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--- pp:2025:scala:l03 [2025/03/16 00:06]
cata_chiru
+++ pp:2025:scala:l03 [2025/03/28 12:04] (current)
cata_chiru
@@ Line 3: / Line 3: @@
 ===== 3.1 Abstract Lists =====
-Below you will find the algebraic definition of the datatype ''IList'':
+Below, you will find the algebraic definition of the datatype ''IList'':
 <code>
 Void : IList
@@ Line 9: / Line 9: @@
 </code>
-This definition has already been implemented in Scala, below. Please copy-paste this definition in your worksheet.
+This definition has already been implemented in Scala, as shown below. Please copy-paste this definition in your worksheet.
 <code scala>
 trait IList
@@ Line 23: / Line 23: @@
 </code>
 Implement ''isEmpty'' in Scala:
+''! Hint:'' To pattern match the list l as a Void or a Cons use the keyword ''match'' from Scala :
 <code scala>
-def isEmpty(l: IList) : Boolean = ???
+def isEmpty(l: IList) : Boolean = {
+    l match {
+        case Void => ???
+        case Cons(x, xs) => ???
+    }
+}
 </code>
 **3.1.2.** Write down axioms for ''size : IList -> Int'' and implement the operator in Scala:
@@ Line 32: / Line 40: @@
 </code>
-**3.1.3.** Implement ''contains'' which checks if an element is a member of a list.
+**3.1.3.** Implement ''contains'' to check if an element is a member of a list.
 <code scala>
 def contains(e: Int, l: IList) : Boolean = ???
@@ Line 95: / Line 103: @@
 case class Node(left: BinaryTree, info: Int, right: BinaryTree) extends BinaryTree {
-    override def toString: String = {
+  override def toString: String = {
-        def prettyPrint(tree: BinaryTree, depth: Int): String = {
+    def printTree(
-            tree match {
+                   tree: BinaryTree,
-                case TVoid => tree.toString()
+                   prefix: String = "",
-                case Node(l, value, r) =>
+                   isLeft: Boolean = true
-                    "\t" * (depth + 1) + value.toString() + "\n" +
+                 ): String =
-                    prettyPrint(l, depth+1) + prettyPrint(r, depth+1)
+      tree match {
-            }
+        case TVoid =>
-        }
+          ""
+        case Node(l, value, r) =>
+          val rightStr =
+            printTree(r, prefix + (if (isLeft && prefix.nonEmpty) "│   " else "    "), isLeft = false)
+          val nodeStr =
+            prefix + (if (tree != this) if (isLeft) "└── " else "┌── " else "    ") + value.toString + "\n"
+          val leftStr =
+            printTree(l, prefix + (if (isLeft) "    " else "│   "))
+          rightStr + nodeStr + leftStr
+      }
-        prettyPrint(this, 0)
+    '\n' + printTree(this)
-    }
+  }
 }
 </code>
-A Binary Tree can either be a void object (equivalent to NULL in C), or a Node with its information as an Int and two other trees as children (left and right).
+A Binary Tree can either be a TVoid object (equivalent to NULL in C), or a Node with its information as an Int and two other trees as children (left and right).
-**3.2.0.** Implement ''leaf_node'' that receives an Integer and returns a leaf with that integer as value:
+**3.2.0.** Implement ''leaf_node'' that receives an Int and returns a leaf with that integer as the node's value:
 <code scala>
 def leaf_node(value : Int) : BinaryTree = ???
@@ Line 120: / Line 137: @@
 <code scala>
 val arborica = Node(Node(leaf_node(-1), 5, TVoid), 1, Node(leaf_node(4), 2, Node(leaf_node(3), 6, leaf_node(7))))
-</code>
-and the following print function
-<code scala>
-TBD
 </code>
@@ Line 131: / Line 143: @@
 **3.2.1.** Implement ''mirror'' that mirrors the tree structure:
 <code scala>
-def mirror(t: BinaryTree) : BinaryTree = ???
+def mirror(tree: BinaryTree) : BinaryTree = ???
 </code>
--- 6. Implement the function flatten:
-flatten :: Tree a -> List a
-flatten TVoid = GVoid
-flatten (Node l k r) = app (GenCel k (flatten l)) (flatten r)
--- flatten (Node l k r) = app (GenCel k (flatten l)) (flatten r)
--- 7. Define list concatenation over type List a:
+**3.2.1.** Implement ''flatten'' that squashes the tree traversed in preorder into a list:
-app :: (List a) -> (List a) -> (List a)
+<code scala>
-app GVoid GVoid = GVoid
+def flatten(tree: BinaryTree): List[Int] = ???
-app l1 GVoid = l1
+</code>
-app GVoid l2 = l2
-app (GenCel val pointer) l2 = GenCel val (app pointer l2)
--- 8. Define the function tmap which is the Tree a correspondent to map::(a→b) → [a] → [b].
+**3.2.2.** Define the function ''tmap'' which is the Tree a correspondent to map::(a→b) → [a] → [b].
-tmap:: (a->b) -> (Tree a) -> (Tree b)
+<code scala>
-tmap f TVoid = TVoid
+def tmap(f: Int => Int, tree: BinaryTree) : BinaryTree = ???
-tmap f (Node l k r) = Node (tmap f l) (f k) (tmap f r)
+</code>
--- 10. Define the function tfoldr:
+**3.2.3.** ! Define the function ''tfoldr'', equivalent of foldr for trees: foldr :: (a -> b -> b) -> b -> Tree a -> b
-tfoldr :: (a -> b -> b) -> b -> Tree a -> b
+<code scala>
-tfoldr f acc TVoid = acc
+def tfoldr[B](f: (Int, B) => B, acc: B, tree: BinaryTree): B = ???
-tfoldr f acc (Node l k r) = tfoldr f (tfoldr f (f k acc) l) r
+</code>
+**3.2.4.** ! Implement the ''flattening'' function using tfoldr. The order of squashing the tree does not necessarily need to match the previous exercise:
+<code scala>
+def flattening(tree: BinaryTree): List[Int] = ???
+</code>
--- 11. Implement the flattening function using tfoldr:
-flattening :: Tree a -> List a
-flattening (Node l k r) = tfoldr GenCel GVoid (Node l k r)