C++ Program for Sieve of Eratosthenes
Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. For example, if n is 10, the output should be “2, 3, 5, 7”. If n is 20, the output should be “2, 3, 5, 7, 11, 13, 17, 19”.
CPP
// C++ program to print all primes smaller than or equal to // n using Sieve of Eratosthenes #include <bits/stdc++.h> using namespace std; void SieveOfEratosthenes( int n) { // Create a boolean array "prime[0..n]" and initialize // all entries it as true. A value in prime[i] will // finally be false if i is Not a prime, else true. bool prime[n + 1]; memset (prime, true , sizeof (prime)); for ( int p = 2; p * p <= n; p++) { // If prime[p] is not changed, then it is a prime if (prime[p] == true ) { // Update all multiples of p for ( int i = p * p; i <= n; i += p) prime[i] = false ; } } // Print all prime numbers for ( int p = 2; p <= n; p++) if (prime[p]) cout << p << " " ; } // Driver Program to test above function int main() { int n = 30; cout << "Following are the prime numbers smaller " << " than or equal to " << n << endl; SieveOfEratosthenes(n); return 0; } |
Output
Following are the prime numbers smaller than or equal to 30 2 3 5 7 11 13 17 19 23 29
Time Complexity : O ( n* log(logn))
Auxiliary Space : O ( 1 )
Please refer complete article on Sieve of Eratosthenes for more details!