Problems.P57

Description

Part of Ninety-Nine Haskell Problems. Some solutions are in Solutions.P57.

Synopsis

# Documentation

construct :: Ord a => [a] -> Tree a Source #

Write an addedTo function which adds an element to a binary search tree to obtain another binary search tree. Use this function to construct a binary search tree from a list of ordered elements. Each element should be added from the front to the back of the list.

### Examples

>>> construct [3, 2, 5, 7, 1]
Branch 3 (Branch 2 (Branch 1 Empty Empty) Empty) (Branch 5 Empty (Branch 7 Empty Empty))

>>> symmetric . construct $[5, 3, 18, 1, 4, 12, 21] True  >>> symmetric . construct$ [3, 2, 5, 7, 1]
True


### Notes

Expand

The original problem refers to a predicate which had not appeared in previous problems: Use the predicate add/3, developed in chapter 4 of the course, to write a predicate to construct a binary search tree from a list of integer numbers. This is presumably a reference to course material used at the time the problems were written. Given the different context, the problem was revised to also implement the function that would have taken the role that the add/3 predicate would have had in the original context.

For consistent examples, the condition to also use naive binary search tree insertion was imposed. For the same reason, the order for which elements in a list are added to the tree is also specified. Of course, anyone is free to implement whatever they want, although that could mean they would not pass the available tests.

addedTo :: Ord a => a -> Tree a -> Tree a Source #

Return a binary search tree with an element added to another binary search tree.

Use a simple insertion algorithm which leaves the tree mostly the same except for the new element in a leaf node. In particular, no balancing should be done.

### Examples

>>> 8 addedTo Branch 5 Empty (Branch 7 Empty (Branch 9 Empty Empty))
Branch 5 Empty (Branch 7 Empty (Branch 9 (Branch 8 Empty Empty) Empty))