Fix variations

Author: justcoding121

Advanced.Algorithms.Tests/Combinatorics/Variation_Tests.cs

@@ -41,11 +41,11 @@ public void Variation_With_Repetitions_Smoke_Test()
         {
             var input = "abcd".ToCharArray().ToList();
             var variations = Variation.Find<char>(input, 2, true);
-            Assert.AreEqual(Math.Pow(input.Count, 2), variations.Count);
+            Assert.AreEqual(combination(input.Count + 2 - 1, 2) * factorial(2), variations.Count);
 
             input = "scan".ToCharArray().ToList();
             variations = Variation.Find<char>(input, 3, true);
-            Assert.AreEqual(Math.Pow(input.Count, 3), variations.Count);
+            Assert.AreEqual(combination(input.Count + 3 - 1, 3) * factorial(3), variations.Count);
 
             input = "".ToCharArray().ToList();
             variations = Variation.Find<char>(input, 3, true);

Advanced.Algorithms/Combinatorics/Variation.cs

@@ -9,49 +9,31 @@ namespace Advanced.Algorithms.Combinatorics
     public class Variation
     {
         /*Variations are arrangements of selections of objects, where the order of the selected objects matters.
-        To count k-element variations of n objects, we first need to choose a k-element combination and then
+        To count r-element variations of n objects, we first need to choose a r-element combination and then
         a permutation of the selected objects*/
 
         //Without repetition
-        /* It is also the number of ways of putting r distinct balls into input.Count distinct boxes such that each box
+        /* It is also the number of ways of putting n distinct balls into r distinct boxes such that each box
         receives at most one element. */
 
         //With repetition
-        /* It is the number of all ways of putting r distinct balls into input.Count distinct boxes */
+        /* It is the number of all ways of putting n distinct balls into r distinct boxes */
         public static List<List<T>> Find<T>(List<T> input, int r, bool withRepetition)
         {
-            var result = new List<List<T>>();
+            var combinations = new List<List<T>>();
 
-            Recurse(input, r, withRepetition, new List<T>(), new HashSet<int>(), result);
+            combinations.AddRange(Combination.Find(input, r, withRepetition));
 
-            return result;
-        }
+            var variations = new List<List<T>>();
 
-        private static void Recurse<T>(List<T> input, int r, bool withRepetition,
-         List<T> prefix, HashSet<int> prefixIndices,
-         List<List<T>> result)
-        {
-            if (prefix.Count == r)
+            foreach (var combination in combinations)
             {
-                result.Add(new List<T>(prefix));
-                return;
+                variations.AddRange(Permutation.Find(combination, combination.Count));
             }
 
-            for (int j = 0; j < input.Count; j++)
-            {
-                if (prefixIndices.Contains(j) && !withRepetition)
-                {
-                    continue;
-                }
-
-                prefix.Add(input[j]);
-                prefixIndices.Add(j);
-
-                Recurse(input, r, withRepetition, prefix, prefixIndices, result);
-
-                prefix.RemoveAt(prefix.Count - 1);
-                prefixIndices.Remove(j);
-            }
+            return variations;
         }
+
+      
     }
 }