Implemented seive of erathsthenes in cpp

Author: dibyam-jalan27

snippets/cpp/math-and-numbers/sieve-of-eratosthenes.md

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+---
+title: Sieve of Eratosthenes
+description: Generate all prime numbers up to a given integer using the Sieve of Eratosthenes algorithm
+tags: number, prime
+author: dibyam-jalan27
+---
+
+```cpp
+#include <vector>
+
+using namespace std;
+
+vector<int> sieve_of_eratosthenes(int n) {
+    vector<bool> is_prime(n + 1, true);
+    vector<int> primes;
+    is_prime[0] = is_prime[1] = false;
+    for (int i = 2; i * i <= n; ++i) {
+        if (is_prime[i]) {
+            for (int j = i * i; j <= n; j += i) {
+                is_prime[j] = false;
+            }
+        }
+    }
+    for (int i = 2; i <= n; ++i) {
+        if (is_prime[i]) {
+            primes.push_back(i);
+        }
+    }
+    return primes;
+}
+
+// Usage:
+sieve_of_eratosthenes(30); // Returns: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
+```