# 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

## Exception messages

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to
indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not
every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include
a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
`raise Exception`, you should write:

```python
raise Exception("Meaningful message indicating the source of the error")
```

## Running the tests

To run the tests, run the appropriate command below ([why they are different](https://github.com/pytest-dev/pytest/issues/1629#issue-161422224)):

- Python 2.7: `py.test binary_search_tree_test.py`
- Python 3.3+: `pytest binary_search_tree_test.py`

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
`python -m pytest binary_search_tree_test.py`

### Common `pytest` options

- `-v` : enable verbose output
- `-x` : stop running tests on first failure
- `--ff` : run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

## Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the `$EXERCISM_WORKSPACE/python/binary-search-tree` directory.

You can find your Exercism workspace by running `exercism debug` and looking for the line that starts with `Workspace`.

For more detailed information about running tests, code style and linting,
please see the [help page](http://exercism.io/languages/python).

## 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.