Initial data commit

Task/Modular-inverse/Scala/modular-inverse-1.scala

@@ -0,0 +1,15 @@
+def gcdExt(u: Int, v: Int): (Int, Int, Int) = {
+  @tailrec
+  def aux(a: Int, b: Int, x: Int, y: Int, x1: Int, x2: Int, y1: Int, y2: Int): (Int, Int, Int) = {
+    if(b == 0) (x, y, a) else {
+      val (q, r) = (a / b, a % b)
+      aux(b, r, x2 - q * x1, y2 - q * y1, x, x1, y, y1)
+    }
+  }
+  aux(u, v, 1, 0, 0, 1, 1, 0)
+}
+
+def modInv(a: Int, m: Int): Option[Int] = {
+  val (i, j, g) = gcdExt(a, m)
+  if (g == 1) Option(if (i < 0) i + m else i) else Option.empty
+}

Task/Modular-inverse/Scala/modular-inverse-2.scala

@@ -0,0 +1 @@
+def modInv(a: Int, m: Int, x:Int = 1, y:Int = 0) : Int = if (m == 0) x else modInv(m, a%m, y, x - y*(a/m))