Create sieve_of_eratosthenes.cpp

Author: mujtaba1747

Math/Sieve of Eratosthenes/C++/sieve_of_eratosthenes.cpp

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+// C++ program to print all primes smaller than or equal to 
+// n using Sieve of Eratosthenes in O(n*log(log(n)))
+
+#include <iostream>
+#include<vector> 
+using namespace std;
+
+vector < bool > prime; // vector of bool to store whether number is prime or not.
+void sieve(int n) 
+{ 
+	prime.resize(n + 1); // re-sizing the vector to required size
+
+	for(int j = 0; j <= n; j++)
+		prime[j] = true;        // Initially we consider all numbers to be prime and then sieve them out
+								            // prime[x] is true implies x is a prime number
+
+	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 greater than or 
+			// equal to the square of it 
+			// numbers which are multiple of p and are 
+			// less than p^2 are already been marked. 
+			for (int i=p*p; i<=n; i += p) 
+				prime[i] = false; 
+		} 
+	} 
+} 
+
+// Program to test the algorithm
+int main() 
+{ 
+	int n = 100; 
+	sieve(n);
+	cout << "Following are the prime numbers smaller than or equal to " << n << endl;
+	for(int j = 2; j <= n; j++)
+		if(prime[j])
+			cout << j << endl;  
+	return 0; 
+}