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Diffstat (limited to 'test/files/scalacheck/redblacktree.scala')
-rw-r--r-- | test/files/scalacheck/redblacktree.scala | 216 |
1 files changed, 216 insertions, 0 deletions
diff --git a/test/files/scalacheck/redblacktree.scala b/test/files/scalacheck/redblacktree.scala new file mode 100644 index 0000000000..e4b356c889 --- /dev/null +++ b/test/files/scalacheck/redblacktree.scala @@ -0,0 +1,216 @@ +import collection.immutable.{RedBlackTree => RB} +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. +*/ + +package scala.collection.immutable.redblacktree { + abstract class RedBlackTreeTest extends Properties("RedBlackTree") { + def minimumSize = 0 + def maximumSize = 5 + + import RB._ + + def nodeAt[A](tree: Tree[String, A], n: Int): Option[(String, A)] = if (n < iterator(tree).size && n >= 0) + Some(iterator(tree).drop(n).next) + else + None + + def treeContains[A](tree: Tree[String, A], key: String) = iterator(tree).map(_._1) contains key + + def height(tree: Tree[_, _]): Int = if (tree eq null) 0 else (1 + math.max(height(tree.left), height(tree.right))) + + def mkTree(level: Int, parentIsBlack: Boolean = false, label: String = ""): Gen[Tree[String, Int]] = + if (level == 0) { + value(null) + } 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[String, Int]): Gen[ModifyParm] + def modify(tree: Tree[String, Int], parm: ModifyParm): Tree[String, Int] + + def genInput: Gen[(Tree[String, Int], ModifyParm, Tree[String, Int])] = for { + tree <- genTree + parm <- genParm(tree) + } yield (tree, parm, modify(tree, parm)) + } + + trait RedBlackTreeInvariants { + self: RedBlackTreeTest => + + import RB._ + + def rootIsBlack[A](t: Tree[String, A]) = isBlack(t) + + def areAllLeavesBlack[A](t: Tree[String, A]): Boolean = t match { + case null => isBlack(t) + case ne => List(ne.left, ne.right) forall areAllLeavesBlack + } + + def areRedNodeChildrenBlack[A](t: Tree[String, A]): Boolean = t match { + case RedTree(_, _, left, right) => List(left, right) forall (t => isBlack(t) && areRedNodeChildrenBlack(t)) + case BlackTree(_, _, left, right) => List(left, right) forall areRedNodeChildrenBlack + case null => true + } + + def blackNodesToLeaves[A](t: Tree[String, A]): List[Int] = t match { + case null => 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[String, A]): Boolean = t match { + case null => true + case ne => + ( + blackNodesToLeaves(ne).distinct.size == 1 + && areBlackNodesToLeavesEqual(ne.left) + && areBlackNodesToLeavesEqual(ne.right) + ) + } + + def orderIsPreserved[A](t: Tree[String, A]): Boolean = + iterator(t) zip iterator(t).drop(1) forall { case (x, y) => x._1 < y._1 } + + def heightIsBounded(t: Tree[_, _]): Boolean = height(t) <= (2 * (32 - Integer.numberOfLeadingZeros(count(t) + 2)) - 2) + + def setup(invariant: Tree[String, 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) + property("height is bounded") = setup(heightIsBounded) + } + + object TestInsert extends RedBlackTreeTest with RedBlackTreeInvariants { + import RB._ + + override type ModifyParm = Int + override def genParm(tree: Tree[String, Int]): Gen[ModifyParm] = choose(0, iterator(tree).size + 1) + override def modify(tree: Tree[String, Int], parm: ModifyParm): Tree[String, Int] = update(tree, generateKey(tree, parm), 0) + + def generateKey(tree: Tree[String, 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 RedBlackTreeTest { + import RB._ + + def newValue = 1 + override def minimumSize = 1 + override type ModifyParm = Int + override def genParm(tree: Tree[String, Int]): Gen[ModifyParm] = choose(0, iterator(tree).size) + override def modify(tree: Tree[String, Int], parm: ModifyParm): Tree[String, Int] = nodeAt(tree, parm) map { + case (key, _) => update(tree, key, newValue) + } getOrElse tree + + property("update modifies values") = forAll(genInput) { case (tree, parm, newTree) => + nodeAt(tree,parm) forall { case (key, _) => + iterator(newTree) contains (key, newValue) + } + } + } + + object TestDelete extends RedBlackTreeTest with RedBlackTreeInvariants { + import RB._ + + override def minimumSize = 1 + override type ModifyParm = Int + override def genParm(tree: Tree[String, Int]): Gen[ModifyParm] = choose(0, iterator(tree).size) + override def modify(tree: Tree[String, Int], parm: ModifyParm): Tree[String, Int] = nodeAt(tree, parm) map { + case (key, _) => delete(tree, 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 RedBlackTreeTest with RedBlackTreeInvariants { + import RB._ + + override type ModifyParm = (Option[Int], Option[Int]) + override def genParm(tree: Tree[String, Int]): Gen[ModifyParm] = for { + from <- choose(0, iterator(tree).size) + to <- choose(0, iterator(tree).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[String, Int], parm: ModifyParm): Tree[String, Int] = { + val from = parm._1 flatMap (nodeAt(tree, _) map (_._1)) + val to = parm._2 flatMap (nodeAt(tree, _) map (_._1)) + rangeImpl(tree, 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 => keysIterator(newTree) forall (key <=)))) && + ("upper boundary" |: (to forall ( key => keysIterator(newTree) 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 = (keysIterator(tree) + .filter(key => from forall (key >=)) + .filter(key => to forall (key <)) + .toList) + filteredTree == keysIterator(newTree).toList + } + } +} + +object Test extends Properties("RedBlackTree") { + import collection.immutable.redblacktree._ + include(TestInsert) + include(TestModify) + include(TestDelete) + include(TestRange) +} |