implemented the LongestCommonSubSequence dynamic program

Author: JakubSchwenkbeck

src/main/scala/algorithms/dynamic/LongestCommonSubSequence.scala

@@ -1 +1,58 @@
 package algorithms.dynamic
+
+/// Longest Common Subsequence (LCS) Algorithm
+/// Computes the length and reconstructs the LCS of two sequences using dynamic programming.
+///
+/// Uses a 2D table to store LCS values for substrings of A and B.
+///
+/// Time Complexity: O(n * m), where n and m are the lengths of the input sequences.
+
+def LCS(A: Array[Char], B: Array[Char]): (Array[Array[Int]], Int, String) = {
+  val n = A.length
+  val m = B.length
+
+  val L: Array[Array[Int]] = Array.fill(n + 1, m + 1)(0)
+
+  // Fill the DP table
+  for (i <- 1 to n) {
+    for (j <- 1 to m) {
+      if (A(i - 1) == B(j - 1)) {
+        L(i)(j) = L(i - 1)(j - 1) + 1
+      } else {
+        L(i)(j) = Math.max(L(i - 1)(j), L(i)(j - 1))
+      }
+    }
+  }
+
+  // LCS Length
+  val lcsLength = L(n)(m)
+
+  // Reconstruct the LCS string
+  val lcsBuilder = new StringBuilder()
+  var i = n
+  var j = m
+  while (i > 0 && j > 0) {
+    if (A(i - 1) == B(j - 1)) {
+      lcsBuilder.append(A(i - 1))
+      i -= 1
+      j -= 1
+    } else if (L(i - 1)(j) > L(i)(j - 1)) {
+      i -= 1
+    } else {
+      j -= 1
+    }
+  }
+
+  (L, lcsLength, lcsBuilder.reverse.toString)
+}
+
+@main
+def lcsMain(): Unit = {
+  val x: Array[Char] = Array('A', 'L', 'G', 'O', 'R', 'I', 'T', 'H', 'M')
+  val y: Array[Char] = Array('A', 'L', 'T', 'R', 'U', 'I', 'S', 'T', 'I', 'C')
+
+  val (mat, res, lcs) = LCS(x, y)
+  mat.foreach(row => println(row.mkString(" ")))
+  println(s" The Longest subsequence has length : $res ")
+  println(s" The Longest subsequence is : $lcs")
+}