documentation and bug fixes

math/sieve_of_eratosthenes.cpp

@@ -1,69 +1,65 @@
-/*
- * Sieve of Eratosthenes is an algorithm to find the primes 
+/**
+ * @file
+ * @brief Get list of prime numbers using Sieve of Eratosthenes
+ * Sieve of Eratosthenes is an algorithm to find the primes
  * that is between 2 to N (as defined in main).
  *
- * Time Complexity  : O(N * log N)
- * Space Complexity : O(N)
+ * Time Complexity  : \f$O(N \cdot\log N)\f$
+ * <br/>Space Complexity : \f$O(N)\f$
+ *
+ * @see primes_up_to_billion.cpp prime_numbers.cpp
  */
 
 #include <iostream>
-using namespace std;
 
+/** Maximum number of primes */
 #define MAX 10000000
 
-int isprime[MAX];
+/** array to store the primes */
+bool isprime[MAX];
 
-/*
- * This is the function that finds the primes and eliminates 
+/**
+ * This is the function that finds the primes and eliminates
  * the multiples.
  */
-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;
+void sieve(uint32_t N) {
+    isprime[0] = false;
+    isprime[1] = false;
+    for (uint32_t i = 2; i <= N; i++) {
+        if (isprime[i]) {
+            for (uint32_t j = (i << 1); j <= N; j += i) {
+                isprime[j] = false;
             }
         }
     }
 }
 
-/*
+/**
  * This function prints out the primes to STDOUT
  */
-void print(int N)
-{
-    for (int i = 1; i <= N; i++)
-    {
-        if (isprime[i] == 1)
-        {
-            cout << i << ' ';
+void print(uint32_t N) {
+    for (uint32_t i = 1; i <= N; i++) {
+        if (isprime[i]) {
+            std::cout << i << ' ';
         }
     }
-    cout << '\n';
+    std::cout << std::endl;
 }
 
-/*
- * NOTE: This function is important for the 
- * initialization of the array.
+/**
+ * Initialize the array
  */
-void init()
-{
-    for (int i = 1; i < MAX; i++)
-    {
-        isprime[i] = 1;
+void init() {
+    for (uint32_t i = 1; i < MAX; i++) {
+        isprime[i] = true;
     }
 }
 
-int main()
-{
-    int N = 100;
+/** main function */
+int main() {
+    uint32_t N = 100;
     init();
     sieve(N);
     print(N);
+    return 0;
 }