Add eratosthenes sieve method for finding primes below given number

DIRECTORY.md

@@ -254,6 +254,7 @@
   * [Prime Factoriziation](https://github.com/TheAlgorithms/C/blob/master/misc/prime_factoriziation.c)
   * [Quartile](https://github.com/TheAlgorithms/C/blob/master/misc/quartile.c)
   * [Rselect](https://github.com/TheAlgorithms/C/blob/master/misc/rselect.c)
+  * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C/blob/master/misc/sieve_of_eratosthenes.c)
   * [Strong Number](https://github.com/TheAlgorithms/C/blob/master/misc/strong_number.c)
   * [Sudoku Solver](https://github.com/TheAlgorithms/C/blob/master/misc/sudoku_solver.c)
   * [Tower Of Hanoi](https://github.com/TheAlgorithms/C/blob/master/misc/tower_of_hanoi.c)

misc/sieve_of_eratosthenes.c

@@ -0,0 +1,72 @@
+/**
+ * @file
+ * @brief Get list of prime numbers using [Sieve of
+ * Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
+ * @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> /// for 'assert' in 'test' function
+#include <stdbool.h> /// for 'bool' type in 'sieve' and 'test' function
+#include <stdlib.h> /// for 'calloc' in 'sieve' function
+#include <string.h> /// for 'memset' in 'sieve' function
+
+/**
+ * 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);
+    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;
+}
+
+/**
+ * @brief Test function
+ * @return void
+ */
+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]]);
+    }
+
+    /* Example Non-prime numbers */
+    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]]);
+    }
+}
+
+/**
+ * @brief Driver Code
+ * @return 0 on exit
+ */
+int main()
+{
+    test();
+    return 0;
+}