Merge pull request #70 from andreas-roehler/master

solution2.5.2.3.scala

chapter02/worksheets/solution2.5.2.3.scala

@@ -0,0 +1,66 @@
+/** 
+  Exercise 2.5.2.3
+
+  For a given integer 𝑛, compute the sum of cubed digits, then the sum
+  of cubed digits of the result, etc.;
+
+  stop the resulting sequence when it repeats itself, and so determine
+  whether it ever reaches 1.
+
+  (Use Exercise 2.5.2.1.)
+
+  def cubes(n: Int): Stream[Int] = ???
+
+  def cubesReach1(n: Int): Boolean = ???
+
+  scala> cubesReach1(10)
+  res3: Boolean = true
+
+  scala> cubesReach1(4)
+  res4: Boolean = false
+  */
+
+def digitsOf(n: Int): Seq[Int] = {
+  Stream.iterate(n) { nk => nk / 10 }
+    .takeWhile { nk => nk != 0 }
+    .map { nk => nk % 10 }
+    .toList.reverse
+}
+
+def digitsListSum(x: Int, xs: Seq[Int] = Seq(), f: (Int => Int)): Seq[Int] = {
+  val a: Int = digitsOf(x).map{ x => f(x)}.sum
+  if (xs.contains(a))
+    if (a == 1) xs
+    else xs.reverse
+  else digitsListSum(a, a +: xs, f)
+}
+
+def cubes(n: Int): Seq[Int] = {
+  digitsListSum(n, xs = Seq(), { k => k * k * k })
+}
+
+def cubesReach1(x: Int): Boolean = {
+  val a = cubes(x)
+    a(0) == 1
+}
+
+
+cubes(123)
+cubes(10)
+cubes(4)
+
+val result =  cubesReach1(10)
+val expected = true
+assert(result == expected)
+
+val result2 =  cubesReach1(4)
+val expected2 = false
+assert(result2 == expected2)
+
+assert ( cubesReach1(20) == false )
+assert ( cubesReach1(50) == false )
+assert ( cubesReach1(100) == true )
+
+assert ( cubesReach1(112) == true )
+assert ( cubesReach1(114) == false )
+assert ( cubesReach1(778) == true )