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Diffstat (limited to 'test/files')
-rw-r--r-- | test/files/scalacheck/redblack.scala | 213 |
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 index 0000000000..1fcaa46f0e --- /dev/null +++ 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) +} + |