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fix, test: Refactor of sieve_of_eratosthenes (#969)

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* fix, test: Refactor of sieve_of_eratosthenes

* Add missing include.

* Modernize the vector initialization.

* Add @details for the documentation.
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Filip Hlasek 2020-07-23 04:50:38 -07:00 committed by GitHub
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math/sieve_of_eratosthenes.cpp
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@ -1,58 +1,72 @@
/**
* @file
* @brief Get list of prime numbers using Sieve of Eratosthenes
* Sieve of Eratosthenes is an algorithm to find the primes
* that is between 2 to N (as defined in main).
* @details
* Sieve of Eratosthenes is an algorithm that finds all the primes
* between 2 and N.
*
* Time Complexity : \f$O(N \cdot\log N)\f$
* Time Complexity : \f$O(N \cdot\log \log N)\f$
* <br/>Space Complexity : \f$O(N)\f$
*
* @see primes_up_to_billion.cpp prime_numbers.cpp
*/
#include <iostream> // for io operations
#include <cassert>
#include <iostream>
#include <vector>
/**
* This is the function that finds the primes and eliminates
* the multiples.
* This is the function that finds the primes and eliminates the multiples.
* Contains a common optimization to start eliminating multiples of
* a prime p starting from p * p since all of the lower multiples
* have been already eliminated.
* @param N number of primes to check
* @param [out] isprime a boolean array of size `N` identifying if `i`^th number is prime or not
* @return is_prime a vector of `N + 1` booleans identifying if `i`^th number is a prime or not
*/
void sieve(uint32_t N, bool *isprime) {
isprime[0] = true;
isprime[1] = true;
std::vector<bool> sieve(uint32_t N) {
std::vector<bool> is_prime(N + 1, true);
is_prime[0] = is_prime[1] = false;
for (uint32_t i = 2; i * i <= N; i++) {
if (!isprime[i]) {
for (uint32_t j = (i << 1); j <= N; j = j + i) {
isprime[j] = true;
if (is_prime[i]) {
for (uint32_t j = i * i; j <= N; j += i) {
is_prime[j] = false;
}
}
}
return is_prime;
}
/**
* This function prints out the primes to STDOUT
* @param N number of primes to check
* @param [in] isprime a boolean array of size `N` identifying if `i`^th number is prime or not
* @param is_prime a vector of `N + 1` booleans identifying if `i`^th number is a prime or not
*/
void print(uint32_t N, const bool *isprime) {
void print(uint32_t N, const std::vector<bool> &is_prime) {
for (uint32_t i = 2; i <= N; i++) {
if (!isprime[i]) {
if (is_prime[i]) {
std::cout << i << ' ';
}
}
std::cout << std::endl;
}
/**
* Test implementations
*/
void tests() {
// 0 1 2 3 4 5 6 7 8 9 10
std::vector<bool> ans{false, false, true, true, false, true, false, true, false, false, false};
assert(sieve(10) == ans);
}
/**
* Main function
*/
int main() {
uint32_t N = 100;
bool *isprime = new bool[N];
sieve(N, isprime);
print(N, isprime);
delete[] isprime;
tests();
uint32_t N = 100;
std::vector<bool> is_prime = sieve(N);
print(N, is_prime);
return 0;
}