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to Binary Search in the OCaml Track

Published at May 29 2019 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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.

Getting Started

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

Installation

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

Running Tests

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

make

Interactive Shell

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.

Feedback, Issues, Pull Requests

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!

Source

Wikipedia 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.

test.ml

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)
type comp = Gt | Lt | Eq

let compare a b =
  if a = b then Eq
  else if a < b then Lt
  else Gt

let find elements target =
  let rec f es t lower_bound upper_bound =
    let not_found = lower_bound > upper_bound in
    let middle = (lower_bound + upper_bound) / 2 in
    if not_found then None
    else match compare (Array.get es middle) t with
         | Eq -> Some middle
         | Gt -> f es t lower_bound (middle - 1)
         | Lt -> f es t (middle + 1) upper_bound
  in f elements target 0 ((Array.length elements) - 1)

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