Binary search: Difference between revisions

 

=={{header|11l}}==

V low = 0

V high = l.len - 1

E

R mid

 

=={{header|360 Assembly}}==

BINSEAR CSECT

USING BINSEAR,R13 base register

XDEC DS CL12 temp

YREGS

{{out}}

<pre>

Test code is included, which will loop through the values [0..255] and report for each number whether it was in the array or not.

 

jmp test

 

 

rst 0

=={{header|AArch64 Assembly}}==

{{works with|as|Raspberry Pi 3B version Buster 64 bits}}

/* ARM assembly AARCH64 Raspberry PI 3B */

/* program binSearch64.s */

/* for this file see task include a file in language AArch64 assembly */

.include "../includeARM64.inc"

<pre>

Value find at index : 0

=={{header|ACL2}}==

 

(cons name

(compress1 name

(populate-array-ordered

(defarray 'haystack *dim* 0)

 

=={{header|Action!}}==

INT low,high,mid

 

Test(a,8,10)

Test(a,8,7)

{{out}}

[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Binary_search.png Screenshot from Atari 8-bit computer]

Both solutions are generic. The element can be of any comparable type (such that the operation < is visible in the instantiation scope of the function Search). Note that the completion condition is different from one given in the pseudocode example above. The example assumes that the array index type does not overflow when mid is incremented or decremented beyond the corresponding array bound. This is a wrong assumption for Ada, where array bounds can start or end at the very first or last value of the index type. To deal with this, the exit condition is rather directly expressed as crossing the corresponding array bound by the coming interval middle.

;Recursive:

 

procedure Test_Recursive_Binary_Search is

Test ((2, 4, 6, 8, 9), 9);

Test ((2, 4, 6, 8, 9), 5);

;Iterative:

 

procedure Test_Binary_Search is

Test ((2, 4, 6, 8, 9), 9);

Test ((2, 4, 6, 8, 9), 5);

Sample output:

<pre>

 

=={{header|ALGOL 68}}==

MODE ELEMENT = STRING;

test search(recursive binary search, test cases)

)

{{out}}

Shows iterative search output - recursive search output is the same.

=={{header|ALGOL W}}==

Ieterative and recursive binary search procedures, from the pseudo code. Finds the left most occurance/insertion point.

% recursive binary search, left most insertion point %

integer procedure binarySearchLR ( integer array A ( * )

end for_s

end

{{out}}

<pre>

{{works with|Dyalog APL}}

 

⎕IO(⍺{ ⍝ first lower bound is start of array

⍵<⍺:⍬ ⍝ if high < low, we didn't find it

}⍵)⎕IO+(≢⍺)-1 ⍝ first higher bound is top of array

}

 

=={{header|AppleScript}}==

 

repeat until (l = r)

set m to (l + r) div 2

 

set theList to {1, 2, 3, 3, 5, 7, 7, 8, 9, 10, 11, 12}

 

{{output}}

=={{header|ARM Assembly}}==

{{works with|as|Raspberry Pi}}

 

/* ARM assembly Raspberry PI */

iMagicNumber: .int 0xCCCCCCCD

 

 

=={{header|Arturo}}==

 

if high < low -> return ø

mid: shr low+high 1

if? not? null? i -> print ["found" v "at index:" i]

else -> print [v "not found"]

 

{{out}}

 

=={{header|AutoHotkey}}==

StringSplit, A, array, `, ; creates associative array

MsgBox % x := BinarySearch(A, 4, 1, A0) ; Recursive

}

Return not_found

 

=={{header|AWK}}==

{{works with|Nawk}}

'''Recursive'''

if (right < left) return 0

middle = int((right + left) / 2)

return binary_search(array, value, left, middle - 1)

return binary_search(array, value, middle + 1, right)

'''Iterative'''

while (left <= right) {

middle = int((right + left) / 2)

}

return 0

 

=={{header|Axe}}==

BSEARCH takes 3 arguments: a pointer to the start of the data, the data to find, and the length of the array in bytes.

 

0→L

r₃-1→H

End

-1

 

=={{header|BASIC}}==

{{works with|FreeBASIC}}

{{works with|RapidQ}}

DIM middle AS Integer

END SELECT

END IF

'''Iterative'''

{{works with|FreeBASIC}}

{{works with|RapidQ}}

DIM middle AS Integer

WEND

binary_search = 0

'''Testing the function'''

 

The following program can be used to test both recursive and iterative version.

DIM idx AS Integer

 

search test(), 4

search test(), 8

Output:

Value 4 not found

 

==={{header|ASIC}}===

REM Binary search

DIM A(10)

ENDIF

RETURN

{{out}}

<pre>

 

==={{header|BBC BASIC}}===

array%() = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

H% /= 2

UNTIL H%=0

 

==={{header|FreeBASIC}}===

'returns the index of the target number, or -1 if it is not in the array

dim as uinteger lo = lbound(array), hi = ubound(array), md = (lo + hi)\2

wend

return -1

 

==={{header|IS-BASIC}}===

110 RANDOMIZE

120 NUMERIC ARR(1 TO 20)

340 LOOP WHILE BO<=UP AND T(K)<>N

350 IF BO<=UP THEN LET SEARCH=K

 

==={{header|Minimal BASIC}}===

{{works with|Commodore BASIC|3.5}}

{{works with|Nascom ROM BASIC|4.7}}

10 REM Binary search

20 LET N = 10

670 LET I1 = -1

680 RETURN

 

=={{header|BASIC256}}==

====Recursive Solution====

if ub < lb then

return false

if valor = array[mitad] then return mitad

end if

 

====Iterative Solution====

lb = array[?,]

ub = array[?]

end while

return false

'''Test:'''

dim array(items)

for n = 0 to items-1 : array[n] = n : next n

print binarySearchR(array, 3, array[?,], array[?])

print msec - t1; " millisec"

{{out}}

<pre>3

 

=={{header|Batch File}}==

@echo off & setlocal enabledelayedexpansion

 

echo . binchop required !b! iterations

endlocal & exit /b 0

 

=={{header|BQN}}==

BQN has two builtin functions for binary search: <code>⍋</code>(Bins Up) and <code>⍒</code>(Bins Down). This is a recursive method.

 

BS ⟨a, value⟩:

BS ⟨a, value, 0, ¯1+≠a⟩;

}

 

 

=={{header|Brat}}==

true? high < low

{ null }

null? index

{ p "Not found" }

 

=={{header|C}}==

 

 

int bsearch (int *a, int n, int x) {

return 0;

}

{{output}}

<pre>

=={{header|C sharp|C#}}==

'''Recursive'''

using System;

 

}

}

'''Iterative'''

using System;

 

}

}

'''Example'''

 

using System;

#endif

}

 

'''Output'''

=={{header|C++}}==

'''Recursive'''

template <class T> int binsearch(const T array[], int low, int high, T value) {

if (high < low) {

 

return 0;

'''Iterative'''

int binSearch(const T arr[], int len, T what) {

int low = 0;

}

return -1; // indicate not found

'''Library'''

 

The <code>lower_bound()</code> function returns an iterator to the first position where a value could be inserted without violating the order; i.e. the first element equal to the element you want, or the place where it would be inserted.

 

The <code>upper_bound()</code> function returns an iterator to the last position where a value could be inserted without violating the order; i.e. one past the last element equal to the element you want, or the place where it would be inserted.

 

The <code>equal_range()</code> function returns a pair of the results of <code>lower_bound()</code> and <code>upper_bound()</code>.

Note that the difference between the bounds is the number of elements equal to the element you want.

 

The <code>binary_search()</code> function returns true or false for whether an element equal to the one you want exists in the array. It does not give you any information as to where it is.

 

=={{header|Chapel}}==

 

'''iterative''' -- almost a direct translation of the pseudocode

var low = A.domain.dim(1).low;

var high = A.domain.dim(1).high;

}

 

 

{{out}}

=={{header|Clojure}}==

'''Recursive'''

([coll t]

(bsearch coll 0 (dec (count coll)) t))

; we've found our target

; so return its index

 

=={{header|CLU}}==

% If the item is found, returns `true' and the index;

% if the item is not found, returns `false' and the leftmost insertion point

end

end

{{out}}

<pre>1 not found, would be inserted at location 1

=={{header|COBOL}}==

COBOL's <code>SEARCH ALL</code> statement is implemented as a binary search on most implementations.

IDENTIFICATION DIVISION.

PROGRAM-ID. binary-search.

END-SEARCH

.

 

=={{header|CoffeeScript}}==

'''Recursive'''

do recurse = (low = 0, high = xs.length - 1) ->

mid = Math.floor (low + high) / 2

when xs[mid] > x then recurse low, mid - 1

when xs[mid] < x then recurse mid + 1, high

'''Iterative'''

[low, high] = [0, xs.length - 1]

while low <= high

when xs[mid] < x then low = mid + 1

else return mid

'''Test'''

odds = (it for it in [1..n] by 2)

result = (it for it in \

console.assert "#{result}" is "#{[0...odds.length]}"

console.log "#{odds} are odd natural numbers"

Output:

<pre>1,3,5,7,9,11 are odd natural numbers"

=={{header|Common Lisp}}==

'''Iterative'''

(let ((low 0)

(high (1- (length array))))

(setf low (1+ middle)))

'''Recursive'''

(if (< high low)

nil

(binary-search value array (1+ middle) high))

 

=={{header|Crystal}}==

'''Recursive'''

def binary_search(val, low = 0, high = (size - 1))

return nil if high < low

puts "#{val} not found in array"

end

'''Iterative'''

def binary_search_iterative(val)

low, high = 0, size - 1

puts "#{val} not found in array"

end

{{out}}

<pre>

 

=={{header|D}}==

 

/// Recursive.

// Standard Binary Search:

!items.equalRange(x).empty);

{{out}}

<pre> 1 false false false

 

=={{header|E}}==

def binarySearch(collection, value) {

var low := 0

}

return null

 

=={{header|EasyLang}}==

low = 0

high = len a[] - 1

a[] = [ 2 4 6 8 9 ]

call bin_search 8 a[] r

 

=={{header|Eiffel}}==

The following solution is based on the one described in: C. A. Furia, B. Meyer, and S. Velder. ''Loop Invariants: Analysis, Classification, and Examples''. ACM Computing Surveys, 46(3), Article 34, January 2014. (Also available at http://arxiv.org/abs/1211.4470). It includes detailed loop invariants and pre- and postconditions, which make the running time linear (instead of logarithmic) when full contract checking is enabled.

 

APPLICATION

 

end

 

 

=={{header|Elixir}}==

def search(list, value), do: search(List.to_tuple(list), value, 0, length(list)-1)

index -> IO.puts "found #{val} at index #{index}"

end

 

{{out}}

 

=={{header|Emacs Lisp}}==

(defun binary-search (value array)

(let ((low 0)

((< (aref array middle) value)

(setf low (1+ middle)))

 

=={{header|Erlang}}==

%% Author: Abhay Jain

 

Mid

end

 

=={{header|Euphoria}}==

===Recursive===

integer mid, cmp

if high < low then

end if

end if

===Iterative===

integer low, high, mid, cmp

low = 1

end while

return 0 -- not found

 

=={{header|F Sharp|F#}}==

Generic recursive version, using #light syntax:

if (high < low) then

null

binarySearch (myArray, mid+1, high, value)

else

 

=={{header|Factor}}==

Factor already includes a binary search in its standard library. The following code offers an interface compatible with the requirement of this task, and returns either the index of the element if it has been found or f otherwise.

 

: binary-search ( seq elt -- index/f )

 

=={{header|FBSL}}==

FBSL has built-in QuickSort() and BSearch() functions:

 

DIM va[], sign = {1, -1}, toggle

" in ", GetTickCount() - gtc, " milliseconds"

 

Output:<pre>Loading ... done in 906 milliseconds

Sorting ... done in 547 milliseconds

 

'''Iterative:'''

 

DIM va[]

WEND

RETURN -1

Output:<pre>Loading ... done in 391 milliseconds

3141592.65358979 found at index 1000000 in 62 milliseconds

 

'''Recursive:'''

 

DIM va[]

END IF

RETURN midp

Output:<pre>Loading ... done in 390 milliseconds

3141592.65358979 found at index 1000000 in 938 milliseconds

=={{header|Forth}}==

This version is designed for maintaining a sorted array. If the item is not found, then then location returned is the proper insertion point for the item. This could be used in an optimized [[Insertion sort]], for example.

' - is (compare) \ default to numbers

 

10 probe \ 0 11

11 probe \ -1 11

 

=={{header|Fortran}}==

'''Recursive'''

In ISO Fortran 90 or later use a RECURSIVE function and ARRAY SECTION argument:

real, intent(in) :: a(:), value

integer :: bsresult, mid

bsresult = mid ! SUCCESS!!

end if

'''Iterative'''

<br>

In ISO Fortran 90 or later use an ARRAY SECTION POINTER:

integer :: binarySearch_I

real, intent(in), target :: a(:)

end if

end do

 

===Iterative, exclusive bounds, three-way test.===

The use of "exclusive" bounds simplifies the adjustment of the bounds: the appropriate bound simply receives the value of P, there is ''no'' + 1 or - 1 adjustment ''at every step''; similarly, the determination of an empty span is easy, and avoiding the risk of integer overflow via (L + R)/2 is achieved at the same time. The "inclusive" bounds version by contrast requires ''two'' manipulations of L and R ''at every step'' - once to see if the span is empty, and a second time to locate the index to test.

Careful: it is surprisingly difficult to make this neat, due to vexations when N = 0 or 1.

REAL X,A(*) !Where is X in array A(1:N)?

Curse it!

5 FINDI = -L !X is not found. Insert it at L + 1, i.e. at A(1 - FINDI).

 

[[File:BinarySearch.Flowchart.png]]

 

====An alternative version====

Careful: it is surprisingly difficult to make this neat, due to vexations when N = 0 or 1.

REAL X,A(*) !Where is X in array A(1:N)?

Curse it!

5 FINDI = -L !X is not found. Insert it at L + 1, i.e. at A(1 - FINDI).

The point of this is that the IF-test is going to initiate some jumps, so why not arrange that one of the bound adjustments needs no subsequent jump to the start of the next iteration - in the first version, both bound adjustments needed such a jump, the GO TO 1 statements. This was done by shifting the code for label 2 up to precede the code for label 1 - and removing its now pointless GO TO 1 (executed each time), but adding an initial GO TO 1, executed once only. This sort of change is routine when manipulating spaghetti code...

 

Straightforward translation of imperative iterative algorithm.

 

fun main(as: [n]int, value: int): int =

let low = 0

else (mid, mid-1) -- Force termination.

in low

 

=={{header|GAP}}==

local low, high, mid;

low := 1;

# fail

Find(u, 35);

 

=={{header|Go}}==

'''Recursive''':

if high < low {

return -1

}

return mid

'''Iterative''':

low := 0

high := len(a) - 1

}

return -1

'''Library''':

 

//...

 

Exploration of library source code shows that it uses the <tt>mid = low + (high - low) / 2</tt> technique to avoid overflow.

 

Both solutions use ''sublists'' and a tracking offset in preference to "high" and "low".

====Recursive Solution====

def binSearchR

//define binSearchR closure.

: [index: offset + m]

}

 

====Iterative Solution====

def a = aList

def offset = 0

}

return ["insertion point": offset]

Test:

def random = new Random()

while (a.size() < 20) { a << random.nextInt(30) }

println """

Answer: ${answers[0]}, : ${source[answers[0].values().iterator().next()]}"""

Output:

<pre>[1, 2, 5, 8, 9, 10, 11, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29]

 

The algorithm itself, parametrized by an "interrogation" predicate ''p'' in the spirit of the explanation above:

 

-- BINARY SEARCH --------------------------------------------------------------

case found of

Nothing -> "' Not found"

{{Out}}

<pre>'mu' found at index 9</pre>

A common optimisation of recursion is to delegate the main computation to a helper function with simpler type signature. For the option type of the return value, we could also use an Either as an alternative to a Maybe.

 

 

-- BINARY SEARCH USING A HELPER FUNCTION WITH A SIMPLER TYPE SIGNATURE

("' " ++)

(("' found at index " ++) . show)

{{Out}}

<pre>'lambda' found at index 8</pre>

It returns the result of applying '''f''' until '''p''' holds.

 

 

-- BINARY SEARCH USING THE ITERATIVE ALGORITHM

("' " ++)

(("' found at index " ++) . show)

{{Out}}

<pre>'kappa' found at index 7</pre>

 

=={{header|HicEst}}==

 

array = NINT( RAN(n) )

ENDIF

ENDDO

 

=={{header|Hoon}}==

=/ lo=@ud 0

=/ hi=@ud (dec (lent arr))

?: (lth x val) $(hi (dec mid))

?: (gth x val) $(lo +(mid))

 

=={{header|Icon}} and {{header|Unicon}}==

Only a recursive solution is shown here.

if *A = 0 then fail

mid := *A/2 + 1

}

return mid

A program to test this is:

target := integer(!args) | 3

every put(A := [], 1 to 18 by 2)

every writes(!A," ")

write()

with some sample runs:

<pre>

=={{header|J}}==

J already includes a binary search primitive (<code>I.</code>). The following code offers an interface compatible with the requirement of this task, and returns either the index of the element if it has been found or 'Not Found' otherwise:

'''Examples:'''

6

2 3 5 6 8 10 11 15 19 20 bs 12

Direct tacit iterative and recursive versions to compare to other implementations follow:

 

'''Iterative'''

f=. &({::) NB. Fetching the contents of a box

o=. @: NB. Composing verbs (functions)

return=. (M f) o ((<@:('Not Found'"_) M} ]) ^: (_ ~: L f))

 

'''Recursive'''

f=. &({::) NB. Fetching the contents of a box

o=. @: NB. Composing verbs (functions)

recur=. (X f bs Y f ; L f ; (_1 + M f))`(M f)`(X f bs Y f ; (1 + M f) ; H f)@.case

 

 

=={{header|Java}}==

'''Iterative'''

 

public static int binarySearch(int[] nums, int check) {

}

}

 

'''Recursive'''

 

 

public static int binarySearch(int[] haystack, int needle, int lo, int hi) {

}

}

'''Library'''

When the key is not found, the following functions return <code>~insertionPoint</code> (the bitwise complement of the index where the key would be inserted, which is guaranteed to be a negative number).

 

For arrays:

 

int index = Arrays.binarySearch(array, thing);

// for objects, also optionally accepts an additional comparator argument:

int index = Arrays.binarySearch(array, thing, comparator);

For Lists:

 

int index = Collections.binarySearch(list, thing);

 

=={{header|JavaScript}}==

===ES5===

Recursive binary search implementation

if (hi < lo) { return null; }

 

}

return mid;

Iterative binary search implementation

var mid, lo = 0,

hi = a.length - 1;

}

return null;

 

===ES6===

Recursive and iterative, by composition of pure functions, with tests and output:

 

'use strict';

 

// MAIN ---

return main();

{{Out}}

<pre>[

If the input array is sorted, then binarySearch(value) as defined here will return an index (i.e. offset) of value in the array if the array contains the value, and otherwise (-1 - ix), where ix is the insertion point, if the value cannot be found. binarySearch will always terminate.

 

# To avoid copying the array, simply pass in the current low and high offsets

def binarySearch(low; high):

end

end;

{{Out}}

2

 

=={{header|Jsish}}==

Binary search, in Jsish, based on Javascript entry

Tectonics: jsish -u -time true -verbose true binarySearch.jsi

puts('Iterative:', Util.times(function() { binarySearchIterative(arr, 42); }, 100), 'µs');

puts('Recursive:', Util.times(function() { binarySearchRecursive(arr, 42, 0, arr.length - 1); }, 100), 'µs');

 

{{out}}

{{works with|Julia|0.6}}

'''Iterative''':

low = 1

high = length(lst)

end

return 0

 

'''Recursive''':

if isempty(lst) return 0 end

if low ≥ high

return mid

end

 

=={{header|K}}==

Recursive:

bs:{[a;t]

if[0=#a; :_n];

{bs[v;x]}' v

0 1 2 3 4 5 6 7 8 9

 

=={{header|Kotlin}}==

var hi = size - 1

var lo = 0

r = a.recursiveBinarySearch(target, 0, a.size)

println(if (r < 0) "$target not found" else "$target found at index $r")

{{Out}}

<pre>6 found at index 4

=={{header|Lambdatalk}}==

Can be tested in (http://lambdaway.free.fr)[http://lambdaway.free.fr/lambdaway/?view=binary_search]

{def BS

{def BS.r {lambda {:a :v :i0 :i1}

{BS {B} 100} -> 100 is not found

{BS {B} 12345} -> 12345 is at array[6172]

 

=={{header|Liberty BASIC}}==

dim theArray(100)

for i = 1 to 100

END IF

END FUNCTION

 

=={{header|Logo}}==

if :upper < :lower [output []]

localmake "mid int (:lower + :upper) / 2

if item :mid :a < :value [output bsearch :value :a :mid+1 :upper]

output :mid

 

=={{header|Lolcode}}==

'''Iterative'''

HAI 1.2

CAN HAS STDIO?

KTHXBYE

Output

<pre>

=={{header|Lua}}==

'''Iterative'''

local low = 1

local high = #list

end

return false

'''Recursive'''

local function search(low, high)

if low > high then return false end

end

return search(1,#list)

 

=={{header|M2000 Interpreter}}==

\\ binary search

const N=10

Print A()

 

 

=={{header|M4}}==

define(`midsearch',`ifelse(defn($1[$4]),$2,$4,

`ifelse(eval(defn($1[$4])>$2),1,`binarysearch($1,$2,$3,decr($4))',`binarysearch($1,$2,incr($4),$5)')')')dnl

dnl

binarysearch(`a',5,1,asize)

Output:

<pre>

 

'''Recursive'''

description "recursive binary search";

if high < low then

end if

end if

 

'''Iterative'''

description "iterative binary search";

local low, high;

end do;

FAIL

We can use either lists or Arrays (or Vectors) for the first argument for these.

> P := [seq]( ithprime( i ), i = 1 .. N ):

> BinarySearch( P, 12, 1, N ); # recursive version

 

> PP[ 3 ];

 

=={{header|Mathematica}} / {{header|Wolfram Language}}==

'''Recursive'''

Module[{mid = lo + Round@((hi - lo)/2)},

If[hi < lo, Return[-1]];

True, mid]

];

'''Iterative'''

While[lo <= hi,

mid = lo + Round@((hi - lo)/2);

];

Return[-1];

 

=={{header|MATLAB}}==

'''Recursive'''

 

if( high < low )

end

Sample Usage:

 

ans =

 

'''Iterative'''

 

low = 1;

mid = [];

Sample Usage:

 

ans =

 

 

=={{header|Maxima}}==

if n < L[i] or n > L[j] then 0 else (

while j - i > 0 do (

0

find(a, 421);

 

=={{header|MAXScript}}==

'''Iterative'''

(

lower = 1

 

arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)

'''Recursive'''

(

if lower == upper then

 

arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)

 

=={{header|MiniScript}}==

'''Recursive:'''

if high < low then return null

mid = floor((low + high) / 2)

if A[mid] < value then return binarySearch(A, value, mid+1, high)

return mid

 

'''Iterative:'''

low = 0

high = A.len - 1

end if

end while

 

=={{header|N/t/roff}}==

 

{{works with|GNU TROFF|1.22.2}}

..

.de array

.ie \n[guess]=0 The item \fBdoesn't exist\fP.

.el The item \fBdoes exist\fP.

 

=={{header|Nim}}==

'''Library'''

 

let s = @[2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,25,27,30]

 

'''Iterative''' (from the standard library)

var b = len(a)

while result < b:

if a[mid] < key: result = mid + 1

else: b = mid

 

=={{header|Niue}}==

'''Library'''

3 bsearch . ( => 2 )

5 bsearch . ( => 0 )

'tom bsearch . ( => 0 )

'kenny bsearch . ( => 2 )

 

=={{header|Objeck}}==

'''Iterative'''

 

bundle Default {

}

}

 

=={{header|Objective-C}}==

'''Iterative'''

 

@interface NSArray (BinarySearch)

}

return 0;

'''Recursive'''

 

@interface NSArray (BinarySearchRecursive)

}

return 0;

'''Library'''

{{works with|Mac OS X|10.6+}}

 

int main()

}

return 0;

Using Core Foundation (part of Cocoa, all versions):

 

CFComparisonResult myComparator(const void *x, const void *y, void *context) {

}

return 0;

 

=={{header|OCaml}}==

'''Recursive'''

if high = low then

if a.(low) = value then

binary_search a value (mid + 1) high

else

Output:

<pre>

=={{header|Octave}}==

'''Recursive'''

if ( high < low )

i = 0;

endif

endif

'''Iterative'''

low = 1;

high = numel(array);

endif

endwhile

'''Example of using'''

disp(r);

binsearch_r(r, 5, 1, numel(r))

 

=={{header|Ol}}==

(define (binary-search value vector)

(let helper ((low 0)

(binary-search 12 [1 2 3 4 5 6 7 8 9 10 11 12 13]))

; ==> 12

 

=={{header|ooRexx}}==

data = .array~of(1, 3, 5, 7, 9, 11)

-- search keys with a number of edge cases

end

return 0

Output:

<pre>

=={{header|Oz}}==

'''Recursive'''

fun {BinarySearch Arr Val}

fun {Search Low High}

in

{System.printInfo "searching 4: "} {Show {BinarySearch A 4}}

'''Iterative'''

fun {BinarySearch Arr Val}

Low = {NewCell {Array.low Arr}}

in

{System.printInfo "searching 4: "} {Show {BinarySearch A 4}}

 

=={{header|PARI/GP}}==

Note that, despite the name, <code>setsearch</code> works on sorted vectors as well as sets.

 

The following is another implementation that takes a more manual approach. Instead of using an intrinsic function, a general binary search algorithm is implemented using the language alone.

{{trans|N/t/roff}}

 

local(

minm = 1,

print("Item exists on index ", idx), \

print("Item does not exist anywhere.") \

 

=={{header|Pascal}}==

'''Iterative'''

var

l, m, h: integer;

end;

end;

Usage:

list: array[0 .. 9] of real;

// ...

 

=={{header|Perl}}==

'''Iterative'''

my ($array_ref, $value, $left, $right) = @_;

while ($left <= $right) {

}

return -1;

'''Recursive'''

my ($array_ref, $value, $left, $right) = @_;

return -1 if ($right < $left);

binary_search($array_ref, $value, $middle + 1, $right);

}

 

=={{header|Phix}}==

Standard autoinclude builtin/bsearch.e, reproduced here (for reference only, don't copy/paste unless you plan to modify and rename it)

<span style="color: #008080;">global</span> <span style="color: #008080;">function</span> <span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">needle</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">haystack</span><span style="color: #0000FF;">)</span>

<span style="color: #004080;">integer</span> <span style="color: #000000;">lo</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>

<span style="color: #008080;">return</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">mid</span> <span style="color: #000080;font-style:italic;">-- where it would go, if inserted now</span>

<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>

The low + (high-low)/2 trick is not needed, since interim integer results are accurate to 53 bits (on 32 bit, 64 bits on 64 bit) on Phix.

 

Returns a positive index if found, otherwise the negative index where it would go if inserted now. Example use

<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- -1</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 3</span>

<span style="color: #0000FF;">?</span><span style="color: #7060A8;">binary_search</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- -4</span>

 

=={{header|PHP}}==

'''Iterative'''

{

do

 

return $guess;

'''Recursive'''

{

$guess = (int)($start + ( ( $end - $start ) / 2 ));

 

return $guess;

 

=={{header|Picat}}==

===Iterative===

A = [2, 4, 6, 8, 9],

TestValues = [2,1,8,10,9,5],

end,

V = V1.

 

{{out}}

 

===Recursive version===

Ret = binary_search_rec(A,Value, 1, A.length).

 

Mid1 := binary_search_rec(A, Value, Mid1+1, High)

end,

 

=={{header|PicoLisp}}==

'''Recursive'''

(unless (=0 Len)

(let (N (inc (/ Len 2)) L (nth Lst N))

((> Val (car L))

(recursiveSearch Val (cdr L) (- Len N)) )

Output:

<pre>: (recursiveSearch 5 (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)

-> NIL</pre>

'''Iterative'''

(use (N L)

(loop

(if (> Val (car L))

(setq Lst (cdr L) Len (- Len N))

Output:

<pre>: (iterativeSearch 5 (2 3 5 8 "abc" "klm" "xyz" (7) (a b)) 9)

 

=={{header|PL/I}}==

search: procedure (A, M) returns (fixed binary);

declare (A(*), M) fixed binary;

end;

return (lbound(A,1)-1);

 

=={{header|Pop11}}==

'''Iterative'''

lvars low = 1, high = length(A), mid;

while low <= high do

BinarySearch(A, 4) =>

BinarySearch(A, 5) =>

'''Recursive'''

define do_it(low, high);

if high < low then

enddefine;

do_it(1, length(A));

 

=={{header|PowerShell}}==

function BinarySearch-Iterative ([int[]]$Array, [int]$Value)

{

}

}

Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 41 -Function Iterative

Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 99 -Function Iterative

Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 86 -Function Recursive

Show-SearchResult -Array 10, 28, 41, 46, 58, 74, 76, 86, 89, 98 -Search 11 -Function Recursive

{{Out}}

<pre>

=={{header|Prolog}}==

Tested with Gnu-Prolog.

length(List,N), bin_search_inner(Elt,List,1,N,Result).

MidElt > Elt,

NewEnd is Mid-1,

 

{{out|Output examples}}

=={{header|PureBasic}}==

Both recursive and iterative procedures are included and called in the code below.

#Iterative = 1 ;iterative binary search method

#NotFound = -1 ;search result if item not found

Input()

CloseConsole()

Sample output:

<pre>

=={{header|Python}}==

===Python: Iterative===

low = 0

high = len(l)-1

elif l[mid] < value: low = mid+1

else: return mid

 

We can also generalize this kind of binary search from direct matches to searches using a custom comparator function.

In addition to a search for a particular word in an AZ-sorted list, for example, we could also perform a binary search for a word of a given '''length''' (in a word-list sorted by rising length), or for a particular value of any other comparable property of items in a suitably sorted list:

 

def findIndexBinary(p):

def isFound(bounds):

if __name__ == '__main__':

main()

{{Out}}

<pre>Word found at index 6

 

===Python: Recursive===

if not l: return -1

if(high == -1): high = len(l)-1

if l[mid] > value: return binary_search(l, value, low, mid-1)

elif l[mid] < value: return binary_search(l, value, mid+1, high)

 

Generalizing again with a custom comparator function (see preamble to second iterative version above).

This time using the recursive definition:

 

def findIndexBinary_(p):

def go(xs):

'Word of given length found at index ' + str(mb2)

)

{{Out}}

<pre>Word found at index 9

===Python: Library===

<br>Python's <code>bisect</code> module provides binary search functions

index = bisect.bisect_right(list, item) # rightmost insertion point

index = bisect.bisect(list, item) # same as bisect_right

bisect.insort_left(list, item)

bisect.insort_right(list, item)

 

====Python: Alternate====

Complete binary search function with python's <code>bisect</code> module:

 

 

def binary_search(a, x, lo=0, hi=None): # can't use a to specify default for hi

hi = hi if hi is not None else len(a) # hi defaults to len(a)

pos = bisect_left(a,x,lo,hi) # find insertion position

 

===Python: Approximate binary search===

Returns the nearest item of list l to value.

low = 0

high = len(l)-1

else:

return mid

 

=={{header|Quackery}}==

Written from pseudocode for rightmost insertion point, iterative.

 

[ stack ] is nest.bs ( --> n )

[ stack ] is test.bs ( --> n )

[ say " could go into position " ]

echo

 

{{out}}

=={{header|R}}==

'''Recursive'''

if ( high < low ) {

return(NULL)

mid

}

'''Iterative'''

low = 1

high = length(A)

}

NULL

'''Example'''

IterBinSearch(a, 50)

BinSearch(a, 50, 1, length(a)) # output 50

 

=={{header|Racket}}==

#lang racket

(define (binary-search x v)

[else m])]))

(loop 0 (vector-length v)))

Examples:

<pre>

(formerly Perl 6)

With either of the below implementations of <code>binary_search</code>, one could write a function to search any object that does <code>Positional</code> this way:

binary_search { $x cmp @a[$^i] }, 0, @a.end

'''Iterative'''

{{works with|Rakudo|2015.12}}

until $lo > $hi {

my Int $mid = ($lo + $hi) div 2;

}

fail;

'''Recursive'''

{{trans|Haskell}}

{{works with|Rakudo|2015.12}}

$lo <= $hi or fail;

my Int $mid = ($lo + $hi) div 2;

default { $mid }

}

 

=={{header|REXX}}==

Incidentally, REXX doesn't care if the values in the list are integers (or even numbers), as long as they're in order.

<br><br>(includes the extra credit)

@= 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181,

193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 409 421 433,

if ?=y then return mid

if y>? then return binarySearch(low, mid-1)

{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> 499.1 </tt>}}

<pre>

===iterative version===

(includes the extra credit)

@= 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181,

193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 409 421 433,

end /*while*/

 

{{out|output|text=&nbsp; when using the input of: &nbsp; &nbsp; <tt> -314 </tt>}}

<pre>

 

=={{header|Ring}}==

decimals(0)

array = [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]

return -1

ok

Output:

<pre>

=={{header|Ruby}}==

'''Recursive'''

def binary_search(val, low=0, high=(length - 1))

return nil if high < low

puts "#{val} not found in array"

end

'''Iterative'''

def binary_search_iterative(val)

low, high = 0, length - 1

puts "#{val} not found in array"

end

{{out}}

<pre>

'''Built in'''

Since Ruby 2.0, arrays ship with a binary search method "bsearch":

needles = [0,42,45,24324,99999]

 

needles.select{|needle| haystack.bsearch{|hay| needle <=> hay} } # => [0, 45, 24324]

 

=={{header|Run BASIC}}==

'''Recursive'''

global theArray

for i = 1 to 100

if val = theArray(middle) then binarySearch = middle

END IF

 

=={{header|Rust}}==

'''Iterative'''

let mut lower = 0 as usize;

let mut upper = v.len() - 1;

 

None

 

=={{header|Scala}}==

'''Recursive'''

def recurse(low: Int, high: Int): Option[Int] = (low + high) / 2 match {

case _ if high < low => None

}

recurse(0, a.size - 1)

'''Iterative'''

var low: Int = 0

var high: Int = xs.size - 1

}

None //not found

'''Test'''

val odds = 1 to n by 2

val result = (0 to n).flatMap(binarySearch(odds, _))

}

 

Output:

<pre>Range(1, 3, 5, 7, 9, 11) are odd natural numbers

=={{header|Scheme}}==

'''Recursive'''

(let helper ((low 0)

(high (- (vector-length vector) 1)))

((< (vector-ref vector middle) value)

(helper (+ middle 1) high))

Example:

<pre>

=={{header|Seed7}}==

'''Iterative'''

result

var integer: result is 0;

end if;

end while;

'''Recursive'''

result

var integer: result is 0;

 

const func integer: binarySearchRecursive (in array elemType: arr, in elemType: aKey) is

 

=={{header|SequenceL}}==

'''Recursive'''

let

mid := low + (high - low) / 2;

binarySearch(A, value, mid + 1, high) when A[mid] < value

else

 

=={{header|Sidef}}==

Iterative:

var l = 0

return -1

Recursive:

high < low && return -1

var middle = ((high+low) // 2)

}

}

 

Usage:

 

=={{header|Simula}}==

 

 

END;

 

{{out}}

<pre>

 

The first version has a postcondition that if Found is True the Position value returned is correct. This version also has a number of 'check' annotations. These are inserted to allow the Simplifier to prove all the verification conditions. See [[SPARK_Proof_Process|the SPARK Proof Process]].

 

subtype Item_Type is Integer; -- From specs.

end Search;

 

The second version of the package has a stronger postcondition on Search, which also states that if Found is False then there is no value in Source equal to Item. This postcondition cannot be proved without a precondition that Source is ordered. This version needs four user rules (see [[SPARK_Proof_Process|the SPARK Proof Process]]) to be provided to the Simplifier so that it can prove all the verification conditions.

 

subtype Item_Type is Integer; -- From specs.

end Search;

 

The user rules for this version of the package (written in FDL, a language for modelling algorithms).

<pre>binary_search_rule(1): (X + Y) div 2 >= X

</pre>

The test program:

with SPARK_IO;

 

Run_Search (Source => Array_Type9'(1, 2, 3, 4, 5, 6, 7, 8, 9), Item => 6);

end Test_Binary_Search;

 

Test output (for the last three tests the array is indexed from 91):

=={{header|Standard ML}}==

'''Recursive'''

let

fun aux slice =

in

aux (ArraySlice.full arr)

Usage:

<pre>

=={{header|Swift}}==

'''Recursive'''

var recurse: ((Int, Int) -> Int?)!

recurse = {(low, high) in switch (low + high) / 2 {

}}

return recurse(0, xs.count - 1)

'''Iterative'''

var (low, high) = (0, xs.count - 1)

while low <= high {

}

return nil

'''Test'''

let odds = Array(stride(from: 1, through: n, by: 2))

let result = flatMap(0...n) {binarySearch(odds, $0)}

func flatMap<T, U>(source: [T], transform: (T) -> U?) -> [U] {

return source.reduce([]) {(var xs, x) in if let x = transform(x) {xs.append(x)}; return xs}

Output:

<pre>[1, 3, 5, 7, 9, 11] are odd natural numbers

 

=={{header|Symsyn}}==

 

a : 1 : 2 : 27 : 44 : 46 : 57 : 77 : 154 : 212

"'result = ' R" []

 

 

=={{header|Tcl}}==

ref: [http://wiki.tcl.tk/22796 Tcl wiki]

set len [llength $lst]

if {$len == 0} {

puts "element $x found at index $idx"

}

Note also that, from Tcl 8.4 onwards, the <tt>lsearch</tt> command includes the <tt>-sorted</tt> option to enable binary searching of Tcl lists.

set idx [lsearch -sorted -exact $lst $x]

if {$idx == -1} {

puts "element $x found at index $idx"

}

 

=={{header|TI-83 BASIC}}==

:Disp "INPUT A LIST:"

:Input L1

:Disp A

:Disp "IS NOT IN"

 

=={{header|uBasic/4tH}}==

{{trans|Run BASIC}}

The overflow is fixed - which is a bit of overkill, since uBasic/4tH has only one array of 256 elements.

@(i-1) = i

Next

If a@ > @(d@) Then Return (FUNC(_binarySearch (a@, d@+1, c@)))

If a@ = @(d@) Then Return (d@) ' We found it, return index!

 

=={{header|UNIX Shell}}==

'''Reading values line by line'''

 

#!/bin/ksh

# This should work on any clone of Bourne Shell, ksh is the fastest.

array[${#array[*]}]=$line

done

 

 

'''Iterative'''

left=0

right=$(($size - 1))

done

echo 'ERROR 404 : NOT FOUND'

 

'''Recursive'''

 

=={{header|UnixPipes}}==

'''Parallel'''

a=$1; s=$2; l=$3; r=$4;

mid=$(expr ${#a[*]} / 2);

}

 

 

=={{header|VBA}}==

'''Recursive version''':

'search for "value" in ordered array a(low..high)

'return index point if found, -1 if not found

BinarySearch = midd

End If

Here are some test functions:

Dim a(1 To 100)

'create an array with values = multiples of 10

a = Array("AA", "Maestro", "Mario", "Master", "Mattress", "Mister", "Mistress", "ZZ")

Debug.Print BinarySearch(a, w, LBound(a), UBound(a))

and sample output:

<pre>

 

'''Iterative version:'''

'search for "value" in array a

'return index point if found, -1 if not found

Loop

BinarySearch2 = -1 'not found

 

=={{header|VBScript}}==

{{trans|BASIC}}

'''Recursive'''

If hi < lo Then

binary_search = 0

WScript.StdOut.Write n & " not found"

WScript.StdOut.WriteLine

{{out}}

'''Note: Array index starts at 0.'''

For this implementation, the numbers to be searched must be stored in current edit buffer, one number per line.

(Could be for example a csv table where the first column is used as key field.)

#3 = Get_Num("Value to search: ")

EOF

}

}

 

=={{header|Visual Basic .NET}}==

'''Iterative'''

Dim low As Integer = 0

Dim high As Integer = A.Length - 1

 

Return Nothing

'''Recursive'''

Dim middle As Integer = 0

 

Return middle

End If

 

=={{header|Vlang}}==

if high <= low {

return -1

println(binary_search_it(f_list,9))

println(binary_search_it(f_list,15))

 

{{out}}

=={{header|Wortel}}==

{{trans|JavaScript}}

@var rec &[a v l h] [

@if < h l @return null

]

null

 

=={{header|Wren}}==

static recursive(a, value, low, high) {

if (high < low) return -1

System.print(" %(value) was not found in the array.")

}

 

{{out}}

{{trans|C}}

{{works with|EXPL-32}}

\Binary search

code CrLf=9, IntOut=11, Text=12;

PrintResult(X, I);

end

{{out}}

<pre>

=={{header|Yabasic}}==

{{trans|Lua}}

return int(n + .5)

end sub

 

print binarySearch(list(), 3)

 

=={{header|z/Arch Assembler}}==

This optimized version for z/Arch, uses six general regs and avoid branch misspredictions for high/low cases.

BINSRCH LA R5,TABLE Begin of table

SR R2,R2 low = 0

LOCRH R3,R0 High? => HIGH = MID-1

LOCRL R2,R1 Low? => LOW = MID+1

 

=={{header|zkl}}==

This algorithm is tail recursive, which means it is both recursive and iterative (since tail recursion optimizes to a jump). Overflow is not possible because Ints (64 bit) are a lot bigger than the max length of a list.

fcn(list,value, low,high){

if (high < low) return(Void); // not found

return(mid); // found

}(list,value,0,list.len()-1);

foreach i in ([0..12]){

n:=bsearch(list,i);

if (Void==n) println("Not found: ",i);

else println("found ",i," at index ",n);

{{out}}

<pre>

{{trans|FreeBASIC}}

Iterative method:

20 DIM t(10)

30 FOR i=1 TO 10

180 IF idx=0 THEN PRINT " not found": RETURN

190 PRINT " found at index ";idx: RETURN