From 46bc6738d78de3a05901881c919e8d91a28b8ef4 Mon Sep 17 00:00:00 2001
From: obelisk0114 <obelisk0114@yahoo.com.tw>
Date: Fri, 26 Jul 2019 03:25:38 -0700
Subject: [PATCH] Add doctest to maths/sieve_of_eratosthenes.py and remove
 other/finding_primes.py (#1078)

Both of the two files implemented sieve of eratosthenes.
However, there was a bug in other/finding_primes.py, and the time complexity was larger than the other.
Therefore, remove other/finding_primes.py and add doctest tomaths/sieve_of_eratosthenes.py.
---
 maths/sieve_of_eratosthenes.py | 38 ++++++++++++++++++++++++++++++++--
 other/finding_primes.py        | 21 -------------------
 2 files changed, 36 insertions(+), 23 deletions(-)
 delete mode 100644 other/finding_primes.py

diff --git a/maths/sieve_of_eratosthenes.py b/maths/sieve_of_eratosthenes.py
index cedd04f92..44c7f8a02 100644
--- a/maths/sieve_of_eratosthenes.py
+++ b/maths/sieve_of_eratosthenes.py
@@ -1,19 +1,53 @@
-"""Sieve of Eratosthones."""
+# -*- coding: utf-8 -*-
+
+"""
+Sieve of Eratosthones
+
+The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or equal to a given value.
+Illustration: https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
+Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+
+doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
+Also thanks Dmitry (https://github.com/LizardWizzard) for finding the problem
+"""
+
 
 import math
 
+
 def sieve(n):
-    """Sieve of Eratosthones."""
+    """
+    Returns a list with all prime numbers up to n.
+    
+    >>> sieve(50)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
+    >>> sieve(25)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23]
+    >>> sieve(10)
+    [2, 3, 5, 7]
+    >>> sieve(9)
+    [2, 3, 5, 7]
+    >>> sieve(2)
+    [2]
+    >>> sieve(1)
+    []
+    """
+
     l = [True] * (n + 1)
     prime = []
     start = 2
     end = int(math.sqrt(n))
+
     while start <= end:
+        # If start is a prime
         if l[start] is True:
             prime.append(start)
+
+            # Set multiples of start be False
             for i in range(start * start, n + 1, start):
                 if l[i] is True:
                     l[i] = False
+
         start += 1
 
     for j in range(end + 1, n + 1):
diff --git a/other/finding_primes.py b/other/finding_primes.py
deleted file mode 100644
index 035a14f4a..000000000
--- a/other/finding_primes.py
+++ /dev/null
@@ -1,21 +0,0 @@
-'''
--The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or equal to a given value.
--Illustration: https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
-'''
-from __future__ import print_function
-
-
-from math import sqrt
-def SOE(n):
-    check = round(sqrt(n)) #Need not check for multiples past the square root of n
-    
-    sieve = [False if i <2 else True for i in range(n+1)] #Set every index to False except for index 0 and 1
-    
-    for i in range(2, check):
-        if(sieve[i] == True):                  #If i is a prime  
-            for j in range(i+i, n+1, i):       #Step through the list in increments of i(the multiples of the prime)   
-                sieve[j] = False               #Sets every multiple of i to False 
-    
-    for i in range(n+1):
-        if(sieve[i] == True):
-            print(i, end=" ")