Published at Jul 13 2018
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Instructions

Test suite

Solution

Insert and search for numbers in a binary tree.

When we need to represent sorted data, an array does not make a good data structure.

Say we have the array `[1, 3, 4, 5]`

, and we add 2 to it so it becomes
`[1, 3, 4, 5, 2]`

now we must sort the entire array again! We can
improve on this by realizing that we only need to make space for the new
item `[1, nil, 3, 4, 5]`

, and then adding the item in the space we
added. But this still requires us to shift many elements down by one.

Binary Search Trees, however, can operate on sorted data much more efficiently.

A binary search tree consists of a series of connected nodes. Each node
contains a piece of data (e.g. the number 3), a variable named `left`

,
and a variable named `right`

. The `left`

and `right`

variables point at
`nil`

, or other nodes. Since these other nodes in turn have other nodes
beneath them, we say that the left and right variables are pointing at
subtrees. All data in the left subtree is less than or equal to the
current node's data, and all data in the right subtree is greater than
the current node's data.

For example, if we had a node containing the data 4, and we added the data 2, our tree would look like this:

```
4
/
2
```

If we then added 6, it would look like this:

```
4
/ \
2 6
```

If we then added 3, it would look like this

```
4
/ \
2 6
\
3
```

And if we then added 1, 5, and 7, it would look like this

```
4
/ \
/ \
2 6
/ \ / \
1 3 5 7
```

For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

```
gem install minitest
```

If you would like color output, you can `require 'minitest/pride'`

in
the test file, or note the alternative instruction, below, for running
the test file.

Run the tests from the exercise directory using the following command:

```
ruby binary_search_tree_test.rb
```

To include color from the command line:

```
ruby -r minitest/pride binary_search_tree_test.rb
```

Josh Cheek https://twitter.com/josh_cheek

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
require 'minitest/autorun'
require_relative 'binary_search_tree'
class BstTest < Minitest::Test
def test_data_is_retained
assert_equal 4, Bst.new(4).data
end
def test_inserting_less
skip
four = Bst.new 4
four.insert 2
assert_equal 4, four.data
assert_equal 2, four.left.data
end
def test_inserting_same
skip
four = Bst.new 4
four.insert 4
assert_equal 4, four.data
assert_equal 4, four.left.data
end
def test_inserting_right
skip
four = Bst.new 4
four.insert 5
assert_equal 4, four.data
assert_equal 5, four.right.data
end
def test_complex_tree
skip
four = Bst.new 4
four.insert 2
four.insert 6
four.insert 1
four.insert 3
four.insert 7
four.insert 5
assert_equal 4, four.data
assert_equal 2, four.left.data
assert_equal 1, four.left.left.data
assert_equal 3, four.left.right.data
assert_equal 6, four.right.data
assert_equal 5, four.right.left.data
assert_equal 7, four.right.right.data
end
def record_all_data(bst)
all_data = []
bst.each { |data| all_data << data }
all_data
end
def test_iterating_one_element
skip
assert_equal [4], record_all_data(Bst.new(4))
end
def test_iterating_over_smaller_element
skip
four = Bst.new 4
four.insert 2
assert_equal [2, 4], record_all_data(four)
end
def test_iterating_over_larger_element
skip
four = Bst.new 4
four.insert 5
assert_equal [4, 5], record_all_data(four)
end
def test_iterating_over_complex_tree
skip
four = Bst.new 4
four.insert 2
four.insert 1
four.insert 3
four.insert 6
four.insert 7
four.insert 5
assert_equal [1, 2, 3, 4, 5, 6, 7], record_all_data(four)
end
def test_each_returns_enumerator_if_no_block
skip
tree = Bst.new 4
[2, 1, 3, 6, 7, 5].each { |x| tree.insert x }
each_enumerator = tree.each
assert_kind_of Enumerator, each_enumerator
(1..7).each { |x| assert_equal(x, each_enumerator.next) }
assert_raises(StopIteration) { each_enumerator.next }
end
# Problems in exercism evolve over time, as we find better ways to ask
# questions.
# The version number refers to the version of the problem you solved,
# not your solution.
#
# Define a constant named VERSION inside of the top level BookKeeping
# module, which may be placed near the end of your file.
#
# In your file, it will look like this:
#
# module BookKeeping
# VERSION = 1 # Where the version number matches the one in the test.
# end
#
# If you are curious, read more about constants on RubyDoc:
# http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html
def test_bookkeeping
skip
assert_equal 1, BookKeeping::VERSION
end
end
```

```
Bst = Struct.new(:data, :left, :right) do
def each(&blk)
left.each(&blk) if left
yield data
right.each(&blk) if right
end
def insert(value)
value <= data ? insert_left(value) : insert_right(value)
end
def insert_left(value)
if left.nil?
self.left = Bst.new(value)
else
left.insert(value)
end
end
def insert_right(value)
if right.nil?
self.right = Bst.new(value)
else
right.insert(value)
end
end
end
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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