Update sieve_of_Eratosthenes.cpp

Multiple changes:
Time complexity updated.
Fixed Indentation issues.
Global array primes[ ] was misleading because primes[x] = 0 means x is prime. Updated the array name to isprime[ ] and now isprime[x] = 1 means x is prime. Updated the code accordingly.

sieve_of_Eratosthenes.cpp

@@ -2,7 +2,7 @@
  * Sieve of Eratosthenes is an algorithm to find the primes 
  * that is between 2 to N (as defined in main).
  *
- * Time Complexity  : O(N)
+ * Time Complexity  : O(N * log N)
  * Space Complexity : O(N)
  */
 
@@ -11,50 +11,49 @@ using namespace std;
 
 #define MAX 10000000
 
-int primes[MAX];
-
+int isprime[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;
+void sieve(int N) {
+    isprime[0] = 0;
+    isprime[1] = 0;
+    for (int i = 2; i <= N; i++) {
+        if (isprime[i]) {
+            for (int j = i * 2; j <= N; j += i) {
+                isprime[j] = 0;
+            }
+        }
     }
 }
 
 /*
  * 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';
+void print(int N) {
+    for (int i = 1; i <= N; i++) {
+        if (isprime[i] == 1) {
+            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;
+void init() {
+    for (int i = 1; i < MAX; i++) {
+        isprime[i] = 1;
+    }
 }
 
-int main()
-{
-  int N = 100;
-  init();
-  sieve(N);
-  print(N);
+int main() {
+    int N = 100;
+    init();
+    sieve(N);
+    print(N);
 }