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- 1. Data Structures In Scala Meetu Maltiar Principal Consultant Knoldus
- 2. AgendaQueueBinary TreeBinary Tree Traversals
- 3. Functional QueueFunctional Queue is a data structure that has threeoperations: head: returns first element of the Queue tail: returns a Queue without its Head enqueue: returns a new Queue with given element at Head Has therefore First In First Out (FIFO) property
- 4. Functional Queue Continuedscala> val q = scala.collection.immutable.Queue(1, 2, 3)q: scala.collection.immutable.Queue[Int] = Queue(1, 2, 3)scala> val q1 = q enqueue 4q1: scala.collection.immutable.Queue[Int] = Queue(1, 2, 3, 4)scala> qres3: scala.collection.immutable.Queue[Int] = Queue(1, 2, 3)scala> q1res4: scala.collection.immutable.Queue[Int] = Queue(1, 2, 3, 4)
- 5. Simple Queue Implementationclass SlowAppendQueue[T](elems: List[T]) { def head = elems.head def tail = new SlowAppendQueue(elems.tail) def enqueue(x: T) = new SlowAppendQueue(elems ::: List(x))}Head and tail operations are fast. Enqueue operation is slow as its performance isdirectly proportional to number of elements.
- 6. Queue Optimizing Enqueueclass SlowHeadQueue[T](smele: List[T]) { // smele is elems reversed def head = smele.last // Not efficient def tail = new SlowHeadQueue(smele.init) // Not efficient def enqueue(x: T) = new SlowHeadQueue(x :: smele)}smele is elems reversed. Head operation is not efficient. Neither is tail operation. As bothlast and init performance is directly proportional to number of elements in Queue
- 7. Functional Queueclass Queue[T](private val leading: List[T], private val trailing:List[T]) { private def mirror = if (leading.isEmpty) new Queue(trailing.reverse, Nil) else this def head = mirror.leading.head def tail = { val q = mirror new Queue(q.leading.tail, q.trailing) } def enqueue(x: T) = new Queue(leading, x :: trailing)}
- 8. Binary Search TreeBST is organized tree.BST has nodes one of them is specified as Root node.Each node in BST has not more than two Children.Each Child is also a Sub-BST.Child is a leaf if it just has a root.
- 9. Binary Search PropertyThe keys in Binary Search Tree is stored to satisfyfollowing property:Let x be a node in BST.If y is a node in left subtree of xThen Key[y] less than equal key[x]If y is a node in right subtree of xThen key[x] less than equal key[y]
- 10. Binary Search Property The Key of the root is 6 The keys 2, 5 and 5 in left subtree is no larger than 6. The key 5 in root left child is no smaller than the key 2 in that nodes left subtree and no larger than key 5 in the right sub tree
- 11. Tree Scala Representationcase class Tree[+T](value: T, left:Option[Tree[T]], right: Option[Tree[T]])This Tree representation is a recursive definition and has typeparameterization and is covariant due to is [+T] signatureThis Tree class definition has following properties:1. Tree has value of the given node2. Tree has left sub-tree and it may have or do not contain value3. Tree has right sub-tree and it may have or do not contain valueIt is covariant to allow subtypes to be contained in the Tree
- 12. Tree In-order TraversalBST property enables us to print out allthe Keys in a sorted order using simplerecursive In-order traversal.It is called In-Order because it printskey of the root of a sub-tree betweenprinting of the values in its left sub-tree and printing those in its right sub-tree
- 13. Tree In-order AlgorithmINORDER-TREE-WALK(x)1. if x != Nil2. INORDER-TREE-WALK(x.left)3. println x.key4. INORDER-TREE-WALK(x.right)For our BST in example before the output expected will be:255678
- 14. Tree In-order Scala def inOrder[A](t: Option[Tree[A]], f: Tree[A] =>Unit): Unit = t match { case None => case Some(x) => if (x.left != None) inOrder(x.left, f) f(x) if (x.right != None) inOrder(x.right, f) }
- 15. Tree Pre-order AlgorithmPREORDER-TREE-WALK(x)1. if x != Nil2. println x.key3. PREORDER-TREE-WALK(x.left)4. PREORDER-TREE-WALK(x.right)For our BST in example before the output expected will be:652578
- 16. Tree Pre-order Scaladef preOrder[A](t: Option[Tree[A]], f: Tree[A]=> Unit): Unit = t match { case None => case Some(x) => f(x) if (x.left != None) inOrder(x.left, f) if (x.right != None) inOrder(x.right, f) }Pre-Order traversal is good for creating a copy of the Tree
- 17. Tree Post-Order AlgorithmPOSTORDER-TREE-WALK(x)1. if x != Nil2. POSTORDER-TREE-WALK(x.left)3. POSTORDER-TREE-WALK(x.right)4. println x.keyFor our BST in example before the output expected will be:255876Useful in deleting a tree. In order to free up resources anode in the tree can only be deleted if all the children (leftand right) are also deletedPost-Order does exactly that. It processes left and rightsub-trees before processing current node
- 18. Tree Post-order Scaladef postOrder[A](t: Option[Tree[A]], f: Tree[A]=> Unit): Unit = t match { case None => case Some(x) => if (x.left != None) postOrder(x.left, f) if (x.right != None) postOrder(x.right, f) f(x) }
- 19. References1. Cormen Introduction to Algorithms2. Binary Search Trees Wikipedia3. Martin Odersky “Programming In Scala”4. Daniel spiewak talk “Extreme Cleverness:Functional Data Structures In Scala”
- 20. Thank You!!

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