Add Problem009 and refactor Problem007

src/ProjectEuler/ProjectEuler.Problems/Helpers/Funcs.cs

@@ -1,11 +1,44 @@
 using System;
+using System.Linq;
 using static System.String;
 using static System.Environment;
+using static System.Math;
 
 namespace ProjectEuler.Problems.Helpers
 {
     public static class Funcs
     {
+        /// <summary>
+        /// Sieve of Eratosthenes
+        /// <see cref="http://www.wikizero.biz/index.php?q=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvU2lldmVfb2ZfRXJhdG9zdGhlbmVz"/>
+        /// </summary>
+        public static int[] Sieve(int upperBound)
+        {
+            if (upperBound < 2) return new int[0];
+
+            var isComposite = new bool[upperBound + 1];
+            var primes = new int[upperBound / (int)Log10(upperBound)];
+
+            isComposite[0] = isComposite[1] = true;
+
+            for (var i = 2; i * i <= upperBound; i++)
+            {
+                if (isComposite[i]) continue;
+                for (var j = i * i; j <= upperBound; j += i)
+                    isComposite[j] = true;
+            }
+
+            var p = 0;
+            for (var k = 0; k <= upperBound; k++)
+            {
+                if (isComposite[k]) continue;
+                primes[p] = k;
+                p++;
+            }
+
+            return primes.TakeWhile(i => i > 0).ToArray();
+        }
+
         public static string ToText(this int[] values)
         {
             const int colSize  = 7;

src/ProjectEuler/ProjectEuler.Problems/Solutions/Problem007.cs

@@ -1,6 +1,5 @@
-using System.Linq;
-using ProjectEuler.Problems.Helpers;
-using static System.Math;
+using ProjectEuler.Problems.Helpers;
+using static ProjectEuler.Problems.Helpers.Funcs;
 
 namespace ProjectEuler.Problems.Solutions
 {
@@ -21,36 +20,5 @@ public class Problem007 : IProblem
             "What is the 10 001st prime number?";
 
         public string GetSolution() => Sieve(UpperBound).ToText();
-
-        /// <summary>
-        /// Sieve of Eratosthenes
-        /// <see cref="http://www.wikizero.biz/index.php?q=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvU2lldmVfb2ZfRXJhdG9zdGhlbmVz"/>
-        /// </summary>
-        private static int[] Sieve(int upperBound)
-        {
-            if (upperBound < 2) return new int[0];
-
-            var isComposite = new bool[upperBound + 1];
-            var primes = new int[upperBound / (int)Log10(upperBound)];
-
-            isComposite[0] = isComposite[1] = true;
-
-            for (var i = 2; i * i <= upperBound; i++)
-            {
-                if (isComposite[i]) continue;
-                for (var j = i * i; j <= upperBound; j += i)
-                    isComposite[j] = true;
-            }
-
-            var p = 0;
-            for (var k = 0; k <= upperBound; k++)
-            {
-                if (isComposite[k]) continue;
-                primes[p] = k;
-                p++;
-            }
-
-            return primes.Where(i => i > 0).ToArray();
-        }
     }
 }

src/ProjectEuler/ProjectEuler.Problems/Solutions/Problem009.cs

@@ -0,0 +1,41 @@
+using System;
+
+namespace ProjectEuler.Problems.Solutions
+{
+    /// <summary>
+    /// Special Pythagorean triplet
+    /// <see cref="https://projecteuler.net/problem=9"/>
+    /// <seealso cref="http://www.wikizero.biz/index.php?q=aHR0cHM6Ly9lbi53aWtpcGVkaWEub3JnL3dpa2kvRm9ybXVsYXNfZm9yX2dlbmVyYXRpbmdfUHl0aGFnb3JlYW5fdHJpcGxlcw"/>
+    /// </summary>
+    public class Problem009 : IProblem
+    {
+        public int Id => 9;
+        public string Title => "Special Pythagorean triplet";
+
+        public string Description =>
+            "A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, \r\n" +
+            "a² + b² = c² \r\n" +
+            "For example, 32 + 42 = 9 + 16 = 25 = 5². \r\n" +
+            "There exists exactly one Pythagorean triplet for which a + b + c = 1000. \r\n" +
+            "Find the product abc.";
+
+        public string GetSolution()
+        {
+            for (int k = 1; k <= 10; k++)
+            {
+                for (int m = 20; m > 2; m--)
+                {
+                    for (int n = 2; n < m - 1; n++)
+                    {
+                        var a = k * (2 * m * n);
+                        var b = k * ((m * m) - (n * n));
+                        var c = k * ((m * m) + (n * n));
+                        if (a + b + c == 1000)
+                            return $"{a} * {b} * {c} = {a * b * c}";
+                    }
+                }
+            }
+            throw new Exception("NOT FOUND!");
+        }
+    }
+}