added Maze DP

Author: JakubSchwenkbeck

src/main/scala/algorithms/dynamic/EditDistance.scala

@@ -15,10 +15,10 @@ def editDistance(X: Array[Char], Y: Array[Char]): (Array[Array[Int]], Int) = {
   for (i <- 0 until n - 1) {
     Edit(0)(i) = i
   }
-  for (i <- 0 until m - 1) {
+  for (i <- 1 until m) {
     Edit(i)(0) = i
 
-    for (j <- 0 until n - 1) {
+    for (j <- 1 until n) {
       val ins: Int = Edit(i)(j - 1) + 1
       val del: Int = Edit(i - 1)(j) + 1
       var rep: Int = Int.MaxValue
@@ -33,3 +33,14 @@ def editDistance(X: Array[Char], Y: Array[Char]): (Array[Array[Int]], Int) = {
   }
   (Edit, Edit(m - 1)(n - 1))
 }
+
+@main
+def editDistanceMain(): 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) = editDistance(x, y)
+  mat.foreach(row => println(row.mkString(" ")))
+  println(s" The shortest edit distance is : $res ")
+
+}

src/main/scala/algorithms/dynamic/Maze.scala

@@ -0,0 +1,39 @@
+package algorithms.dynamic
+
+/// Maze Path Counting Algorithm
+/// Computes the number of unique paths from the top-left corner to the bottom-right
+/// of an n x m grid, moving only right or down.
+///
+/// Uses dynamic programming to store intermediate results in a 2D table.
+///
+/// Time Complexity: O(n * m), where n and m are the grid dimensions.
+def maze(n: Int, m: Int): (Array[Array[Int]], Int) = {
+  val Mem: Array[Array[Int]] = Array.fill(n, m)(0)
+
+  for (i <- 0 until n) {
+    Mem(i)(0) = 1
+  }
+  for (j <- 0 until m) {
+    Mem(0)(j) = 1
+  }
+
+  for (i <- 1 until n) {
+    for (j <- 1 until m) {
+      Mem(i)(j) = Mem(i - 1)(j) + Mem(i)(j - 1)
+
+    }
+  }
+
+  (Mem, Mem(n - 1)(m - 1))
+}
+
+@main
+def mazeMain(): Unit = {
+  val n: Int = 18
+  val m: Int = 6
+
+  val (mat, res) = maze(n, m)
+  mat.foreach(row => println(row.mkString(" ")))
+  println(s" The number of paths is: $res ")
+
+}