Csharp updates for 4, 9 chapters (#245)

* GetGCDList fix

* Csharp longest_common_subsequence update

* Csharp levenshtein added

* Couple changes in levenshtein

09_dynamic_programming/csharp/01_longest_common_subsequence/Program.cs

@@ -6,15 +6,67 @@ namespace ConsoleApplication
     {
         public static void Main(string[] args)
         {
+            var result = LongestCommonSubsequence("fish", "vistafh");
+            Console.WriteLine($"{result.Item1}: {result.Item2}"); // ish: 3
+        }
 
-            if (word_a[i] == word_b[1])
+        public static (string, int) LongestCommonSubsequence(string word1, string word2)
+        {
+            if (string.IsNullOrEmpty(word1) || string.IsNullOrEmpty(word2))
+                return ("", 0);
+
+            string subSeq;
+            var matrix = new int[word1.Length + 1, word2.Length + 1];
+
+            for (int i = 1; i <= word1.Length; i++)
             {
-                cell[i][j] = cell[i - 1][j - 1] + 1;
+                for (int j = 1; j <= word2.Length; j++)
+                {
+                    if (word1[i - 1] == word2[j - 1])
+                    {
+                        matrix[i, j] = matrix[i - 1, j - 1] + 1;
+                    }
+                    else
+                    {
+                        matrix[i, j] = Math.Max(matrix[i, j - 1], matrix[i - 1, j]);
+                    }
+                }
             }
-            else
+
+            subSeq = Read(matrix, word1, word2);
+
+            return (subSeq, subSeq.Length);
+        }
+
+        private static string Read(int[,] matrix, string word1, string word2)
+        {
+            string subSeq = null;
+            int x = word1.Length;
+            int y = word2.Length;
+
+            while (x > 0 && y > 0)
             {
-                cell[i][j] = Math.Max(cell[i - 1][j], cell[i][j - 1]);
+                if (word1[x - 1] == word2[y - 1])
+                {
+                    subSeq += word1[x - 1];
+                    x--;
+                    y--;
+                }
+                else if (matrix[x - 1, y] > matrix[x, y - 1])
+                {
+                    x--;
+                }
+                else
+                {
+                    y--;
+                }
             }
+
+            var charArray = subSeq.ToCharArray();
+            Array.Reverse(charArray);
+            subSeq = new string(charArray);
+
+            return subSeq;
         }
     }
 }

09_dynamic_programming/csharp/02_levenshtein/Program.cs

@@ -0,0 +1,46 @@
+using System;
+
+namespace ConsoleApplication
+{
+    public class Program
+    {
+        public static int LevenshteinDistance(string source, string target)
+        {
+            var matrix = CreateMatrix(source, target);
+
+            for (int i = 1; i <= source.Length; i++)
+            {
+                for (int j = 1; j <= target.Length; j++)
+                {
+                    matrix[i, j] = Math.Min(matrix[i, j - 1] + 1, Math.Min(
+                        matrix[i - 1, j] + 1,
+                        matrix[i - 1, j - 1] + (source[i - 1] != target[j - 1] ? 1 : 0)));
+                }
+            }
+
+            return matrix[source.Length, target.Length];
+        }
+
+        private static int[,] CreateMatrix(string source, string target)
+        {
+            var matrix = new int[source.Length + 1, target.Length + 1];
+
+            if (source.Length < target.Length)
+            {
+                (source, target) = (target, source);
+            }
+
+            for (int i = 0; i <= source.Length; i++)
+            {
+                matrix[i, 0] = i;
+
+                if (i <= target.Length)
+                {
+                    matrix[0, i] = i;
+                }
+            }
+
+            return matrix;
+        }
+    }
+}