Dynamic Programming

src/main/scala/DynamicProgramming/Fibonacci.scala

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+package DynamicProgramming
+
+object Fibonacci extends ProblemDP[Int]{
+  type S = Int
+  type F[x] = (x, x)
+
+  def decompose(problem: Int): Either[Int, (Int, Int)] =
+    problem match {
+      case x if x<=1 => Left(1)
+      case x => Right((x-1, x-2))
+    }
+
+  def compose(solution: (Int, Int)): Int = {
+    val (x1, x2) = solution
+    x1+x2
+  }
+}
+

src/main/scala/DynamicProgramming/ProblemDP.scala

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+package DynamicProgramming
+
+import cats.Functor
+import cats.implicits.toFunctorOps
+
+import scala.collection.immutable.HashMap
+
+trait ProblemDP[T] {
+  type S
+  type F[_]
+  var map=  HashMap[T, S]()
+
+  def decompose(problem: T): Either[S, F[T]]
+  def compose(solution: F[S]): S
+
+  def apply(problem: T)(implicit F: Functor[F]): S =
+    map.get(problem) match {
+      case None =>
+        decompose(problem) match {
+          case Left(s) =>
+            map+= (problem -> s)
+          case Right(p)=>
+            map+= (problem -> compose(p.map(apply)))
+        }
+        apply(problem)
+      case Some(s) => s
+    }
+
+
+
+}

src/test/scala/DynamicProgramming/FibonacciTest.scala

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+package DynamicProgramming
+
+import org.scalatest.FunSuite
+import DynamicProgramming.Fibonacci._
+
+class FibonacciTest extends FunSuite {
+
+  test("Fibonacci"){
+    assert(apply(0)===1)
+    assert(apply(1)===1)
+    assert(apply(3)===3)
+    assert(apply(4)===5)
+    assert(apply(10)===89)
+  }
+
+}