Implement exercise 2.5.

BinaryTree now knows how to create balanced versions of itself, with
inner structural sharing. Tests included, using ScalaCheck

build.sbt

@@ -4,5 +4,7 @@ version := "1.0"
 
 scalaVersion := "2.9.1"
 
+libraryDependencies += "org.scala-tools.testing" %% "scalacheck" % "1.9" % "test"
+
 libraryDependencies += "org.scalatest" %% "scalatest" % "1.6.1" % "test"
 

src/main/scala/BinaryTree.scala

@@ -1,5 +1,26 @@
 package org.jordanlewis.pfds
 
+object BinaryTree {
+  def complete[T](x: T, d: Int): BinaryTree[T] = d match {
+    case 0 => BinaryTreeLeaf
+    case _ => {
+      val subtree = complete(x, d - 1)
+      BinaryTreeNode(subtree, x, subtree)
+    }
+  }
+
+  def balanced[T](x: T, d: Int)(implicit ordering: Ordering[T]): BinaryTree[T] = d match {
+    case 0 => BinaryTreeLeaf
+    case 1 => BinaryTreeNode(BinaryTreeLeaf, x, BinaryTreeLeaf)
+    case _ => {
+      val half = d / 2
+      val halftree = create(x, half)
+      if (half * 2 == d) BinaryTreeNode(halftree, x, create(x, half - 1))
+      else BinaryTreeNode(halftree, x, halftree)
+    }
+  }
+}
+
 sealed abstract class BinaryTree[+T] {
   def size(): Int
 }

src/test/scala/BinaryTreeTest.scala

@@ -0,0 +1,23 @@
+package org.jordanlewis.pfds
+
+import org.scalatest.matchers.ShouldMatchers
+import org.scalatest.Spec
+import org.scalatest.prop.Checkers
+import org.scalacheck.Prop._
+import org.scalacheck.Gen._
+
+class BinaryTreeTest extends Spec with ShouldMatchers with Checkers {
+  describe("A complete tree") {
+    it("should have 2^n - 1 nodes") {
+      check(forAll(choose(0, 25)){n: Int =>
+          BinaryTree.complete(0, n).size == scala.math.pow(2, n) - 1 })
+    }
+  }
+
+  describe("A balanced tree") {
+    it("should have n nodes") {
+      check(forAll(choose(0, 100)){n: Int =>
+          BinaryTree.balanced(0, n).size == n})
+    }
+  }
+}