August 26, 2024
P57 - Binary search trees (dictionaries).
Write a function to add an element to a binary search tree.
> End.addValue(2)
res0: Node[Int] = T(2 . .)
> res0.addValue(3)
res1: Node[Int] = T(2 . T(3 . .))
> res1.addValue(0)
res2: Node[Int] = T(2 T(0 . .) T(3 . .))Hint: The abstract definition of addValue in Tree should be def addValue[U >: T <% Ordered[U]](x: U): Tree[U]. The >: T is because addValue's parameters need to be contravariant in T. (Conceptually, we're adding nodes above existing nodes. In order for the subnodes to be of type T or any subtype, the upper nodes must be of type T or any supertype.) The <% Ordered[U] allows us to use the < operator on the values in the tree.
Use that function to construct a binary tree from a list of integers.
> Tree.fromList(List(3, 2, 5, 7, 1))
res3: Node[Int] = T(3 T(2 T(1 . .) .) T(5 . T(7 . .)))Finally, use that function to test your solution to P56.
> Tree.fromList(List(5, 3, 18, 1, 4, 12, 21)).isSymmetric
res4: Boolean = true
> Tree.fromList(List(3, 2, 5, 7, 4)).isSymmetric
res5: Boolean = false
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