Problem 75

Ckknight.ProjectEuler/Ckknight.ProjectEuler.csproj

@@ -142,6 +142,7 @@
     <Compile Include="Problems\Problem072.cs" />
     <Compile Include="Problems\Problem073.cs" />
     <Compile Include="Problems\Problem074.cs" />
+    <Compile Include="Problems\Problem075.cs" />
     <Compile Include="Problems\ProblemAttribute.cs" />
     <Compile Include="Program.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />

Ckknight.ProjectEuler/Collections/IMultiSet.cs

@@ -9,5 +9,6 @@ public interface IMultiSet<T> : ICollection<T>
     {
         int GetCount(T item);
         IEnumerable<T> Distinct();
+        IEnumerable<KeyValuePair<T, int>> GetCounts();
     }
 }

Ckknight.ProjectEuler/Collections/MultiHashSet.cs

@@ -3,6 +3,7 @@
 using System.Linq;
 using System.Text;
 using System.Collections;
+using System.Collections.ObjectModel;
 
 namespace Ckknight.ProjectEuler.Collections
 {
@@ -73,6 +74,14 @@ public IEnumerable<T> Distinct()
             return _data.Keys;
         }
 
+        public IEnumerable<KeyValuePair<T, int>> GetCounts()
+        {
+            foreach (var pair in _data)
+            {
+                yield return pair;
+            }
+        }
+
         public void Add(T item)
         {
             int count;

Ckknight.ProjectEuler/Problems/Problem075.cs

@@ -0,0 +1,53 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using Ckknight.ProjectEuler.Collections;
+
+namespace Ckknight.ProjectEuler.Problems
+{
+    [Problem(75,
+        @"It turns out that 12 cm is the smallest length of wire that can be
+        bent to form an integer sided right angle triangle in exactly one way,
+        but there are many more examples.
+
+            12 cm: (3,4,5)
+            24 cm: (6,8,10)
+            30 cm: (5,12,13)
+            36 cm: (9,12,15)
+            40 cm: (8,15,17)
+            48 cm: (12,16,20)
+
+        In contrast, some lengths of wire, like 20 cm, cannot be bent to form
+        an integer sided right angle triangle, and other lengths allow more
+        than one solution to be found; for example, using 120 cm it is possible
+        to form exactly three different integer sided right angle triangles.
+
+            120 cm: (30,40,50), (20,48,52), (24,45,51)
+
+        Given that L is the length of the wire, for how many values of
+        L <= 1,500,000 can exactly one integer sided right angle triangle be
+        formed?
+
+        Note: This problem has been changed recently, please check that you are
+        using the right parameters.")]
+    public class Problem075 : BaseProblem
+    {
+        public override object CalculateResult()
+        {
+            int maximum = 1500000;
+            return new Range(1, int.MaxValue)
+                .TakeWhile(m => 2 * m * m + 2 * m <= maximum)
+                .SelectMany(m => new Range((m % 2 == 0) ? 1 : 2, m, 2)
+                    .Where(n => MathUtilities.AreRelativelyPrime(m, n))
+                    .Select(n => 2 * m * m + 2 * m * n)
+                    .TakeWhile(l => l <= maximum))
+                .SelectMany(l => new Range(1, int.MaxValue)
+                    .Select(v => l * v)
+                    .TakeWhile(p => p <= maximum))
+                .ToMultiHashSet()
+                .GetCounts()
+                .Count(p => p.Value == 1);
+        }
+    }
+}

Ckknight.ProjectEuler/Program.cs

@@ -12,7 +12,7 @@ class Program
     {
         static void Main(string[] args)
         {
-            RunProblem(74);
+            RunProblem(75);
         }
 
         public static void RunProblem(int number)