P31 to P39 problems

micro/s99/jaranda/.gitignore

@@ -10,5 +10,8 @@ project/boot/
 project/plugins/project/
 
 # Scala-IDE specific
-.idea
-.idea_modules
+.scala_dependencies
+
+.settings
+.classpath
+.project

micro/s99/jaranda/.worksheet/src/s99.dummy.scala

@@ -0,0 +1,10 @@
+package s99
+
+import s99.Arithmetic._
+
+object dummy {;import org.scalaide.worksheet.runtime.library.WorksheetSupport._; def main(args: Array[String])=$execute{;$skip(81); 
+
+  println(315.primeFactors);$skip(111); val res$0 = 
+
+  List(3,3,4,5).groupBy(f => f).map(fl => (fl._1, (fl._1, fl._2.size))).values.toList.sortWith(_._1 < _._1);System.out.println("""res0: List[(Int, Int)] = """ + $show(res$0))}
+}

micro/s99/jaranda/project/plugins.sbt

@@ -1,2 +1,2 @@
 
-addSbtPlugin("com.github.mpeltonen" % "sbt-idea" % "1.5.2")
+addSbtPlugin("com.typesafe.sbteclipse" % "sbteclipse-plugin" % "2.4.0")

micro/s99/jaranda/src/main/scala/s99/Arithmetic.scala

@@ -0,0 +1,56 @@
+package s99
+
+import scala.annotation.tailrec
+
+object Arithmetic {
+
+  implicit def int2MyInt(i: Int) = new MyInt(i);
+
+  val primes: Stream[Int] = 2 #:: 3 #:: 5 #:: 7 #:: 11 #:: 13 #:: Stream.from(17).filter(_.isPrime)
+
+  class MyInt(val i: Int) {
+
+    def isPrime: Boolean = {
+	  	(2 to math.sqrt(i).toInt).filter(n => i % n == 0).length == 0
+  	}
+
+    def isCoprimeTo(n: Int): Boolean = {
+      gcd(i, n) == 1
+    }
+
+    def totient: Int = {
+      (1 to i).filter(i.isCoprimeTo(_)).length
+    }
+
+    def totientImproved : Int = {
+      i.primeFactorMultiplicity.map( n => (n._1 - 1) * math.pow((n._1),(n._2 - 1)) ).reduce( (n , m) => n * m).intValue();
+    }
+
+    def primeFactors: List[Int] = {
+      @tailrec
+      def primeFactorsRec(n: Int, ps: Stream[Int], factors: List[Int]) : List[Int] = {
+        if (n.isPrime) n :: factors
+        else if (n % ps.head == 0) primeFactorsRec(n / ps.head, ps, ps.head :: factors)
+        else primeFactorsRec(n, ps.tail, factors)
+      }
+      primeFactorsRec(i, primes, Nil).reverse
+    }
+
+    def primeFactorMultiplicity: List[(Int,Int)] = {
+      val factorsMultiplicity = i.primeFactors.groupBy(f => f).map(f1 => (f1, (f1._1, f1._2.size))).values.toList
+      factorsMultiplicity.sortWith(_._1 < _._1)
+    }
+
+  }
+
+  def gcd(a: Int, b: Int) : Int = (a,b) match {
+    case (a, 0) => a
+    case _ => gcd(b, a%b)
+  }
+
+  def listPrimesInRange(r: Range) : List[Int] = {
+    primes.dropWhile(_ < r.head).takeWhile(_ <= r.last).toList
+  }
+
+}
+

micro/s99/jaranda/src/main/scala/s99/Lists.scala

@@ -2,14 +2,6 @@ package s99
 
 import scala.annotation.tailrec
 
-/**
- * Created with IntelliJ IDEA.
- * User: jaranda
- * Date: 05/01/14
- * Time: 09:47
- * To change this template use File | Settings | File Templates.
- */
-
 object Lists {
 
   /**

micro/s99/jaranda/src/main/scala/s99/dummy.sc

@@ -0,0 +1,14 @@
+package s99
+
+import s99.Arithmetic._
+
+object dummy {
+
+  println(315.primeFactors)                       //> List(3, 3, 5, 7)
+
+  List(3,3,4,5).groupBy(f => f).map(fl => (fl._1, (fl._1, fl._2.size))).values.toList.sortWith(_._1 < _._1)
+                                                  //> res0: List[(Int, Int)] = List((3,2), (4,1), (5,1))
+
+  listPrimesInRange(7 to 31)                      //> res1: List[Int] = List(7, 11, 13, 17, 19, 23, 29, 31)
+
+}

micro/s99/jaranda/src/test/scala/s99/ArithmeticSpec.scala

@@ -0,0 +1,41 @@
+package s99
+
+import org.scalatest.FunSuite
+
+class ArithmeticSpec extends FunSuite {
+
+  import s99.Arithmetic._;
+
+  test("Determine whether a given integer number is prime.") {
+    assert{ 7.isPrime == true } 
+  }
+
+  test("Determine the greatest common divisor of two positive integer numbers.") {
+	  assert{ gcd(36, 63) == 9 }
+  }
+
+  test("Determine whether two positive integer numbers are coprime.") {
+    assert{ 35.isCoprimeTo(64) }
+  }
+
+  test("Calculate Euler's totient function phi(m).") {
+    assert{ 10.totient == 4 }
+  }
+
+  test("Determine the prime factors of a given positive integer.") {
+    assert{ 315.primeFactors == List(3, 3, 5, 7) }
+  }
+
+  test("Determine the prime factors of a given positive integer (2).") {
+    assert{ 315.primeFactorMultiplicity == List((3,2), (5,1), (7,1)) }
+  }
+
+  test("Calculate Euler's totient function phi(m) (improved)."){
+    assert{ 10.totientImproved == 4 }
+  }
+
+  test("Given a range of integers by its lower and upper limit, construct a list of all prime numbers in that range.") {
+    assert{ listPrimesInRange(7 to 31) == List(7, 11, 13, 17, 19, 23, 29, 31) }
+  }
+
+}

micro/s99/jaranda/src/test/scala/s99/Lists.scala

@@ -3,14 +3,6 @@ package s99
 import org.scalatest.matchers.ShouldMatchers
 import org.scalatest.FlatSpec
 
-/**
- * Created with IntelliJ IDEA.
- * User: jaranda
- * Date: 05/01/14
- * Time: 10:27
- * To change this template use File | Settings | File Templates.
- */
-
 class ListsSpec extends FlatSpec with ShouldMatchers {
 
   "Lists problems set" should "find the last element of a list" in {