Published at Jul 13 2018
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Instructions

Test suite

Solution

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.

Wikipedia http://en.wikipedia.org/wiki/Binary_search_algorithm

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

```
module Test.Main where
import Prelude
import Control.Monad.Eff (Eff)
import Control.Monad.Eff.AVar (AVAR)
import Control.Monad.Eff.Console (CONSOLE)
import Data.Maybe (Maybe(..))
import Test.Unit.Assert as Assert
import Test.Unit (TestSuite, suite, test)
import Test.Unit.Console (TESTOUTPUT)
import Test.Unit.Main (runTest)
import BinarySearch (find)
main :: forall eff
. Eff ( avar :: AVAR
, console :: CONSOLE
, testOutput :: TESTOUTPUT
| eff
)
Unit
main = runTest suites
suites :: forall e. TestSuite e
suites = do
suite "BinarySearch.find" do
test "finds a value in an array with one element" $
Assert.equal (Just 0)
(find 6 [6])
test "finds a value in the middle of an array" $
Assert.equal (Just 3)
(find 6 [1,3,4,6,8,9,11])
test "finds a value at the beginning of an array" $
Assert.equal (Just 0)
(find 1 [1,3,4,6,8,9,11])
test "finds a value at the end of an array" $
Assert.equal (Just 6)
(find 11 [1,3,4,6,8,9,11])
test "finds a value in an array of odd length" $
Assert.equal (Just 9)
(find 144 [1,3,5,8,13,21,34,55,89,144,233,377,634])
test "finds a value in an array of even length" $
Assert.equal (Just 5)
(find 21 [1,3,5,8,13,21,34,55,89,144,233,377])
test "identifies that a value is not included in the array" $
Assert.equal Nothing
(find 7 [1,3,4,6,8,9,11])
test "a value smaller than the array's smallest value is not included" $
Assert.equal Nothing
(find 0 [1,3,4,6,8,9,11])
test "a value larger than the array's largest value is not included" $
Assert.equal Nothing
(find 13 [1,3,4,6,8,9,11])
test "nothing is included in an empty array" $
Assert.equal Nothing
(find 1 [])
```

```
module BinarySearch
( find
) where
import Data.Array (length, (!!))
import Data.Maybe (Maybe(..))
import Prelude
find ∷ ∀ a. Ord a ⇒ a → Array a → Maybe Int
find x xs = find' 0 (length xs)
where
find' ∷ Int → Int → Maybe Int
find' lo hi
| lo > hi = Nothing
| otherwise = do
let mid = div (lo + hi) 2
ord ← compare x <$> (xs !! mid)
case ord of
EQ → Just mid
LT → find' lo (mid - 1)
GT → find' (mid + 1) hi
```

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?