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--- fp:lab04 [2022/05/15 23:53]
vbadoiu
+++ fp:lab04 [2022/05/15 23:54] (current)
vbadoiu old revision restored (2022/03/25 10:15)
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 def honorsList(g: Gradebook): List[String] = ???
 </code>
-===== 5. Functional data representation =====
-==== 5.1. Nats ===
-Consider the following toy implementation of the type ''Nat'' which encodes natural numbers.
-<code scala>
-trait Nat {}
-case object Zero extends Nat {}
-case class Succ(n: Nat) extends Nat {}
-</code>
-For instance, ''3'' will be encoded as the value: ''Succ(Succ(Succ(Zero)))''.
-**5.1.1.** Write a function which implements addition over Nats:
-<code scala>
-def add(n: Nat, m: Nat): Nat = ???
-</code>
-**5.1.2.** Write a function which converts a ''Nat'' to an ''Int'':
-<code scala>
-def toInt(n: Nat): Int = ???
-</code>
-**5.1.3.** Write a function which converts an ''Int'' to a ''Nat''.
-<code scala>
-def fromInt(i: Int): Nat
-</code>
-==== 5.2. Binary Search Trees ===
-In a [[https://en.wikipedia.org/wiki/Binary_search_tree| binary search tree (BST)]], the key of the current node, is always:
-  * **smaller** or equal than **all** keys in the **right** sub-tree.
-  * **larger** or equal than **all** keys in the **left** sub-tree.
-Consider a binary search tree with keys as integers, encoded as follows:
-<code scala>
-trait ITree {}
-case object Empty extends ITree
-case class INode(key: Int, left: ITree, right: ITree) extends ITree
-</code>
-**5.2.1.** Create the tree shown below:
-<code scala>
-val tree = ???
-/*
-      /   \
-     7
-    / \     \
-  3      9
-*/
-</code>
-**5.2.2.** Implement the method ''size'' which determines the number of non-empty nodes from the BST.
-**5.2.3.** Define the method ''contains'', which checks if a given integer is a member of the BST.
-**5.2.4.** Implement the method ''ins'' which inserts a new integer in the BST. **Note:** the insertion must return a new BST (the //binary search tree// property mentioned above must hold after insertion).
-**5.2.5.** Implement a method ''flatten'' which converts a BST into a list of integers. You must carefully choose the flattening method in such a way as to obtain **a sorted list** from the BST. Hint: you may use the list concatenation operator '':::'' (triple colons; example usage: ''List(1,2,3):::List(4,5)''.
-**5.2.6.** Implement a method ''depth'' which returns the maximal depth of a BST. Hint: use the method: ''_.max(_)''.
-**(!) 5.2.8.** Implement a method ''minimum'' which returns the smallest integer from a BST. (If the tree is empty, we return -1). Hint: use the example above, to guide your implementation.
-**5.2.9.** Implement a similar method ''maximum''.
-**(!) 5.2.10.** Implement a method ''successor(k)'' which returns **the smallest** integer from the BST, which is **larger** than ''k''. Use the following examples for your implementation:
-<code>
-             t.successor(2) = 5
-   / \            t.successor(5) = 6
-   7           t.successor(7) = 8
-     / \
-   8
-</code>
-** (!!) 5.2.11.** Implement a method ''remove(k)'' which removes element ''k'' from the BST.