package scala.collection.immutable.redblacktree

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.
*/

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) {
      const(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, true)

  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, true)
  } 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 TestDrop extends RedBlackTreeTest with RedBlackTreeInvariants  {
  import RB._

  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] = drop(tree, parm)

  property("drop") = forAll(genInput) { case (tree, parm, newTree) =>
    iterator(tree).drop(parm).toList == iterator(newTree).toList
  }
}

object TestTake extends RedBlackTreeTest with RedBlackTreeInvariants  {
  import RB._

  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] = take(tree, parm)

  property("take") = forAll(genInput) { case (tree, parm, newTree) =>
    iterator(tree).take(parm).toList == iterator(newTree).toList
  }
}

object TestSlice extends RedBlackTreeTest with RedBlackTreeInvariants  {
  import RB._

  override type ModifyParm = (Int, Int)
  override def genParm(tree: Tree[String, Int]): Gen[ModifyParm] = for {
    from <- choose(0, iterator(tree).size)
    to <- choose(from, iterator(tree).size)
  } yield (from, to)
  override def modify(tree: Tree[String, Int], parm: ModifyParm): Tree[String, Int] = slice(tree, parm._1, parm._2)

  property("slice") = forAll(genInput) { case (tree, parm, newTree) =>
    iterator(tree).slice(parm._1, parm._2).toList == iterator(newTree).toList
  }
}