Merge branch 'develop'

1 files changed, 213 insertions, 0 deletions

diff --git a/test/files/scalacheck/redblack.scala b/test/files/scalacheck/redblack.scala
new file mode 100644
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+++ b/test/files/scalacheck/redblack.scala
@@ -0,0 +1,213 @@
+import org.scalacheck._
+import Prop._
+import Gen._
+
+/*
+Properties of a Red & Black Tree:
+
+A node is either red or black.
+The root is black. (This rule is used in some definitions and not others. Since the
+root can always be changed from red to black but not necessarily vice-versa this 
+rule has little effect on analysis.)
+All leaves are black.
+Both children of every red node are black.
+Every simple path from a given node to any of its descendant leaves contains the same number of black nodes.
+*/
+
+abstract class RedBlackTest extends Properties("RedBlack") {
+  def minimumSize = 0
+  def maximumSize = 5
+
+  object RedBlackTest extends scala.collection.immutable.RedBlack[String] {
+    def isSmaller(x: String, y: String) = x < y
+  }
+  
+  import RedBlackTest._
+  
+  def nodeAt[A](tree: Tree[A], n: Int): Option[(String, A)] = if (n < tree.iterator.size && n >= 0)
+    Some(tree.iterator.drop(n).next)
+  else
+    None
+    
+  def treeContains[A](tree: Tree[A], key: String) = tree.iterator.map(_._1) contains key
+  
+  def mkTree(level: Int, parentIsBlack: Boolean = false, label: String = ""): Gen[Tree[Int]] = 
+    if (level == 0) {
+      value(Empty)
+    } else {
+      for {
+        oddOrEven <- choose(0, 2)
+        tryRed = oddOrEven.sample.get % 2 == 0 // work around arbitrary[Boolean] bug
+        isRed = parentIsBlack && tryRed
+        nextLevel = if (isRed) level else level - 1
+        left <- mkTree(nextLevel, !isRed, label + "L")
+        right <- mkTree(nextLevel, !isRed, label + "R")
+      } yield {
+        if (isRed) 
+          RedTree(label + "N", 0, left, right)
+        else
+          BlackTree(label + "N", 0, left, right)
+      }
+    }
+
+  def genTree = for {
+    depth <- choose(minimumSize, maximumSize + 1)
+    tree <- mkTree(depth)
+  } yield tree
+  
+  type ModifyParm
+  def genParm(tree: Tree[Int]): Gen[ModifyParm]
+  def modify(tree: Tree[Int], parm: ModifyParm): Tree[Int]
+  
+  def genInput: Gen[(Tree[Int], ModifyParm, Tree[Int])] = for {
+    tree <- genTree
+    parm <- genParm(tree)
+  } yield (tree, parm, modify(tree, parm))
+}
+
+trait RedBlackInvariants {
+  self: RedBlackTest =>
+  
+  import RedBlackTest._
+    
+  def rootIsBlack[A](t: Tree[A]) = t.isBlack
+  
+  def areAllLeavesBlack[A](t: Tree[A]): Boolean = t match {
+    case Empty => t.isBlack
+    case ne: NonEmpty[_] => List(ne.left, ne.right) forall areAllLeavesBlack
+  }
+  
+  def areRedNodeChildrenBlack[A](t: Tree[A]): Boolean = t match {
+    case RedTree(_, _, left, right) => List(left, right) forall (t => t.isBlack && areRedNodeChildrenBlack(t)) 
+    case BlackTree(_, _, left, right) => List(left, right) forall areRedNodeChildrenBlack
+    case Empty => true
+  }
+  
+  def blackNodesToLeaves[A](t: Tree[A]): List[Int] = t match {
+    case Empty => List(1)
+    case BlackTree(_, _, left, right) => List(left, right) flatMap blackNodesToLeaves map (_ + 1)
+    case RedTree(_, _, left, right) => List(left, right) flatMap blackNodesToLeaves
+  }
+  
+  def areBlackNodesToLeavesEqual[A](t: Tree[A]): Boolean = t match {
+    case Empty => true
+    case ne: NonEmpty[_] => 
+      (
+        blackNodesToLeaves(ne).distinct.size == 1 
+        && areBlackNodesToLeavesEqual(ne.left) 
+        && areBlackNodesToLeavesEqual(ne.right)
+      )
+  }
+  
+  def orderIsPreserved[A](t: Tree[A]): Boolean = 
+    t.iterator zip t.iterator.drop(1) forall { case (x, y) => isSmaller(x._1, y._1) }
+    
+  def setup(invariant: Tree[Int] => Boolean) = forAll(genInput) { case (tree, parm, newTree) =>
+    invariant(newTree)
+  }
+
+  property("root is black") = setup(rootIsBlack)
+  property("all leaves are black") = setup(areAllLeavesBlack)
+  property("children of red nodes are black") = setup(areRedNodeChildrenBlack)
+  property("black nodes are balanced") = setup(areBlackNodesToLeavesEqual)
+  property("ordering of keys is preserved") = setup(orderIsPreserved)
+}
+
+object TestInsert extends RedBlackTest with RedBlackInvariants {
+  import RedBlackTest._
+  
+  override type ModifyParm = Int
+  override def genParm(tree: Tree[Int]): Gen[ModifyParm] = choose(0, tree.iterator.size + 1)
+  override def modify(tree: Tree[Int], parm: ModifyParm): Tree[Int] = tree update (generateKey(tree, parm), 0)
+
+  def generateKey(tree: Tree[Int], parm: ModifyParm): String = nodeAt(tree, parm) match {
+    case Some((key, _)) => key.init.mkString + "MN"
+    case None => nodeAt(tree, parm - 1) match {
+      case Some((key, _)) => key.init.mkString + "RN"
+      case None  => "N"
+    }
+  }
+
+  property("update adds elements") = forAll(genInput) { case (tree, parm, newTree) =>
+    treeContains(newTree, generateKey(tree, parm))
+  }
+}
+
+object TestModify extends RedBlackTest {
+  import RedBlackTest._
+  
+  def newValue = 1
+  override def minimumSize = 1
+  override type ModifyParm = Int
+  override def genParm(tree: Tree[Int]): Gen[ModifyParm] = choose(0, tree.iterator.size)
+  override def modify(tree: Tree[Int], parm: ModifyParm): Tree[Int] = nodeAt(tree, parm) map { 
+    case (key, _) => tree update (key, newValue)
+  } getOrElse tree
+
+  property("update modifies values") = forAll(genInput) { case (tree, parm, newTree) =>
+    nodeAt(tree,parm) forall { case (key, _) =>
+      newTree.iterator contains (key, newValue)
+    }
+  }
+}
+
+object TestDelete extends RedBlackTest with RedBlackInvariants  {
+  import RedBlackTest._
+
+  override def minimumSize = 1
+  override type ModifyParm = Int
+  override def genParm(tree: Tree[Int]): Gen[ModifyParm] = choose(0, tree.iterator.size)
+  override def modify(tree: Tree[Int], parm: ModifyParm): Tree[Int] = nodeAt(tree, parm) map { 
+    case (key, _) => tree delete key
+  } getOrElse tree
+  
+  property("delete removes elements") = forAll(genInput) { case (tree, parm, newTree) =>
+    nodeAt(tree, parm) forall { case (key, _) =>
+      !treeContains(newTree, key)
+    }
+  }
+}
+
+object TestRange extends RedBlackTest with RedBlackInvariants  {
+  import RedBlackTest._
+  
+  override type ModifyParm = (Option[Int], Option[Int])
+  override def genParm(tree: Tree[Int]): Gen[ModifyParm] = for {
+    from <- choose(0, tree.iterator.size)
+    to <- choose(0, tree.iterator.size) suchThat (from <=)
+    optionalFrom <- oneOf(Some(from), None, Some(from)) // Double Some(n) to get around a bug
+    optionalTo <- oneOf(Some(to), None, Some(to)) // Double Some(n) to get around a bug
+  } yield (optionalFrom, optionalTo)
+  
+  override def modify(tree: Tree[Int], parm: ModifyParm): Tree[Int] = {
+    val from = parm._1 flatMap (nodeAt(tree, _) map (_._1))
+    val to = parm._2 flatMap (nodeAt(tree, _) map (_._1))
+    tree range (from, to)
+  }
+  
+  property("range boundaries respected") = forAll(genInput) { case (tree, parm, newTree) =>
+    val from = parm._1 flatMap (nodeAt(tree, _) map (_._1))
+    val to = parm._2 flatMap (nodeAt(tree, _) map (_._1))
+    ("lower boundary" |: (from forall ( key => newTree.iterator.map(_._1) forall (key <=)))) &&
+    ("upper boundary" |: (to forall ( key => newTree.iterator.map(_._1) forall (key >))))
+  }
+  
+  property("range returns all elements") = forAll(genInput) { case (tree, parm, newTree) =>
+    val from = parm._1 flatMap (nodeAt(tree, _) map (_._1))
+    val to = parm._2 flatMap (nodeAt(tree, _) map (_._1))
+    val filteredTree = (tree.iterator
+      .map(_._1) 
+      .filter(key => from forall (key >=))
+      .filter(key => to forall (key <))
+      .toList)
+    filteredTree == newTree.iterator.map(_._1).toList
+  }
+}
+
+object Test extends Properties("RedBlack") {
+  include(TestInsert)
+  include(TestModify)
+  include(TestDelete)
+  include(TestRange)
+}
+