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fp:lab05 [2022/03/28 17:52]
pdmatei 		fp:lab05 [2022/03/31 08:53] (current)
pdmatei
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 </​code>​ </​code>​
  
-For instance, ''​3''​ will be encoded as the value: ''​Succ(Succ(Succ(3)))''​.+For instance, ''​3''​ will be encoded as the value: ''​Succ(Succ(Succ(Zero)))''​.
  
 **5.1.1.** Write a function which implements addition over Nats: **5.1.1.** Write a function which implements addition over Nats:
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 In a [[https://​en.wikipedia.org/​wiki/​Binary_search_tree| binary search tree (BST)]], the key of the current node, is always: 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 **left** sub-tree. +  * **smaller** or equal than **all** keys in the **right** sub-tree. 
-  * **larger** 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: Consider a binary search tree with keys as integers, encoded as follows:
 <code scala> <code scala>
 +trait ITree {}
 case object Empty extends ITree  case object Empty extends ITree 
 case class INode(key: Int, left: ITree, right: ITree) extends ITree  case class INode(key: Int, left: ITree, right: ITree) extends ITree 
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 **5.2.6.** Implement a method ''​depth''​ which returns the maximal depth of a BST. Hint: use the method: ''​_.max(_)''​. **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.+**(!) 5.2.8.** 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''​. ​ **5.2.9.** 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:​+**(!) 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>​ <​code>​
     5             ​t.successor(2) = 5                      ​     5             ​t.successor(2) = 5                      ​
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 </​code>​ </​code>​
  
-**5.2.11.** Implement a method ''​remove(k)''​ which removes element ''​k''​ from the BST.+** (!!) 5.2.11.** Implement a method ''​remove(k)''​ which removes element ''​k''​ from the BST.