sieve_of_eratosthenes.cpp File Reference

Get list of prime numbers using Sieve of Eratosthenes. More...

#include <cassert>
#include <iostream>
#include <vector>

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Functions
std::vector< bool >	sieve (uint32_t N)
void	print (uint32_t N, const std::vector< bool > &is_prime)
void	tests ()
int	main ()

Detailed Description

Get list of prime numbers using Sieve of Eratosthenes.

Sieve of Eratosthenes is an algorithm that finds all the primes between 2 and N.

Time Complexity : \(O(N \cdot\log \log N)\)
Space Complexity : \(O(N)\)

See also

primes_up_to_billion.cpp prime_numbers.cpp

Function Documentation

main()

int main

(

void

)

Main function

           {
    tests();
 
    uint32_t N = 100;
    std::vector<bool> is_prime = sieve(N);
    print(N, is_prime);
    return 0;
}

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print()

void print	(	uint32_t	N,
		const std::vector< bool > &	is_prime
	)

This function prints out the primes to STDOUT

Parameters

N	number of primes to check
is_prime	a vector of N + 1 booleans identifying if i^th number is a prime or not

                                                        {
    for (uint32_t i = 2; i <= N; i++) {
        if (is_prime[i]) {
            std::cout << i << ' ';
        }
    }
    std::cout << std::endl;
}

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sieve()

std::vector< bool > sieve

(

uint32_t

N

)

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.

Parameters

N	number of primes to check

Returns

is_prime a vector of N + 1 booleans identifying if i^th number is a prime or not

                                  {
    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 (is_prime[i]) {
            for (uint32_t j = i * i; j <= N; j += i) {
                is_prime[j] = false;
            }
        }
    }
    return is_prime;
}

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tests()

void tests

(

)

Test implementations

             {
  //                    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);
}

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