::sieve_of_eratosthenes::sieve(static_cast<uint32_t>(100));
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std::vector<bool> expected_1{false, false, true, true, false, true,
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false, true, false, false, false};
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assert(is_prime_1 == expected_1);
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std::vector<bool> expected_2{false, false, true, true, false, true,
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false, true, false, false, false, true,
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false, true, false, false, false, true,
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false, true, false};
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assert(is_prime_2 == expected_2);
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std::vector<bool> expected_3{
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false, false, true, true, false, true, false, true, false, false,
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false, true, false, true, false, false, false, true, false, true,
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false, false, false, true, false, false, false, false, false, true,
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false, true, false, false, false, false, false, true, false, false,
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false, true, false, true, false, false, false, true, false, false,
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false, false, false, true, false, false, false, false, false, true,
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false, true, false, false, false, false, false, true, false, false,
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false, true, false, true, false, false, false, false, false, true,
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false, false, false, true, false, false, false, false, false, true,
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false, false, false, false, false, false, false, true, false, false,
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false};
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assert(is_prime_3 == expected_3);
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std::cout << "All tests have passed successfully!\n";
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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tests();
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return 0;
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}
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