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C++/program-28/Readme

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+Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number. 
+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.
+Following is the algorithm to find all the prime numbers less than or equal to a given integer n by the Eratosthene’s method: 
+
+When the algorithm terminates, all the numbers in the list that are not marked are prime. 
+
+Explanation with Example: 
+1. Let us take an example when n = 50. So we need to print all prime numbers smaller than or equal to 50. 
+2. We create a list of all numbers from 2 to 50. 
+3. According to the algorithm we will mark all the numbers which are divisible by 2 and are greater than or equal to the square of it. 
+4. Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3 and are greater than or equal to the square of it. 
+5. We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the square of it. 
+6. We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the square of it. 
+
+
+
+Example:    Input : n =10
+            Output : 2 3 5 7 
+
+            Input : n = 20 
+            Output: 2 3 5 7 11 13 17 19
+
+
+MAIN 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(log(n))) 

C++/program-28/Sieve_of_eratosthenes.cpp

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+// 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 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;
+        }
+    }
+
+    // Print all prime numbers
+    for (int p = 2; p <= n; p++)
+        if (prime[p])
+            cout << p << " ";
+}
+
+// Driver Code
+int main()
+{
+    int n = 30;
+    cout << "Following are the prime numbers smaller "
+         << " than or equal to " << n << endl;
+    SieveOfEratosthenes(n);
+    return 0;
+}