From 34edb993f2c1457be4d8e2eec64ab2bf3c7a9f08 Mon Sep 17 00:00:00 2001
From: Mattrixwv <m_ellison@ymail.com>
Date: Wed, 30 Jun 2021 12:02:13 -0400
Subject: [PATCH] Added function for SieveOfEratosthenes

---
 CSClasses/Algorithms.cs         | 67 ++++++++++++++++++++++++++++++++-
 TestCSClasses/TestAlgorithms.cs | 24 +++++++++++-
 2 files changed, 89 insertions(+), 2 deletions(-)

diff --git a/CSClasses/Algorithms.cs b/CSClasses/Algorithms.cs
index 03ca134..067fbcc 100644
--- a/CSClasses/Algorithms.cs
+++ b/CSClasses/Algorithms.cs
@@ -1,7 +1,7 @@
 //C#/CSClasses/Algorithms.cs
 //Matthew Ellison
 // Created: 08-23-20
-//Modified: 06-29-21
+//Modified: 06-30-21
 //This file contains a class that is used to time the execution time of other programs
 /*
 Copyright (C) 2021  Matthew Ellison
@@ -836,5 +836,70 @@ namespace mee{
 			}
 			return binaryString;
 		}
+		//Sieve of Eratosthenese for generating primes
+		public static IEnumerable<long> SieveOfEratosthenes(){
+			yield return 2;
+
+			//A dictionary for holding the results of all primes that have already been found
+			Dictionary<long, List<long>> dict = new Dictionary<long, List<long>>();
+
+			//Start checking for primes with the number 3 and skip all even numbers
+			for(long possiblePrime = 3;true;possiblePrime += 2){
+				//If possiblePrime is not in the dictionary it is a new prime number
+				//Return it and mark its next multiple
+				if(!dict.ContainsKey(possiblePrime)){
+					yield return possiblePrime;
+					List<long> tempList = new List<long>(){possiblePrime};
+					dict.Add(possiblePrime * possiblePrime, tempList);
+				}
+				//If possiblePrime is in the dictionary it is a composite number
+				else{
+					//Move each witness to it's next multiple
+					foreach(long num in dict[possiblePrime]){
+						if(dict.ContainsKey(num + num + possiblePrime)){
+							dict[num + num + possiblePrime].Add(num);
+						}
+						else{
+							List<long> tempList = new List<long>(){num};
+							dict.Add(num + num + possiblePrime, tempList);
+						}
+					}
+					//We no longer need this, free the memory
+					dict.Remove(possiblePrime);
+				}
+			}
+		}
+		public static IEnumerable<BigInteger> SieveOfEratosthenesBig(){
+			yield return 2;
+
+			//A dictionary for holding the results of all primes that have already been found
+			Dictionary<BigInteger, List<BigInteger>> dict = new Dictionary<BigInteger, List<BigInteger>>();
+
+			//Start checking for priems with the number 3 and skip all even numbers
+			for(BigInteger possiblePrime = 3;true;possiblePrime += 2){
+				//If possiblePrime is not in the dictionary it is a new priem number
+				//Return it and mark its next multiple
+				if(!dict.ContainsKey(possiblePrime)){
+					yield return possiblePrime;
+					List<BigInteger> tempList = new List<BigInteger>(){possiblePrime};
+					dict.Add(possiblePrime * possiblePrime, tempList);
+				}
+				//If possiblePrime is in the dictionary it is a composite number
+				else{
+					//Move each witness to ti's next multiple
+					foreach(BigInteger num in dict[possiblePrime]){
+						if(dict.ContainsKey(num + num + possiblePrime)){
+							dict[num + num + possiblePrime].Add(num);
+						}
+						else{
+							List<BigInteger> tempList = new List<BigInteger>(){num};
+							dict.Add(num + num + possiblePrime, tempList);
+						}
+					}
+					//We no longer need this, free the memory
+					dict.Remove(possiblePrime);
+				}
+			}
+		}
 	}
 }
diff --git a/TestCSClasses/TestAlgorithms.cs b/TestCSClasses/TestAlgorithms.cs
index 4174027..eaa83b7 100644
--- a/TestCSClasses/TestAlgorithms.cs
+++ b/TestCSClasses/TestAlgorithms.cs
@@ -1,7 +1,7 @@
 //C#/CSClasses/TestCSClasses/TestAlgorithms.cs
 //Matthew Ellison
 // Created: 03-11-21
-//Modified: 06-29-21
+//Modified: 06-30-21
 //This file contains the tests for the Algorithms class
 /*
 Copyright (C) 2021  Matthew Ellison
@@ -400,5 +400,27 @@ namespace TestCSClasses{
 			answer = mee.Algorithms.ToBin(bigNum);
 			Assert.AreEqual(correctAnswer, answer, "ToBin big 3 failed");
 		}
+		[TestMethod]
+		public void TestSieveOfEratosthenes(){
+			//Test 1
+			IEnumerator<long> sieve = mee.Algorithms.SieveOfEratosthenes().GetEnumerator();
+			List<long> correctAnswer = new List<long>(){2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
+			List<long> answer = new List<long>();
+			for(int cnt = 0;cnt < 25;++cnt){
+				sieve.MoveNext();
+				answer.Add(sieve.Current);
+			}
+			CollectionAssert.AreEqual(correctAnswer, answer, "SieveOfEratosthenes failed");
+
+			//Test 2
+			IEnumerator<BigInteger> bigSieve = mee.Algorithms.SieveOfEratosthenesBig().GetEnumerator();
+			List<BigInteger> bigCorrectAnswer = new List<BigInteger>(){2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
+			List<BigInteger> bigAnswer = new List<BigInteger>();
+			for(int cnt = 0;cnt < 25;++cnt){
+				bigSieve.MoveNext();
+				bigAnswer.Add(bigSieve.Current);
+			}
+			CollectionAssert.AreEqual(bigCorrectAnswer, bigAnswer, "SieveOfEratosthenesBig failed");
+		}
 	}
 }