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# Binary Search
Implement a binary search algorithm.
Searching a sorted collection is a common task. A dictionary is a sorted
list of word definitions. Given a word, one can find its definition. A
telephone book is a sorted list of people's names, addresses, and
telephone numbers. Knowing someone's name allows one to quickly find
their telephone number and address.
If the list to be searched contains more than a few items (a dozen, say)
a binary search will require far fewer comparisons than a linear search,
but it imposes the requirement that the list be sorted.
In computer science, a binary search or half-interval search algorithm
finds the position of a specified input value (the search "key") within
an array sorted by key value.
In each step, the algorithm compares the search key value with the key
value of the middle element of the array.
If the keys match, then a matching element has been found and its index,
or position, is returned.
Otherwise, if the search key is less than the middle element's key, then
the algorithm repeats its action on the sub-array to the left of the
middle element or, if the search key is greater, on the sub-array to the
right.
If the remaining array to be searched is empty, then the key cannot be
found in the array and a special "not found" indication is returned.
A binary search halves the number of items to check with each iteration,
so locating an item (or determining its absence) takes logarithmic time.
A binary search is a dichotomic divide and conquer search algorithm.
## Restrictions
Rust provides in its standard library already a
[binary search function](https://doc.rust-lang.org/std/primitive.slice.html#method.binary_search).
For this exercise you should not use this function but just other basic tools instead.
## Hints
[Slices](https://doc.rust-lang.org/book/2018-edition/ch04-03-slices.html) have additionally to
the normal element access via indexing (slice[index]) many useful functions like
[split_at](https://doc.rust-lang.org/std/primitive.slice.html#method.split_at) or [getting
subslices](https://doc.rust-lang.org/std/primitive.slice.html#method.get) (slice[start..end]).
You can solve this exercise by just using boring old element access via indexing, but maybe the
other provided functions can make your code cleaner and safer.
## For bonus points
Did you get the tests passing and the code clean? If you want to, there
are some additional things you could try.
- Currently your find function will probably only work for slices of numbers,
but the Rust type system is flexible enough to create a find function which
works on all slices which contains elements which can be ordered.
- Additionally this find function can work not only on slices, but at the
same time also on a Vec or an Array.
To run the bonus tests, remove the `#[ignore]` flag and execute the tests with
the `generic` feature, like this:
```bash
$ cargo test --features generic
```
Then please share your thoughts in a comment on the submission. Did this
experiment make the code better? Worse? Did you learn anything from it?
### Hints for Bonus Points
- To get your function working with all kind of elements which can be ordered,
have a look at the [Ord Trait](https://doc.rust-lang.org/std/cmp/trait.Ord.html).
- To get your function working directly on Vec and Array, you can use the
[AsRef Trait](https://doc.rust-lang.org/std/convert/trait.AsRef.html)
## Rust Installation
Refer to the [exercism help page][help-page] for Rust installation and learning
resources.
## Writing the Code
Execute the tests with:
```bash
$ cargo test
```
All but the first test have been ignored. After you get the first test to
pass, open the tests source file which is located in the `tests` directory
and remove the `#[ignore]` flag from the next test and get the tests to pass
again. Each separate test is a function with `#[test]` flag above it.
Continue, until you pass every test.
If you wish to run all ignored tests without editing the tests source file, use:
```bash
$ cargo test -- --ignored
```
To run a specific test, for example `some_test`, you can use:
```bash
$ cargo test some_test
```
If the specific test is ignored use:
```bash
$ cargo test some_test -- --ignored
```
To learn more about Rust tests refer to the [online test documentation][rust-tests]
Make sure to read the [Modules][modules] chapter if you
haven't already, it will help you with organizing your files.
## Further improvements
After you have solved the exercise, please consider using the additional utilities, described in the [installation guide](https://exercism.io/tracks/rust/installation), to further refine your final solution.
To format your solution, inside the solution directory use
```bash
cargo fmt
```
To see, if your solution contains some common ineffective use cases, inside the solution directory use
```bash
cargo clippy --all-targets
```
## Submitting the solution
Generally you should submit all files in which you implemented your solution (`src/lib.rs` in most cases). If you are using any external crates, please consider submitting the `Cargo.toml` file. This will make the review process faster and clearer.
## Feedback, Issues, Pull Requests
The [exercism/rust](https://github.com/exercism/rust) repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the rust track team are happy to help!
If you want to know more about Exercism, take a look at the [contribution guide](https://github.com/exercism/docs/blob/master/contributing-to-language-tracks/README.md).
[help-page]: https://exercism.io/tracks/rust/learning
[modules]: https://doc.rust-lang.org/book/ch07-02-defining-modules-to-control-scope-and-privacy.html
[cargo]: https://doc.rust-lang.org/book/ch14-00-more-about-cargo.html
[rust-tests]: https://doc.rust-lang.org/book/ch11-02-running-tests.html
## Source
Wikipedia [http://en.wikipedia.org/wiki/Binary_search_algorithm](http://en.wikipedia.org/wiki/Binary_search_algorithm)
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
|
