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--- pp:2025:scala:l05 [2025/03/30 15:51]
cata_chiru created
+++ pp:2025:scala:l05 [2025/04/04 15:09] (current)
tpruteanu
@@ Line 50: / Line 50: @@
 </code>
-==== 4.3 Binary Trees ====
+==== 5.3 Binary Trees ====
 Given the implementation of binary trees from the previous lab:
 <code scala>
-trait BinaryTree {
+trait BTree
-    override def toString: String = super.toString: String
-}
-case object TVoid extends BinaryTree {
+case object TVoid extends BTree
-    override def toString: String = "-"
+case class Node(left: BTree, info: Int, right: BTree) extends BTree
+def leaf_node(value : Int) : BTree = {
+  Node(TVoid, value, TVoid)
 }
-case class Node(left: BinaryTree, info: Int, right: BinaryTree) extends BinaryTree {
+object BTreePrinter {
-  override def toString: String = {
+  case class PrintInfo(len: Int, center: Int, text: List[String])
-    def printTree(
-                   tree: BinaryTree,
-                   prefix: String = "",
-                   isLeft: Boolean = true
-                 ): String =
-      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
-      }
-    '\n' + printTree(this)
+  def pp(tree: BTree): PrintInfo = tree match {
+    case TVoid => PrintInfo(3, 2, List("Nil"))
+    case Node(left, value, right) =>
+      val strValue = value.toString
+      val ppL = pp(left)
+      val ppR = pp(right)
+      val nlen = ppL.len + ppR.len + 1
+      val ncenter = ppL.len + 1
+      require(strValue.length <= nlen, "Nice try")
+      val alignedX = " " * (ncenter - (strValue.length / 2) - 1) + strValue
+      val centerLine = " " * (ncenter - 1) + "|"
+      val dottedLine = " " * (ppL.center - 1) + "-" * (nlen - ppL.center - (ppR.len - ppR.center + 1) + 2)
+      val downLines = " " * (ppL.center - 1) + "|" + " " * (nlen - ppL.center - (ppR.len - ppR.center +1)) + "|"
+      val combinedLines = zipPad("",(l, r) => l ++ (" " * (ppL.len - l.size + 1 )) ++ r, ppL.text, ppR.text)
+      PrintInfo(nlen, ncenter, alignedX :: centerLine :: dottedLine :: downLines :: combinedLines)
   }
+  def zipPad[A](pad: A, f: (A, A) => A, left: List[A], right: List[A]): List[A] = (left, right) match {
+    case (Nil, Nil) => Nil
+    case (x :: xs, Nil) => x :: zipPad(pad, f, xs, List(pad))
+    case (Nil, y :: ys) => f(pad, y) :: zipPad(pad, f, List(pad), ys)
+    case (x :: xs, y :: ys) => f(x, y) :: zipPad(pad, f, xs, ys)
+  }
+  def printTree(tree: BTree): String = "\n" + pp(tree).text.mkString("\n")
 }
-def leaf_node(value : Int) : BinaryTree = {
+extension(t: BTree) {
-    Node(TVoid, value, TVoid)
+  def toStringTree: String = BTreePrinter.printTree(t)
 }
 </code>
@@ Line 93: / Line 106: @@
 <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))))
+arborica.toStringTree
 </code>
@@ Line 208: / Line 222: @@
 def matSum(m1: Matrix, m2: Matrix): Matrix = ???
 </code>
+**5.5.5** Write a function that transposed a matrix:
-**5.5.5** Write a function that computes the matrix product:
+$math[ \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right)^{T} = \left(\begin{array}{ccc} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ \end{array}\right)]
-$math[ \displaystyle 2 * \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right) = \left(\begin{array}{ccc} 2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18 \\ \end{array}\right)]
+<code scala>
+def transposed(m: Matrix): Matrix = ???
+</code>
+**5.5.6** Write a function that computes the matrix product:
+$math[ \left(\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array}\right)  * \left(\begin{array}{ccc} 1 & 2 \\ 3 & 4 \\ 5 & 6 \\ \end{array}\right) = \left(\begin{array}{ccc} 22 & 28 \\ 49 & 64 \\ 76 & 100 \\ \end{array}\right)]
+(For an element of the result $math[a_{ij}] the value is obtained by selecting the i-th row and the j-th column, computing the products of the elements at the same index and adding all those results up:
+E. g. 22 = 1 * 1 + 2 * 3 + 3 * 5)
 <code scala>