From 06945b6dcfc7bbb0efb5f8429ffeab7fbde9be5b Mon Sep 17 00:00:00 2001
From: Lucien Pereira <pereira.lucien@laposte.net>
Date: Sat, 28 Jan 2012 14:52:01 +0100
Subject: Scalacheck test in order to ensure AVL invariants are respected.

---
 test/files/scalacheck/avl.scala | 114 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 114 insertions(+)
 create mode 100644 test/files/scalacheck/avl.scala

diff --git a/test/files/scalacheck/avl.scala b/test/files/scalacheck/avl.scala
new file mode 100644
index 0000000000..51fb1fe8c3
--- /dev/null
+++ b/test/files/scalacheck/avl.scala
@@ -0,0 +1,114 @@
+import org.scalacheck.Gen
+import org.scalacheck.Prop.forAll
+import org.scalacheck.Properties
+
+import util.logging.ConsoleLogger
+
+package scala.collection.mutable {
+
+  /**
+   * Property of an AVL Tree : Any node of the tree has a balance value beetween in [-1; 1]
+   */
+  abstract class AVLTreeTest(name: String) extends Properties(name) with ConsoleLogger {
+
+    def `2^`(n: Int) = (1 to n).fold(1)((a, b) => b*2)
+
+    def capacityMax(depth: Int): Int = `2^`(depth+1) - 1
+
+    def minDepthForCapacity(x: Int): Int = {
+      var depth = 0
+      while(capacityMax(depth) < x)
+        depth += 1
+      depth
+    }
+
+    def numberOfElementsInLeftSubTree(n: Int): collection.immutable.IndexedSeq[Int] = {
+      val mid = n/2 + n%2
+      ((1 until mid)
+        .filter { i => math.abs(minDepthForCapacity(i) - minDepthForCapacity(n-i)) < 2 }
+          .flatMap { i => Seq(i, n-(i+1)) }).toIndexedSeq.distinct
+    }
+
+    def makeAllBalancedTree[A](elements: List[A]): List[AVLTree[A]] = elements match {
+      case Nil => Leaf::Nil
+      case first::Nil => Node(first, Leaf, Leaf)::Nil
+      case first::second::Nil => Node(second, Node(first, Leaf, Leaf), Leaf)::Node(first, Leaf, Node(second, Leaf, Leaf))::Nil
+      case first::second::third::Nil => Node(second, Node(first, Leaf, Leaf), Node(third, Leaf, Leaf))::Nil
+      case _ => {
+        val combinations = for {
+          left <- numberOfElementsInLeftSubTree(elements.size)
+          root = elements(left)
+          right = elements.size - (left + 1)
+        } yield (root, left, right)
+        (combinations.flatMap(triple => for {
+          l <- makeAllBalancedTree(elements.take(triple._2))
+          r <- makeAllBalancedTree(elements.takeRight(triple._3))
+        } yield Node(triple._1, l, r))).toList
+      }
+    }
+
+    def genInput: Gen[(Int, List[AVLTree[Int]])] = for {
+      size <- Gen.choose(20, 25)
+      elements <- Gen.listOfN(size, Gen.choose(0, 1000))
+      selected <- Gen.choose(0, 1000)
+    } yield {
+      // selected mustn't be in elements already
+      val list = makeAllBalancedTree(elements.sorted.distinct.map(_*2))
+      (selected*2+1, list) 
+    }
+
+    def genInputDelete: Gen[(Int, List[AVLTree[Int]])] = for {
+      size <- Gen.choose(20, 25)
+      elements <- Gen.listOfN(size, Gen.choose(0, 1000))
+      e = elements.sorted.distinct
+      selected <- Gen.choose(0, e.size-1)
+    } yield {
+      // selected must be in elements already
+      val list = makeAllBalancedTree(e)
+      (e(selected), list) 
+    }
+  }
+
+  trait AVLInvariants {
+    self: AVLTreeTest =>
+
+    def isBalanced[A](t: AVLTree[A]): Boolean = t match {
+      case node: Node[A] => math.abs(node.balance) < 2 && (List(node.left, node.right) forall isBalanced)
+      case Leaf => true
+    }
+
+    def setup(invariant: AVLTree[Int] => Boolean) = forAll(genInput) {
+      case (selected: Int, trees: List[AVLTree[Int]]) => 
+      trees.map(tree => invariant(tree)).fold(true)((a, b) => a && b)
+    }
+
+    property("Every tree is initially balanced.") = setup(isBalanced)
+  }
+
+  object TestInsert extends AVLTreeTest("Insert") with AVLInvariants {
+    import math.Ordering.Int
+    property("`insert` creates a new tree containing the given element. The tree remains balanced.") = forAll(genInput) {
+      case (selected: Int, trees: List[AVLTree[Int]]) =>
+      trees.map(tree => {
+        val modifiedTree = tree.insert(selected, Int)
+        modifiedTree.contains(selected, Int) && isBalanced(modifiedTree)
+      }).fold(true)((a, b) => a && b)
+    }
+  }
+
+  object TestRemove extends AVLTreeTest("Remove") with AVLInvariants {
+    import math.Ordering.Int
+    property("`remove` creates a new tree without the given element. The tree remains balanced.") = forAll(genInputDelete) {
+      case (selected: Int, trees: List[AVLTree[Int]]) =>
+      trees.map(tree => {
+        val modifiedTree = tree.remove(selected, Int)
+        tree.contains(selected, Int) && !modifiedTree.contains(selected, Int) && isBalanced(modifiedTree)
+      }).fold(true)((a, b) => a && b)
+    }
+  }
+}
+
+object Test extends Properties("AVL") {
+  include(scala.collection.mutable.TestInsert)
+  include(scala.collection.mutable.TestRemove)
+}
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