From a06995a686c0509f50a481e7d7d41bb35ffe8f19 Mon Sep 17 00:00:00 2001
From: Shubham Lad <30789414+ShuLaPy@users.noreply.github.com>
Date: Mon, 21 Oct 2019 23:40:19 +0530
Subject: [PATCH] add simple improved Sieve Of Eratosthenes Algorithm (#1412)

* add simple improved Sieve Of Eratosthenes Algorithm

* added doctests

* name changed
---
 maths/prime_sieve_eratosthenes.py | 41 +++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 maths/prime_sieve_eratosthenes.py

diff --git a/maths/prime_sieve_eratosthenes.py b/maths/prime_sieve_eratosthenes.py
new file mode 100644
index 000000000..7d039aaad
--- /dev/null
+++ b/maths/prime_sieve_eratosthenes.py
@@ -0,0 +1,41 @@
+'''
+Sieve of Eratosthenes
+
+Input : n =10
+Output : 2 3 5 7 
+
+Input : n = 20 
+Output: 2 3 5 7 11 13 17 19
+
+you can read in detail about this at 
+https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+'''
+
+def prime_sieve_eratosthenes(num):
+    """
+    print the prime numbers upto n
+    
+    >>> prime_sieve_eratosthenes(10)
+    2 3 5 7 
+    >>> prime_sieve_eratosthenes(20)
+    2 3 5 7 11 13 17 19 
+    """
+    
+    
+    primes = [True for i in range(num + 1)]
+    p = 2
+    
+    while p * p <= num:
+        if primes[p] == True:
+            for i in range(p*p, num+1, p):
+                primes[i] = False
+        p+=1
+
+    for prime in range(2, num+1):
+        if primes[prime]:
+            print(prime, end=" ")
+
+if __name__ == "__main__":
+    num = int(input())
+    
+    prime_sieve_eratosthenes(num)