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Add eratosthenes sieve method for finding primes below given number #672

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Add eratosthenes sieve method for finding primes below given number #672

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6cdb91f
Add eratosthenes sieve method for finding primes below given number
anoopemacs Oct 17, 2020
dc1cb7f
Add Wikipedia link explaining the Sieve of Eratosthenes alogrithm
anoopemacs Oct 18, 2020
f50c966
Fix the three commenting mistakes pointed out by @Panquesito7
anoopemacs Oct 18, 2020
2460c07
updating DIRECTORY.md
Oct 18, 2020
3bfa418
Change variable name to convention, from 'NonPrimers' to 'nonPrimers'
anoopemacs Oct 18, 2020
a3eb8ce
Explain the need for each header and remove unused header <stdio.h>
anoopemacs Oct 18, 2020
a702d15
Fix a mistake in header file need explaination comment
anoopemacs Oct 18, 2020
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72 changes: 72 additions & 0 deletions misc/sieve_of_eratosthenes.c
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/**
* @file
* @brief Get list of prime numbers using Sieve of Eratosthenes
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Provide a Wikipedia link in Markdown format (if possible).
If there's no Wikipedia link, provide another web source for algorithm explanation. 🙂

* @details
* Sieve of Eratosthenes is an algorithm that finds all the primes
* between 2 and N.
*
* Time Complexity : \f$O(N \cdot\log \log N)\f$
* <br/>Space Complexity : \f$O(N)\f$
*
*/

#include <assert.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
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Provide a brief description of the headers (what do they add).

Suggested change
#include <assert.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h> /// for assert
#include <stdbool.h> ///
#include <stdio.h> ///
#include <stdlib.h> ///
#include <string.h> ///


/**
* Return all primes between 2 and the given number
* @param N the largest number to be checked for primality
* @return is_prime a dynamically allocated array of `N + 1` booleans identifying if `i`^th number is a prime or not
*/
bool* sieve(int N)
{
bool* primep = calloc(N+1, 1);
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dynamically allocated memory must be freeed.
In this case, a note should be added to the function that the function free() must be called on the output pointer after its use.

For example, on line# 48, pointer to a new memory is returned. Hence, before the end of that function, there must be a free(primep);

memset(primep, true, N+1);
primep[0] = false; //0 is not a prime number
primep[1] = false; //1 is not a prime number

int i, j;
for (i=2; i!=N/2; ++i)// i!=N+1 also works
for (j=2; j<=N/i; ++j)// i*j <= N also works
primep[i*j] = false;

return primep;
}

/**
* Test function
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Suggested change
* Test function
* @brief Test function

* @return void
*/
void test()
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Suggested change
void test()
static void test()

{
/* all the prime numbers less than 100 */
int primers[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
bool* primep = sieve(100);
for (size_t i = 0, size = sizeof(primers) / sizeof(primers[0]); i < size;
++i)
{
assert(primep[primers[i]]);
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the correct loop check would be:

for (size_t j = 0, p = 0; j < 100; j++) 
{
  if (j == primers[p]) // j is a known prime number
  {
      assert(prime[j]);
      p++; // this variable is used to keep a track of the index of known prime numbers array
  } else { // j is a known composite number
      assert(!prime[j]);
  }
}

This will check that your function ensures that both primes and composites are classified correctly.

}

/* Example Non-prime numbers */
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good code :)
but becomes redundant after the above suggested loop. You can keep this loop as well - I like it as it is a good exercise

int NonPrimers[] = {4, 6, 8, 9, 10, 12, 16, 51};
for (size_t i = 0, size = sizeof(NonPrimers) / sizeof(NonPrimers[0]);
i < size; ++i)
{
assert(!primep[NonPrimers[i]]);
}
}

/**
* Driver Code
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Suggested change
* Driver Code
* @brief Driver Code

* @return None
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Suggested change
* @return None
* @returns 0 on exit

*/
int main()
{
test();
return 0;
}