From 15c0ae012c1e3958e4a911ee648f2d127eb3c325 Mon Sep 17 00:00:00 2001
From: Masoom9587 <93204893+Masoom9587@users.noreply.github.com>
Date: Fri, 21 Oct 2022 12:06:50 +0530
Subject: [PATCH] Sieve of Eratosthenes

The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million or so
#cpp #c++
---
 seive.cpp | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 seive.cpp

diff --git a/seive.cpp b/seive.cpp
new file mode 100644
index 00000000..3fd4caf6
--- /dev/null
+++ b/seive.cpp
@@ -0,0 +1,32 @@
+// the following implementation
+// stores only halves of odd numbers
+// the algorithm is a faster by some constant factors
+
+#include <bitset>
+#include <iostream>
+using namespace std;
+
+bitset<500001> Primes;
+void SieveOfEratosthenes(int n)
+{
+	Primes[0] = 1;
+	for (int i = 3; i*i <= n; i += 2) {
+		if (Primes[i / 2] == 0) {
+			for (int j = 3 * i; j <= n; j += 2 * i)
+				Primes[j / 2] = 1;
+		}
+	}
+}
+
+int main()
+{
+	int n = 100;
+	SieveOfEratosthenes(n);
+	for (int i = 1; i <= n; i++) {
+		if (i == 2)
+			cout << i << ' ';
+		else if (i % 2 == 1 && Primes[i / 2] == 0)
+			cout << i << ' ';
+	}
+	return 0;
+}