Data commit

Task/Taxicab-numbers/C-sharp/taxicab-numbers-1.cs

@@ -0,0 +1,76 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+
+namespace TaxicabNumber
+{
+    class Program
+    {
+        static void Main(string[] args)
+        {
+            IDictionary<long, IList<Tuple<int, int>>> taxicabNumbers = GetTaxicabNumbers(2006);
+            PrintTaxicabNumbers(taxicabNumbers);
+            Console.ReadKey();
+        }
+
+        private static IDictionary<long, IList<Tuple<int, int>>> GetTaxicabNumbers(int length)
+        {
+            SortedList<long, IList<Tuple<int, int>>> sumsOfTwoCubes = new SortedList<long, IList<Tuple<int, int>>>();
+
+            for (int i = 1; i < int.MaxValue; i++)
+            {
+                for (int j = 1; j < int.MaxValue; j++)
+                {
+                    long sum = (long)(Math.Pow((double)i, 3) + Math.Pow((double)j, 3));
+
+                    if (!sumsOfTwoCubes.ContainsKey(sum))
+                    {
+                        sumsOfTwoCubes.Add(sum, new List<Tuple<int, int>>());
+                    }
+
+                    sumsOfTwoCubes[sum].Add(new Tuple<int, int>(i, j));
+
+                    if (j >= i)
+                    {
+                        break;
+                    }
+                }
+
+                // Found that you need to keep going for a while after the length, because higher i values fill in gaps
+                if (sumsOfTwoCubes.Count(t => t.Value.Count >= 2) >= length * 1.1)
+                {
+                    break;
+                }
+            }
+
+            IDictionary<long, IList<Tuple<int, int>>> values = (from t in sumsOfTwoCubes where t.Value.Count >= 2 select t)
+                .Take(2006)
+                .ToDictionary(u => u.Key, u => u.Value);
+
+            return values;
+        }
+
+        private static void PrintTaxicabNumbers(IDictionary<long, IList<Tuple<int, int>>> values)
+        {
+            int i = 1;
+
+            foreach (long taxicabNumber in values.Keys)
+            {
+                StringBuilder output = new StringBuilder().AppendFormat("{0,10}\t{1,4}", i, taxicabNumber);
+
+                foreach (Tuple<int, int> numbers in values[taxicabNumber])
+                {
+                    output.AppendFormat("\t= {0}^3 + {1}^3", numbers.Item1, numbers.Item2);
+                }
+
+                if (i <= 25 || (i >= 2000 && i <= 2006))
+                {
+                    Console.WriteLine(output.ToString());
+                }
+
+                i++;
+            }
+        }
+    }
+}

Task/Taxicab-numbers/C-sharp/taxicab-numbers-2.cs

@@ -0,0 +1,35 @@
+using System; using static System.Console;
+using System.Collections.Generic; using System.Linq;
+
+class Program {
+
+  static void Main(string[] args) {
+
+    List<uint> cubes = new List<uint>(), sums = new List<uint>();
+
+    void dump(string title, Dictionary <int, uint> items) {
+      Write(title); foreach (var item in items) {
+        Write("\n{0,4} {1,10}", item.Key, item.Value);
+        foreach (uint x in cubes) { uint y = item.Value - x;
+          if (y < x) break; if (cubes.Contains(y))
+            Write(" = {0,4}³ + {1,3}³", cubes.IndexOf(y), cubes.IndexOf(x));
+      } } }
+
+    DateTime st = DateTime.Now;
+    // create sorted list of cube sums
+    for (uint i = 0, cube; i < 1190; i++) { cube = i * i * i;
+      cubes.Add(cube); foreach (uint j in cubes)
+        sums.Add(cube + j); } sums.Sort();
+    // now seek consecutive sums that match
+    uint nm1 = sums[0], n = sums[1]; int idx = 0;
+    Dictionary <int, uint> task = new Dictionary <int, uint>(),
+                           trips = new Dictionary <int, uint>();
+    foreach (var np1 in sums.Skip(2)) {
+      if (nm1 == np1) trips.Add(idx, n); if (nm1 != n && n == np1)
+        if (++idx <= 25 || idx >= 2000 == idx <= 2006)
+          task.Add(idx, n); nm1 = n; n = np1; }
+    // show results
+    dump("First 25 Taxicab Numbers, the 2000th, plus the next half-dozen:", task);
+    dump(string.Format("\n\nFound {0} triple Taxicabs under {1}:", trips.Count, 2007), trips);
+    Write("\n\nElasped: {0}ms", (DateTime.Now - st).TotalMilliseconds); }
+}