binary_search
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{
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"authors": [
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"bernardoamc"
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],
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"contributors": [
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"angelikatyborska",
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"Cohen-Carlisle",
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"devonestes",
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"lpil",
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"martinsvalin",
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"neenjaw",
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"parkerl",
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"screamingjungle",
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"sotojuan",
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"waiting-for-dev"
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],
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"files": {
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"solution": [
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"lib/binary_search.ex"
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],
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"test": [
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"test/binary_search_test.exs"
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],
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"example": [
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".meta/example.ex"
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]
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},
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"blurb": "Implement a binary search algorithm.",
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"source": "Wikipedia",
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"source_url": "https://en.wikipedia.org/wiki/Binary_search_algorithm"
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}
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{"track":"elixir","exercise":"binary-search","id":"46907374d6fd43e0815717c10201d2e0","url":"https://exercism.org/tracks/elixir/exercises/binary-search","handle":"negrienko","is_requester":true,"auto_approve":false}
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# Used by "mix format"
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[
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inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
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]
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# The directory Mix will write compiled artifacts to.
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/_build/
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# If you run "mix test --cover", coverage assets end up here.
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/cover/
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# The directory Mix downloads your dependencies sources to.
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/deps/
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# Where third-party dependencies like ExDoc output generated docs.
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/doc/
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# Ignore .fetch files in case you like to edit your project deps locally.
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/.fetch
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# If the VM crashes, it generates a dump, let's ignore it too.
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erl_crash.dump
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# Also ignore archive artifacts (built via "mix archive.build").
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*.ez
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# Ignore package tarball (built via "mix hex.build").
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binary_search-*.tar
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# Help
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## Running the tests
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From the terminal, change to the base directory of the exercise then execute the tests with:
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```bash
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$ mix test
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```
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This will execute the test file found in the `test` subfolder -- a file ending in `_test.exs`
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Documentation:
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* [`mix test` - Elixir's test execution tool](https://hexdocs.pm/mix/Mix.Tasks.Test.html)
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* [`ExUnit` - Elixir's unit test library](https://hexdocs.pm/ex_unit/ExUnit.html)
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## Pending tests
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In test suites of practice exercises, all but the first test have been tagged to be skipped.
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Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.
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For example:
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```elixir
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# @tag :pending
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test "shouting" do
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assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
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end
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```
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If you wish to run all tests at once, you can include all skipped test by using the `--include` flag on the `mix test` command:
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```bash
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$ mix test --include pending
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```
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Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the file `test/test_helper.exs`.
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```elixir
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# ExUnit.configure(exclude: :pending, trace: true)
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```
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## Useful `mix test` options
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* `test/<FILE>.exs:LINENUM` - runs only a single test, the test from `<FILE>.exs` whose definition is on line `LINENUM`
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* `--failed` - runs only tests that failed the last time they ran
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* `--max-failures` - the suite stops evaluating tests when this number of test failures
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is reached
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* `--seed 0` - disables randomization so the tests in a single file will always be ran
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in the same order they were defined in
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## Submitting your solution
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You can submit your solution using the `exercism submit lib/binary_search.ex` command.
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This command will upload your solution to the Exercism website and print the solution page's URL.
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It's possible to submit an incomplete solution which allows you to:
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- See how others have completed the exercise
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- Request help from a mentor
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## Need to get help?
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If you'd like help solving the exercise, check the following pages:
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- The [Elixir track's documentation](https://exercism.org/docs/tracks/elixir)
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- The [Elixir track's programming category on the forum](https://forum.exercism.org/c/programming/elixir)
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- [Exercism's programming category on the forum](https://forum.exercism.org/c/programming/5)
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- The [Frequently Asked Questions](https://exercism.org/docs/using/faqs)
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Should those resources not suffice, you could submit your (incomplete) solution to request mentoring.
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If you're stuck on something, it may help to look at some of the [available resources](https://exercism.org/docs/tracks/elixir/resources) out there where answers might be found.
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# Binary Search
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Welcome to Binary Search on Exercism's Elixir Track.
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If you need help running the tests or submitting your code, check out `HELP.md`.
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## Introduction
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You have stumbled upon a group of mathematicians who are also singer-songwriters.
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They have written a song for each of their favorite numbers, and, as you can imagine, they have a lot of favorite numbers (like [0][zero] or [73][seventy-three] or [6174][kaprekars-constant]).
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You are curious to hear the song for your favorite number, but with so many songs to wade through, finding the right song could take a while.
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Fortunately, they have organized their songs in a playlist sorted by the title — which is simply the number that the song is about.
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You realize that you can use a binary search algorithm to quickly find a song given the title.
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[zero]: https://en.wikipedia.org/wiki/0
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[seventy-three]: https://en.wikipedia.org/wiki/73_(number)
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[kaprekars-constant]: https://en.wikipedia.org/wiki/6174_(number)
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## Instructions
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Your task is to implement a binary search algorithm.
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A binary search algorithm finds an item in a list by repeatedly splitting it in half, only keeping the half which contains the item we're looking for.
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It allows us to quickly narrow down the possible locations of our item until we find it, or until we've eliminated all possible locations.
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~~~~exercism/caution
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Binary search only works when a list has been sorted.
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~~~~
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The algorithm looks like this:
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- Find the middle element of a _sorted_ list and compare it with the item we're looking for.
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- If the middle element is our item, then we're done!
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- If the middle element is greater than our item, we can eliminate that element and all the elements **after** it.
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- If the middle element is less than our item, we can eliminate that element and all the elements **before** it.
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- If every element of the list has been eliminated then the item is not in the list.
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- Otherwise, repeat the process on the part of the list that has not been eliminated.
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Here's an example:
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Let's say we're looking for the number 23 in the following sorted list: `[4, 8, 12, 16, 23, 28, 32]`.
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- We start by comparing 23 with the middle element, 16.
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- Since 23 is greater than 16, we can eliminate the left half of the list, leaving us with `[23, 28, 32]`.
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- We then compare 23 with the new middle element, 28.
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- Since 23 is less than 28, we can eliminate the right half of the list: `[23]`.
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- We've found our item.
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## Source
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### Created by
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- @bernardoamc
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### Contributed to by
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- @angelikatyborska
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- @Cohen-Carlisle
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- @devonestes
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- @lpil
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- @martinsvalin
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- @neenjaw
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- @parkerl
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- @screamingjungle
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- @sotojuan
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- @waiting-for-dev
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### Based on
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Wikipedia - https://en.wikipedia.org/wiki/Binary_search_algorithm
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defmodule BinarySearch do
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@doc """
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Searches for a key in the tuple using the binary search algorithm.
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It returns :not_found if the key is not in the tuple.
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Otherwise returns {:ok, index}.
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## Examples
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iex> BinarySearch.search({}, 2)
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:not_found
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iex> BinarySearch.search({1, 3, 5}, 2)
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:not_found
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iex> BinarySearch.search({1, 3, 5}, 5)
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{:ok, 2}
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"""
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@spec search(tuple, integer) :: {:ok, integer} | :not_found
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def search({}, _value), do: :not_found
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def search(numbers, value), do: do_search(numbers, value, 0, tuple_size(numbers) - 1)
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defp do_search(_numbers, _value, from, to) when from > to, do: :not_found
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defp do_search(numbers, value, from, to) do
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middle = div(from + to, 2)
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element = elem(numbers, middle)
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cond do
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value == element -> {:ok, middle}
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value < element -> do_search(numbers, value, from, middle - 1)
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value > element -> do_search(numbers, value, middle + 1, to)
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end
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end
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end
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defmodule BinarySearch.MixProject do
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use Mix.Project
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def project do
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[
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app: :binary_search,
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version: "0.1.0",
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# elixir: "~> 1.8",
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start_permanent: Mix.env() == :prod,
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deps: deps()
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]
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end
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# Run "mix help compile.app" to learn about applications.
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def application do
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[
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extra_applications: [:logger]
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]
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end
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# Run "mix help deps" to learn about dependencies.
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defp deps do
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[
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# {:dep_from_hexpm, "~> 0.3.0"},
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# {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"}
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]
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end
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end
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defmodule BinarySearchTest do
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use ExUnit.Case
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test "finds a value in a tuple with one element" do
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assert BinarySearch.search({6}, 6) == {:ok, 0}
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assert BinarySearch.search({3}, 3) == {:ok, 0}
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end
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test "finds a value in the middle of a tuple" do
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assert BinarySearch.search({1, 2, 4, 5, 6}, 4) == {:ok, 2}
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assert BinarySearch.search({1, 3, 4, 6, 8, 9, 11}, 6) == {:ok, 3}
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end
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test "finds a value at the beginning of a tuple" do
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assert BinarySearch.search({1, 2, 4, 5, 6}, 1) == {:ok, 0}
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assert BinarySearch.search({1, 3, 4, 5, 8, 9, 11}, 1) == {:ok, 0}
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end
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test "finds a value at the end of a tuple" do
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assert BinarySearch.search({1, 2, 4, 5, 6}, 6) == {:ok, 4}
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assert BinarySearch.search({1, 3, 4, 5, 8, 9, 11}, 11) == {:ok, 6}
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end
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test "finds a value in a tuple of odd length" do
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tuple = {1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 634}
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assert BinarySearch.search(tuple, 144) == {:ok, 9}
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end
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test "finds a value in a tuple of even length" do
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tuple = {1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377}
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assert BinarySearch.search(tuple, 21) == {:ok, 5}
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assert BinarySearch.search(tuple, 34) == {:ok, 6}
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end
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test "identifies that a value is not included in the tuple" do
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assert BinarySearch.search({2, 4, 6}, 3) == :not_found
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assert BinarySearch.search({1, 3, 4, 6, 8, 9, 11}, 7) == :not_found
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end
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test "a value smaller than the tuple's smallest value is not found" do
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assert BinarySearch.search({2, 4, 6}, 1) == :not_found
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assert BinarySearch.search({1, 3, 4, 6, 8, 9, 11}, 0) == :not_found
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end
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test "a value larger than the tuple's largest value is not found" do
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assert BinarySearch.search({2, 4, 6}, 9) == :not_found
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assert BinarySearch.search({1, 3, 4, 6, 8, 9, 11}, 13) == :not_found
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end
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test "nothing is found in an empty tuple" do
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assert BinarySearch.search({}, 1) == :not_found
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end
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test "nothing is found when the left and right bounds cross" do
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assert BinarySearch.search({1, 2}, 0) == :not_found
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end
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end
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ExUnit.start()
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ExUnit.configure(exclude: :pending, trace: true)
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