feat: created prime_seive.c (#708)

* created prime_seive.c

This function counts the number of prime numbers in O(nlogn) time.

* Apply suggestions from code review

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* updated prime_seive.c

* Update misc/prime_seive.c

Co-authored-by: David Leal <halfpacho@gmail.com>

* added more changes

please take a look at it

* changed 1000000 to MAX_SIZE

* updated line 10

* changed the code back to original

* eliminated the problem of MAX_SIZE

* added for loop to initialise all elements to 0

* made the changes

* changed the code back to original

i have changed my code back to original as some tests were failing

* removed extra spaces & edited some lines

* added new global variable

* added extra space

* added parameter & return statement

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -254,6 +254,7 @@
   * [Poly Add](https://github.com/TheAlgorithms/C/blob/master/misc/poly_add.c)
   * [Prime](https://github.com/TheAlgorithms/C/blob/master/misc/prime.c)
   * [Prime Factoriziation](https://github.com/TheAlgorithms/C/blob/master/misc/prime_factoriziation.c)
+  * [Prime Seive](https://github.com/TheAlgorithms/C/blob/master/misc/prime_seive.c)
   * [Quartile](https://github.com/TheAlgorithms/C/blob/master/misc/quartile.c)
   * [Rselect](https://github.com/TheAlgorithms/C/blob/master/misc/rselect.c)
   * [Strong Number](https://github.com/TheAlgorithms/C/blob/master/misc/strong_number.c)

misc/prime_seive.c

@@ -0,0 +1,77 @@
+/**
+ * @file
+ * @brief [Prime Seive](https://leetcode.com/problems/count-primes/)
+ * algorithm implementation.
+ * @author [Divyansh Kushwaha](https://github.com/webdesignbydivyansh)
+ */
+#include <assert.h>	/// for assert
+#include <stdio.h>	/// for standard input output
+#include <stdlib.h>	/// for general purpose standard library
+
+const unsigned long long MAX_SIZE = 1000000;  /// variable upto which prime numbers are to be found out
+/**
+ * @addtogroup misc
+ * @{
+ */
+/**
+ * @brief Prime Sieve works in O(nlogn) time
+ * @param p array to be updated
+ * @returns void
+ */
+void prime(int *p)
+{
+	for(long long int i=3;i<=MAX_SIZE;i+=2) { p[i]=1; }
+	for(long long int i=3;i<=MAX_SIZE;i+=2)
+	{
+		if(p[i]==1) {
+		    for(long long int j=i*i;j<=MAX_SIZE;j+=i) {
+			p[j]=0;
+		    }
+		}
+	}
+	p[2]=1;
+	p[0]=p[1]=0;    
+}
+/**
+ * @brief Count func counts the number of 
+ * prime numbers.
+ * @param arr contains the prime numbers
+ * @param size denotes upto which prime numbers are to be found out
+ * @returns count of prime numbers
+ */
+int count(int *arr, const int size){
+  int k=0;
+  for(int i=0;i<=size;i++){
+    if(arr[i]==1){
+      k++;
+    }
+  }
+  return k;
+}
+
+/**
+ * @brief Test implementations
+ * @returns void
+ */
+static void test()
+{
+    // Test Case 1
+    const int size = 10; /* array size */
+    printf("Test Case 1...");
+    int arr[1000005]={0};   /* array to store prime numbers */
+    prime(arr);
+    assert(count(arr,size)==4);
+    printf("Passed\n");
+}
+
+/** 
+ * @brief Main function
+ * @param argc commandline argument count (ignored)
+ * @param argv commandline array of arguments (ignored)
+ * @returns 0 on exit
+ */
+int main(int argc, const char *argv[])
+{
+    test();	// execute the tests
+    return 0;
+}