Merge branch 'master' into b-tree

Author: j-rewerts

.github/ISSUE_TEMPLATE/algorithm-request.md

@@ -0,0 +1,26 @@
+---
+name: Algorithm request
+about: Suggest a new algorithm for this project
+title: 'Algorithm request: [NAME]'
+labels: algorithm request
+assignees: ''
+
+---
+
+**Is your algorithm request related to a computational problem? Please describe.**
+A clear and concise description of what the problem is. For example, I am working on the Traveling Sales Man problem, LeetCode problem #123456 and I'd like to ...
+
+**Describe the solution you'd like**
+A clear and concise description of what you want to happen. For example:
+
+> I'd like to have an algorithm with following interface: [...], where I can define a graph-like map with an visitor iterator function and then ...
+
+Or, more concretely:
+
+> I'd like to have an implementation of the A* Search Algorithm, based on the following research paper: [Near Optimal Hierarchical Path-Finding - Botea, Mueller & Schaeffer](https://webdocs.cs.ualberta.ca/~mmueller/ps/hpastar.pdf).
+
+**Describe alternatives you've considered**
+A clear and concise description of any alternative solutions or features you've considered.
+
+**Additional context**
+Add any other context or screenshots about the feature request here.

.github/ISSUE_TEMPLATE/bug_report.md

@@ -0,0 +1,38 @@
+---
+name: Bug report
+about: Create a report to help us improve
+title: ''
+labels: ''
+assignees: ''
+
+---
+
+**Describe the bug**
+A clear and concise description of what the bug is.
+
+**To Reproduce**
+Steps to reproduce the behavior:
+1. Go to '...'
+2. Click on '....'
+3. Scroll down to '....'
+4. See error
+
+**Expected behavior**
+A clear and concise description of what you expected to happen.
+
+**Screenshots**
+If applicable, add screenshots to help explain your problem.
+
+**Desktop (please complete the following information):**
+ - OS: [e.g. iOS]
+ - Browser [e.g. chrome, safari]
+ - Version [e.g. 22]
+
+**Smartphone (please complete the following information):**
+ - Device: [e.g. iPhone6]
+ - OS: [e.g. iOS8.1]
+ - Browser [e.g. stock browser, safari]
+ - Version [e.g. 22]
+
+**Additional context**
+Add any other context about the problem here.

.github/ISSUE_TEMPLATE/data-structure-request.md

@@ -0,0 +1,26 @@
+---
+name: Data structure request
+about: Suggest a new data strcuture for this project
+title: 'Data structure request: [NAME]'
+labels: data structure request
+assignees: ''
+
+---
+
+**Is your data structure request related to a computational problem? Please describe.**
+A clear and concise description of what the problem is. For example, I am working on a new dictionary implementation and I'd like the internal functionality to be based on a BTree implementation.
+
+**Describe the solution you'd like**
+A clear and concise description of what you want to happen. For example:
+
+> I'd like to have a generic BTree implementation where I can specify the types of the keys and values, so that I can define a higher-level interface for a dictionary based on that.
+
+Or, more concretely:
+
+> I'd like to have an implementation of the BTree Data Structure, based on the following research paper: [Organization and Maintenance of Large Ordered Indexes - Bayer & McCreight](https://infolab.usc.edu/csci585/Spring2010/den_ar/indexing.pdf).
+
+**Describe alternatives you've considered**
+A clear and concise description of any alternative solutions or features you've considered.
+
+**Additional context**
+Add any other context or screenshots about the feature request here.

.github/ISSUE_TEMPLATE/feature_request.md

@@ -0,0 +1,22 @@
+---
+name: Feature request
+about: Suggest an idea for this project
+title: ''
+labels: feature
+assignees: ''
+
+---
+
+# THIS IS NOT A REQUEST FOR ALGORITHMS OR DATA STRUCTURES - FOR THAT USE THE APPROPRIATE TEMPLATE. THIS TEMPLATE IS FOR PROJECT-LEVEL FEATURES, E.G.: PACKAGING, CI/CD, NUGET ... ETC
+
+**Is your feature request related to a problem? Please describe.**
+A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]
+
+**Describe the solution you'd like**
+A clear and concise description of what you want to happen.
+
+**Describe alternatives you've considered**
+A clear and concise description of any alternative solutions or features you've considered.
+
+**Additional context**
+Add any other context or screenshots about the feature request here.

Algorithms/Numeric/GreatestCommonDivisor.cs

@@ -1,46 +1,73 @@
-/***
- * Euclidean Algorithm to find the greatest common divisor of two numbers.
- * 
- */
-
+using System;
 
 namespace Algorithms.Numeric
 {
     public static class GreatestCommonDivisor
     {
         /// <summary>
-        /// Finds and returns the greatest common divisor of two numbers
+        ///     Returns the greatest common divisor of two numbers using Euclidean Algorithm.
         /// </summary>
-        public static uint FindGCD(uint a, uint b)
+        public static int FindGCDEuclidean(int a, int b)
         {
+            a = Math.Abs(a);
+            b = Math.Abs(b);
+
             if (a == 0)
                 return b;
             if (b == 0)
                 return a;
+            if (a == b)
+                return a;
 
-            uint _a = a, _b = b;
-            
-            //Bitwise operator '&' works on individual bits of each value
-            //result is 0 or 1
-            //it works like a modulus operator '%' but is more efficient
-            uint r = _a & _b;
+            return Euclidean(a, b);
+        }
 
-            while(r != 0)
-            {
-                _a = _b;
-                _b = r;
-                r = _a & _b;
-            }
+        private static int Euclidean(int a, int b)
+        {
+            if (b == 0)
+                return a;
 
-            return _b;
+            return Euclidean(b, a % b);
         }
 
         /// <summary>
-        /// Determines given two numbers are relatively prime
+        ///     Returns the greatest common divisor of two numbers using Stein Algorithm.
         /// </summary>
-        public static bool IsRelativelyPrime(uint a, uint b)
+        public static int FindGCDStein(int a, int b)
+        {
+            a = Math.Abs(a);
+            b = Math.Abs(b);
+
+            return Stein(a, b);
+        }
+
+        private static int Stein(int a, int b)
         {
-            return FindGCD(a, b) == 1;
+            if (a == 0)
+                return b;
+            if (b == 0)
+                return a;
+            if (a == b)
+                return a;
+
+            if ((~a & 1) == 1)
+            {
+                if ((b & 1) == 1)
+                {
+                    return Stein(a >> 1, b);
+                }
+                else
+                {
+                    return Stein(a >> 1, b >> 1) << 1;
+                }
+            }
+
+            if ((~b & 1) == 1)
+            {
+                return Stein(a, b >> 1);
+            }
+
+            return a > b ? Stein((a - b) >> 1, b) : Stein(a, (b - a) >> 1);
         }
     }
 }

Algorithms/Numeric/SieveOfAtkin.cs

@@ -0,0 +1,73 @@
+using System.Collections.Generic;
+using System.Reflection.Metadata.Ecma335;
+using System.Threading.Tasks;
+
+/***
+* Generates all prime numbers up to a given number
+* Wikipedia: https://en.wikipedia.org/wiki/Sieve_of_Atkin
+*/
+
+
+namespace Algorithms.Numeric
+{
+    public static class SieveOfAtkin
+    {
+        /// <summary>
+        /// Calculate primes up to a given number
+        /// </summary>
+        public static List<int> GeneratePrimesUpTo(int max)
+        {
+            if (max == 2)
+            {
+                return new List<int>() { 2 };
+            }
+
+            if (max < 2)
+            {
+                return new List<int>();
+            }
+
+            var isPrime = new bool[max + 1];
+            var sqrt = (int)System.Math.Sqrt(max);
+
+            Parallel.For(1, sqrt, x =>
+            {
+                var xx = x * x;
+                for (var y = 1; y <= sqrt; y++)
+                {
+                    var yy = y * y;
+                    var n = 4 * xx + yy;
+                    if (n <= max && (n % 12 == 1 || n % 12 == 5))
+                        isPrime[n] ^= true;
+
+                    n = 3 * xx + yy;
+                    if (n <= max && n % 12 == 7)
+                        isPrime[n] ^= true;
+
+                    n = 3 * xx - yy;
+                    if (x > y && n <= max && n % 12 == 11)
+                        isPrime[n] ^= true;
+                }
+            });
+
+            var primes = new List<int>() { 2, 3 };
+            for (var n = 5; n <= sqrt; n++)
+            {
+                if (isPrime[n])
+                {
+                    primes.Add(n);
+                    var nn = n * n;
+                    for (var k = nn; k <= max; k += nn)
+                        isPrime[k] = false;
+                }
+            }
+
+            for (var n = sqrt + 1; n <= max; n++)
+                if (isPrime[n])
+                    primes.Add(n);
+
+            return primes;
+        }
+
+    }
+}

Algorithms/Numeric/SieveOfEratosthenes.cs

@@ -1,5 +1,6 @@
 using System;
 using System.Collections.Generic;
+using System.Linq;
 
 /***
 * Generates all prime numbers up to a given number
@@ -14,43 +15,43 @@ public static class SieveOfEratosthenes
         /// <summary>
         /// Calculate primes up to a given number
         /// </summary>
-        public static List<int> GeneratePrimesUpTo(int x)
+        public static IEnumerable<int> GeneratePrimesUpTo(int x)
         {
 
-            //The list of primes that will be returned
-            List<int> primesList = new List<int>();
+            //The hash of primes that will be returned
+            var primes = new HashSet<int>();
 
             //Returns an empty list if x is a value under 2
             if (x < 2)
             {
-                return primesList;
+                return primes.ToList();
             }
 
-            //Adds every number between 2 and x to the list
+            //Adds every number between 2 and x to the hashset
             for (int i = 2; i <= x; i++)
             {
-                primesList.Add(i);
+                primes.Add(i);
             }
 
-            //integer that all multiples of will be removed from the list
+            //integer that all multiples of will be removed from the hashset
             int removeMultiplesOf;
 
-            //Finds the next number in the list that hasn't been removed and removes all multiples of that number 
-            //from the list
+            //Finds the next number that hasn't been removed and removes all multiples of that number 
+            //from the hashset
             for (int i = 2; i <= Math.Sqrt(x); i++)
             {
-                if (primesList.Contains(i))
+                if (primes.Contains(i))
                 {
                     removeMultiplesOf = i;
-                    for (int j = removeMultiplesOf*removeMultiplesOf; j <= x; j += removeMultiplesOf)
+                    for (int j = removeMultiplesOf * removeMultiplesOf; j <= x; j += removeMultiplesOf)
                     {
-                        primesList.Remove(j);
+                        primes.Remove(j);
                     }
                 }
             }
 
             //The list of primes is returned
-            return primesList;
+            return primes.ToList();
         }
 
     }