From 0fd4ca4b1d08ecc7c6e095b9fbd7912a1e25db6e Mon Sep 17 00:00:00 2001
From: Akash Negi <55234838+NegiAkash890@users.noreply.github.com>
Date: Tue, 18 May 2021 20:37:23 +0530
Subject: [PATCH] chore(CPlusPlus): add prime-sieve algorithm (#303)

---
 algorithms/CPlusPlus/Maths/prime-sieve.cpp | 31 ++++++++++++++++++++++
 algorithms/CPlusPlus/README.md             |  1 +
 2 files changed, 32 insertions(+)
 create mode 100644 algorithms/CPlusPlus/Maths/prime-sieve.cpp

diff --git a/algorithms/CPlusPlus/Maths/prime-sieve.cpp b/algorithms/CPlusPlus/Maths/prime-sieve.cpp
new file mode 100644
index 00000000..fb9f2779
--- /dev/null
+++ b/algorithms/CPlusPlus/Maths/prime-sieve.cpp
@@ -0,0 +1,31 @@
+//Sieve of Eratosthenes
+//Print all prime numbers within given range.
+
+#include<bits/stdc++.h>
+using namespace std;
+void PrimeSieve(int n) {
+    vector <int> sieve(n + 1);              //Create a vector array of size n+1
+    fill(sieve.begin(), sieve.end(), 1);    //Fill the array with 1s, which means all numbers are initially assumed to be prime.
+    sieve[0] = 0;                           //Exception:Zero is not a Prime
+    sieve[1] = 0;                           //Exception:One  is not a Prime
+    for (int i = 2; i * i <= n; i++) { 
+        if (sieve[i] == 1) {               //This condition will only be executed if the sieve[i] is prime, mark all the multiples of Prime Numbers as non-prime. 
+            for (int j = i * i; j <= n; j += i) {
+                sieve[j] = 0;              
+            }
+        }
+    }
+    for (int i = 0; i < n; i++) {
+        if (sieve[i] == 1) {
+            cout << i << " ";
+        }
+    }
+    return;                              
+}
+int main() {
+    int n;
+    cin >> n;
+    PrimeSieve(n); //Call the function
+    return 0;     //Time complexity : O(n*log(log(n))), Auxiliary Space: O(1)
+    //Example : n=10 , Output: 2 3 5 7   
+}
diff --git a/algorithms/CPlusPlus/README.md b/algorithms/CPlusPlus/README.md
index 695e4ef2..8be84cb0 100644
--- a/algorithms/CPlusPlus/README.md
+++ b/algorithms/CPlusPlus/README.md
@@ -66,3 +66,4 @@
 # Maths
 1. [Kaprekar Number](Maths/Kaprekar-number.cpp)
 2. [Prime Number](Maths/prime-check.cpp)
+3. [Prime Sieve](Maths/prime-sieve.cpp)