sieve_of_eratosthenes.cpp File Reference

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). More...

#include <iostream>

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Macros
#define	MAX   10000000

Functions
void	sieve (uint32_t N)
void	print (uint32_t N)
void	init ()
int	main ()

Variables
bool	isprime [MAX]

Detailed Description

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).

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

See also

primes_up_to_billion.cpp prime_numbers.cpp

Macro Definition Documentation

MAX

#define MAX   10000000

Maximum number of primes

Function Documentation

init()

void init

(

)

Initialize the array

            {
    for (uint32_t i = 1; i < MAX; i++) {
        isprime[i] = true;
    }
}

main()

int main

(

)

main function

           {
    uint32_t N = 100;
    init();
    sieve(N);
    print(N);
    return 0;
}

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print()

void print

(

uint32_t

N

)

This function prints out the primes to STDOUT

                       {
    for (uint32_t i = 1; i <= N; i++) {
        if (isprime[i]) {
            std::cout << i << ' ';
        }
    }
    std::cout << std::endl;
}

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sieve()

void sieve

(

uint32_t

N

)

This is the function that finds the primes and eliminates the multiples.

                       {
    isprime[0] = false;
    isprime[1] = false;
    for (uint32_t i = 2; i <= N; i++) {
        if (isprime[i]) {
            for (uint32_t j = (i << 1); j <= N; j += i) {
                isprime[j] = false;
            }
        }
    }
}

Variable Documentation

isprime

bool isprime[MAX]

array to store the primes