Published at Mar 21 2019
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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.

For installation and learning resources, refer to the exercism help page.

To work on the exercises, you will need `Opam`

and `Base`

. Consult opam website for instructions on how to install `opam`

for your OS. Once `opam`

is installed open a terminal window and run the following command to install base:

```
opam install base
```

To run the tests you will need `OUnit`

. Install it using `opam`

:

```
opam install ounit
```

A Makefile is provided with a default target to compile your solution and run the tests. At the command line, type:

```
make
```

`utop`

is a command line program which allows you to run Ocaml code interactively. The easiest way to install it is via opam:

```
opam install utop
```

Consult utop for more detail.

The exercism/ocaml repository on GitHub is the home for all of the Ocaml exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

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.

```
open OUnit2
open Binary_search
let option_to_string f = function
| None -> "None"
| Some x -> "Some " ^ f x
let ae exp got _test_ctxt =
assert_equal ~printer:(option_to_string string_of_int) exp got
let tests = [
"finds a value in an array with one element" >::
ae (Some 0) (find [|6|] 6);
"finds a value in the middle of an array" >::
ae (Some 3) (find [|1; 3; 4; 6; 8; 9; 11|] 6);
"finds a value at the beginning of an array" >::
ae (Some 0) (find [|1; 3; 4; 6; 8; 9; 11|] 1);
"finds a value at the end of an array" >::
ae (Some 6) (find [|1; 3; 4; 6; 8; 9; 11|] 11);
"finds a value in an array of odd length" >::
ae (Some 9) (find [|1; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377; 634|] 144);
"finds a value in an array of even length" >::
ae (Some 5) (find [|1; 3; 5; 8; 13; 21; 34; 55; 89; 144; 233; 377|] 21);
"identifies that a value is not included in the array" >::
ae None (find [|1; 3; 4; 6; 8; 9; 11|] 7);
"a value smaller than the array's smallest value is not included" >::
ae None (find [|1; 3; 4; 6; 8; 9; 11|] 0);
"a value larger than the array's largest value is not included" >::
ae None (find [|1; 3; 4; 6; 8; 9; 11|] 13);
"nothing is included in an empty array" >::
ae None (find [||] 1);
]
let () =
run_test_tt_main ("binary-search tests" >::: tests)
```

```
open! Base
let find haystack needle =
let rec iter low high =
if low > high
then None
else
let pivot = high - low / 2 in
match haystack.(pivot) with
| x when x = needle -> Some pivot
| x when x > needle -> iter low (pivot - 1)
| _ -> iter (low + pivot + 1) high in
iter 0 (Array.length haystack - 1)
```

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?

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