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 +==== Handout ====
 +{{:​parcon17:​|Click here to download}} the handout for this assignment.
 +===== Binary Trees =====
 +Binary trees are tree based data structures where every node has at most two children (left and right).
 +In this exercise, every node stores an integer element.
 +From this we can build a binary search tree by requiring for every node that 
 +  - values of elements in the left subtree are strictly smaller than the node's element
 +  - values of elements in the right subtree are strictly bigger than the node's element ​
 +In addition, there should be no duplicates, hence we obtain a binary tree set.
 +Your task in this assignment is to implement an actor-based binary tree set where each node is 
 +represented by one actor. The advantage of such an actor-based solution is that it can execute ​
 +fully asynchronously and in parallel.
 +==== The API ====
 +You can find the message-based API for the actor-based binary tree to be implemented in the supplied `BinaryTreeSet` object
 +in the file `BinaryTreeSet.scala`.
 +The operations, represented by actor messages, that the implementation should support are the following:
 +  - `Insert`
 +  - `Remove`
 +  - `Contains`
 +All three of the operations expect an `ActorRef` representing the requester of the operation, a numerical identifier of
 +the operation and the element itself. `Insert` and `Remove` operations should result in an `OperationFinished` message sent
 +to the provided requester `ActorRef` reference including the id of the operation. `Insert` and `Remove` should return an
 +`OperationFinished` message even if the element was already present in the tree or was not found, respectively. ​
 +`Contains` should result in a `ContainsResult` message containing the result of the lookup (a Boolean which is 
 +true if and only if the element is in the tree when the query arrives) and the identifier of the `Contains` query.
 +==== Handling of Removal ====
 +You should observe that both the `Insert` and `Contains` operations share an important property, namely, they only
 +traverse a linear path from the root of the tree to the appropriate inner node or leaf. Since the tree nodes are actors
 +which process messages one-by-one, no additional synchronization is needed between these operations. Removal in a
 +binary tree unfortunately results in tree restructuring,​ which means that nodes would need to communicate and coordinate
 +between each other (while additional operations arrive from the external world!).
 +Therefore, instead of implementing the usual binary tree removal, in your solution you should use a flag that is stored
 +in every tree node (`removed`) indicating whether the element in the node has been removed or not. This will result in a very
 +simple implementation that is concurrent and correct with minimal effort. Unfortunately this decision results in the
 +side effect that the tree set accumulates "​garbage"​ (elements that have been removed) over time.
 +==== Garbage Collection ====
 +As we have seen, removal of entries can be implemented simply by using a removal flag with the
 +added cost of growing garbage over time. To overcome this limitation you will need to implement a "​garbage collection"​
 +feature. Whenever your binary tree set receives a `GC` message, it should clean up all the removed elements, while
 +additional operations might arrive from the external world.
 +The garbage collection task can be implemented in two steps. The first subtask is to implement an internal
 +`CopyTo` operation on the binary tree that copies all its non-removed contents from the binary tree to a provided new one. This
 +implementation can assume that no operations arrive while the copying happens (i.e. the tree is protected from modifications
 +while copying takes places).
 +The second part of the implementation is to implement garbage collection in the manager (`BinaryTreeSet`) by using the copy operation.
 +The newly constructed tree should replace the old one and all actors from the old one should be stopped.
 +Since copying assumes no other concurrent operations, the manager should handle the case when operations arrive while still
 +performing the copy in the background. It is your responsibility to implement the manager in such a way that the fact
 +that garbage collection happens is invisible from the outside (of course additional delay is allowed). ​
 +For the sake of simplicity, your implementation should ignore GC requests that arrive while garbage collection is taking place.
 +==== Ordering Guarantees ====
 +Replies to operations may be sent in any order but the contents of `ContainsResult` replies must obey the order of the
 +operations. To illustrate what this means observe the following example:
 +Client sends:
 +    Insert(testActor,​ id=100, elem=1)
 +    Contains(testActor,​ id=50, elem=2)
 +    Remove(testActor,​ id=10, elem=1)
 +    Insert(testActor,​ id=20, elem=2)
 +    Contains(testActor,​ id=80, elem=1)
 +    Contains(testActor,​ id=70, elem=2)
 +Client receives:
 +    ContainsResult(id=70,​ true)
 +    OperationFinished(id=20)
 +    OperationFinished(id=100)
 +    ContainsResult(id=80,​ false)
 +    OperationFinished(id=10)
 +    ContainsResult(id=50,​ false)
 +While the results seem "​garbled",​ they actually strictly correspond to the order of the original operations. On
 +closer examination you can observe that the order of original operations was [100, 50, 10, 20, 80, 70]. Now if you
 +order the responses according to this sequence the result would be:
 +    Insert(testActor,​ id=100, elem=1) -> OperationFinished(id=100)
 +    Contains(testActor,​ id=50, elem=2) -> ContainsResult(id=50,​ false)
 +    Remove(testActor,​ id=10, elem=1) -> OperationFinished(id=10)
 +    Insert(testActor,​ id=20, elem=2) -> Insert(elem=2,​ id=20)
 +    Contains(testActor,​ id=80, elem=1) -> ContainsResult(id=80,​ false)
 +    Contains(testActor,​ id=70, elem=2) -> ContainsResult(id=70,​ true)
 +As you can see, the responses the client received are the same, hence they must have been executed sequentially,​
 +and only the responses have arrived out of order. Thus, the responses obey the semantics of sequential operations
 + -- it is simply their arrival order is not
 +defined. You might find it easier for testing to use sequential identifiers for the operations, since that makes it
 +easier to follow the sequence of responses.
 +You might also note that out-of-order responses can only happen if the client does not wait for each individual answer
 +before continuing with sending operations.
 +While this loose ordering guarantee on responses might look strange at first, it will significantly simplify the
 +implementation of the binary tree and you are encouraged to make full use of it.
 +==== Your task ====
 +You can find code stubs in the file `BinaryTreeSet.scala` which provides you with the API as described above,
 +the `BinaryTreeSet` and `BinaryTreeNode` classes. The `BinaryTreeSet` represents the whole binary tree.
 +This is also the only actor that is explicitly created by the user and the only actor the user sends messages to.
 +You can implement as many or as few message handlers as you like and you can add additional variables or helper
 +functions. We provide suggestions in your code stub, marked with the comment `optional`, but you are free to use
 +it fully or partially; the optional elements are not part of the tested API.
 +To see a binary tree in operation check our provided tests in `BinaryTreeSuite.scala`. Note in particular
 +that it is the user who triggers garbage collection by sending a `GC` message (for the sake of simplicity of this exercise).
 +Don't forget to make sure that no `Operation` messages interfere during garbage collection and that the user does
 +not receive any messages that may result from the copying process. ​
 +The following may be useful for your implementation:​
 +  - Another way to stop an actor, besides the `stop` method you have seen, is to send it a `PoisonPill` message.
 +  - `context.parent` returns the ActorRef of the actor which created the current actor (i.e. its parent).
 +  - If you see a log message like the following
 +    [INFO] [11/21/2013 14:​04:​13.237] [] [akka://​PostponeSpec/​deadLetters] Message [actorbintree.BinaryTreeSet$OperationFinished] from Actor[akka://​PostponeSpec/​user/​$e/​my-actor#​-1012560631] to Actor[akka://​PostponeSpec/​deadLetters] was not delivered. [1] dead letters encountered.
 +it means that one of your messages (here the OperationFinished) message was not delivered from actor `my-actor` to actor `deadLetters`—the latter is where actors forward their messages after they terminate.
 +You should check that you do not stop actors prematurely.
 +=== A word on Actor counts: ===
 +  - The grader verifies that enough Actors are created when inserting elements.
 +  - The grader also verifies that enough Actors are stopped in response to a `GC` command (i.e. for those elements that were previously marked removed from the set).