Added Sieve of Eratostheness

sieve_of_Eratosthenes.cpp

@@ -0,0 +1,60 @@
+/*
+ * Sieve of Eratosthenes is an algorithm to find the primes 
+ * that is between 2 to N (as defined in main).
+ *
+ * Time Complexity  : O(N)
+ * Space Complexity : O(N)
+ */
+
+#include <iostream>
+using namespace std;
+
+#define MAX 10000000
+
+int primes[MAX];
+
+
+/*
+ * This is the function that finds the primes and eliminates 
+ * the multiples.
+ */
+void sieve(int N)
+{
+  primes[0] = 1;
+  primes[1] = 1;
+  for(int i=2;i<=N;i++)
+    {
+      if(primes[i] == 1) continue;
+      for(int j=i+i;j<=N;j+=i)
+	primes[j] = 1;
+    }
+}
+
+/*
+ * This function prints out the primes to STDOUT
+ */
+void print(int N)
+{
+  for(int i=0;i<=N;i++)
+    if(primes[i] == 0)
+      cout << i << ' ';
+  cout << '\n';
+}
+
+/*
+ * NOTE: This function is important for the 
+ * initialization of the array.
+ */
+void init()
+{
+  for(int i=0;i<MAX;i++)
+    primes[i] = 0;
+}
+
+int main()
+{
+  int N = 100;
+  init();
+  sieve(N);
+  print(N);
+}