85 lines
2.4 KiB
Markdown
85 lines
2.4 KiB
Markdown
|
# Binary Search Tree
|
||
|
|
|
||
|
|
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](http://exercism.io/languages/ruby).
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
|
||
|
|
## Source
|
||
|
|
|
||
|
|
Josh Cheek [https://twitter.com/josh_cheek](https://twitter.com/josh_cheek)
|
||
|
|
|
||
|
|
## Submitting Incomplete Solutions
|
||
|
|
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
|