Binary search
From Rosetta Code
Programming Task
This is a programming task. It lays out a problem which Rosetta Code users are encouraged to solve, using languages they know.
A binary search divides a range of values into halves, and continues to narrow down the field of search until the unknown value is found. It is the classic example of a "divide and conquer" algorithm.
As an analogy, consider the children's game "guess a number." The host has a secret number, and will only tell the player if their guessed number is higher than, lower than, or equal to the secret number. The player then uses this information to guess a new number.
As the player, one normally would start by choosing the range's midpoint as the guess, and then asking whether the guess was higher, lower, or equal to the secret number. If the guess was too high, one would select the point exactly between the range midpoint and the beginning of the range. If the original guess was too low, one would ask about the point exactly between the range midpoint and the end of the range. This process repeats until one has reached the secret number.
Given the starting point of a range, the ending point of a range, and the "secret value", implement a binary search through a sorted integer array for a certain number. Implementations can be recursive or iterative (both if you can). Print out whether or not the number was in the array afterwards. If it was, print the index also. The algorithms are as such (from the wikipedia):
Recursive Pseudocode:
BinarySearch(A[0..N-1], value, low, high) {
if (high < low)
return not_found
mid = (low + high) / 2
if (A[mid] > value)
return BinarySearch(A, value, low, mid-1)
else if (A[mid] < value)
return BinarySearch(A, value, mid+1, high)
else
return mid
}
Iterative Pseudocode:
BinarySearch(A[0..N-1], value) {
low = 0
high = N - 1
while (low <= high) {
mid = (low + high) / 2
if (A[mid] > value)
high = mid - 1
else if (A[mid] < value)
low = mid + 1
else
return mid
}
return not_found
}
Contents |
[edit] Ada
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.
[edit] Recursive
with Ada.Text_IO; use Ada.Text_IO; procedure Test_Recursive_Binary_Search is Not_Found : exception; generic type Index is range <>; type Element is private; type Array_Of_Elements is array (Index range <>) of Element; with function "<" (L, R : Element) return Boolean is <>; function Search (Container : Array_Of_Elements; Value : Element) return Index; function Search (Container : Array_Of_Elements; Value : Element) return Index is Mid : Index; begin if Container'Length > 0 then Mid := (Container'First + Container'Last) / 2; if Value < Container (Mid) then if Container'First /= Mid then return Search (Container (Container'First..Mid - 1), Value); end if; elsif Container (Mid) < Value then if Container'Last /= Mid then return Search (Container (Mid + 1..Container'Last), Value); end if; else return Mid; end if; end if; raise Not_Found; end Search; type Integer_Array is array (Positive range <>) of Integer; function Find is new Search (Positive, Integer, Integer_Array); procedure Test (X : Integer_Array; E : Integer) is begin New_Line; for I in X'Range loop Put (Integer'Image (X (I))); end loop; Put (" contains" & Integer'Image (E) & " at" & Integer'Image (Find (X, E))); exception when Not_Found => Put (" does not contain" & Integer'Image (E)); end Test; begin Test ((2, 4, 6, 8, 9), 2); Test ((2, 4, 6, 8, 9), 1); Test ((2, 4, 6, 8, 9), 8); Test ((2, 4, 6, 8, 9), 10); Test ((2, 4, 6, 8, 9), 9); Test ((2, 4, 6, 8, 9), 5); end Test_Recursive_Binary_Search;
[edit] Iterative
with Ada.Text_IO; use Ada.Text_IO; procedure Test_Binary_Search is Not_Found : exception; generic type Index is range <>; type Element is private; type Array_Of_Elements is array (Index range <>) of Element; with function "<" (L, R : Element) return Boolean is <>; function Search (Container : Array_Of_Elements; Value : Element) return Index; function Search (Container : Array_Of_Elements; Value : Element) return Index is Low : Index := Container'First; High : Index := Container'Last; Mid : Index; begin if Container'Length > 0 then loop Mid := (Low + High) / 2; if Value < Container (Mid) then exit when Low = Mid; High := Mid - 1; elsif Container (Mid) < Value then exit when High = Mid; Low := Mid + 1; else return Mid; end if; end loop; end if; raise Not_Found; end Search; type Integer_Array is array (Positive range <>) of Integer; function Find is new Search (Positive, Integer, Integer_Array); procedure Test (X : Integer_Array; E : Integer) is begin New_Line; for I in X'Range loop Put (Integer'Image (X (I))); end loop; Put (" contains" & Integer'Image (E) & " at" & Integer'Image (Find (X, E))); exception when Not_Found => Put (" does not contain" & Integer'Image (E)); end Test; begin Test ((2, 4, 6, 8, 9), 2); Test ((2, 4, 6, 8, 9), 1); Test ((2, 4, 6, 8, 9), 8); Test ((2, 4, 6, 8, 9), 10); Test ((2, 4, 6, 8, 9), 9); Test ((2, 4, 6, 8, 9), 5); end Test_Binary_Search;
Sample output:
2 4 6 8 9 contains 2 at 1 2 4 6 8 9 does not contain 1 2 4 6 8 9 contains 8 at 4 2 4 6 8 9 does not contain 10 2 4 6 8 9 contains 9 at 5 2 4 6 8 9 does not contain 5
[edit] BASIC
[edit] Recursive
Works with: FreeBASIC
Works with: RapidQ
FUNCTION binary_search ( array() AS Integer, value AS Integer, lo AS Integer, hi AS Integer) AS Integer DIM middle AS Integer IF hi < lo THEN binary_search = 0 ELSE middle = (hi + lo) / 2 SELECT CASE value CASE IS < array(middle) binary_search = binary_search(array(), value, lo, middle-1) CASE IS > array(middle) binary_search = binary_search(array(), value, middle+1, hi) CASE ELSE binary_search = middle END SELECT END IF END FUNCTION
[edit] Iterative
Works with: FreeBASIC
Works with: RapidQ
FUNCTION binary_search ( array() AS Integer, value AS Integer, lo AS Integer, hi AS Integer) AS Integer DIM middle AS Integer WHILE lo <= hi middle = (hi + lo) / 2 SELECT CASE value CASE IS < array(middle) hi = middle - 1 CASE IS > array(middle) lo = middle + 1 CASE ELSE binary_search = middle EXIT FUNCTION END SELECT WEND binary_search = 0 END FUNCTION
Testing the function
The following program can be used to test both recursive and iterative version.
SUB search (array() AS Integer, value AS Integer) DIM idx AS Integer idx = binary_search(array(), value, LBOUND(array), UBOUND(array)) PRINT "Value "; value; IF idx < 1 THEN PRINT " not found" ELSE PRINT " found at index "; idx END IF END SUB DIM test(1 TO 10) AS Integer DIM i AS Integer DATA 2, 3, 5, 6, 8, 10, 11, 15, 19, 20 FOR i = 1 TO 10 ' Fill the test array READ test(i) NEXT i search test(), 4 search test(), 8 search test(), 20
Output:
Value 4 not found Value 8 found at index 5 Value 20 found at index 10
[edit] C++
[edit] Recursive
template <class T> int binsearch(const T array[], int len, T what) { if (len == 0) return -1; int mid = len / 2; if (array[mid] == what) return mid; if (array[mid] < what) { int result = binsearch(array+mid+1, len-(mid+1), what); if (result == -1) return -1; else return result + mid+1; } if (array[mid] > what) return binsearch(array, mid, what); } #include <iostream> int main() { int array[] = {2, 3, 5, 6, 8}; int result1 = binsearch(array, sizeof(array)/sizeof(int), 4), result2 = binsearch(array, sizeof(array)/sizeof(int), 8); if (result1 == -1) std::cout << "4 not found!" << std::endl; else std::cout << "4 found at " << result1 << std::endl; if (result2 == -1) std::cout << "8 not found!" << std::endl; else std::cout << "8 found at " << result2 << std::endl; return 0; }
[edit] Iterative
template <class T> int binSearch(const T arr[], int len, T what) { int low = 0; int high = len - 1; while (low <= high) { int mid = (low + high) / 2; if (arr[mid] > what) high = mid - 1; else if (arr[mid] < what) low = mid + 1; else return mid; } return -1; // indicate not found }
[edit] Common Lisp
[edit] Iterative
(defun">defun binary-search (value array) (let ((low 0) (high (1- (length">length">length array)))) (do () ((< high low) nil) (let ((middle (floor (/ (+ low high) 2)))) (cond ((> (aref array middle) value) (setf high (1- middle))) ((< (aref array middle) value) (setf low (1+ middle))) (t (return middle)))))))
[edit] Recursive
(defun">defun binary-search (value array &optional (low 0) (high (1- (length">length">length array)))) (if (< high low) nil (let ((middle (floor (/ (+ low high) 2)))) (cond ((> (aref array middle) value) (binary-search value array low (1- middle))) ((< (aref array middle) value) (binary-search value array (1+ middle) high)) (t middle)))))
[edit] D
[edit] Recursive
The range criterion is omitted because arrays in D can be slices of other arrays, so in a way every array is potentially a range.
size_t binsearch(T) (T[] array, T what) { size_t shift(size_t what, int by) { if (what == size_t.max) return size_t.max; return what + by; } if (!array.length) return size_t.max; auto mid = array.length / 2; if (array[mid] == what) return mid; if (array[mid] < what) return shift(binsearch(array[mid+1 .. $], what), mid + 1); if (array[mid] > what) return binsearch(array[0 .. mid], what); } import std.stdio; void main() { auto array = [2, 3, 5, 6, 8], result1 = array.binsearch(4), result2 = array.binsearch(8); if (result1 == size_t.max) writefln("4 not found!"); else writefln("4 found at ", result1); if (result2 == size_t.max) writefln("8 not found!"); else writefln("8 found at ", result2); }
[edit] Iterative
size_t binSearch(T)(T[] arr, T what) { size_t low = 0 ; size_t high = arr.length - 1 ; while (low <= high) { size_t mid = (low + high) / 2 ; if(arr[mid] > what) high = mid - 1 ; else if(arr[mid] < what) low = mid + 1 ; else return mid ; { } return size_t.max ; // indicate not found }
[edit] 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.
defer (compare)
' - is (compare) \ default to numbers
: cstr-compare ( cstr1 cstr2 -- <=> ) \ counted strings
swap count rot count compare ;
: mid ( u l -- mid ) tuck - 2/ -cell and + ;
: bsearch ( item upper lower -- where found? )
rot >r
begin 2dup >
while 2dup mid
dup @ r@ (compare)
dup
while 0<
if nip cell+ ( upper mid+1 )
else rot drop swap ( mid lower )
then
repeat drop nip nip true
else max ( insertion-point ) false
then
r> drop ;
create test 2 , 4 , 6 , 9 , 11 , 99 , : probe ( n -- ) test 5 cells bounds bsearch . @ . cr ; 1 probe \ 0 2 2 probe \ -1 2 3 probe \ 0 4 10 probe \ 0 11 11 probe \ -1 11 12 probe \ 0 99
[edit] Fortran
[edit] Recursive
In ISO Fortran 90 or later use a RECURSIVE function and ARRAY SECTION argument:
recursive function binarySearch_R (a, value) result (bsresult)
real, intent(in) :: a(:), value
integer :: bsresult, mid
mid = size(a)/2 + 1
if (size(a) == 0) then
bsresult = 0 ! not found
else if (a(mid) > value) then
bsresult= binarySearch_R(a(:mid-1), value)
else if (a(mid) < value) then
bsresult = binarySearch_R(a(mid+1:), value)
if (bsresult /= 0) then
bsresult = mid + bsresult
end if
else
bsresult = mid ! SUCCESS!!
end if
end function binarySearch_R
[edit] Iterative
In ISO Fortran 90 or later use an ARRAY SECTION POINTER:
function binarySearch_I (a, value)
integer :: binarySearch_I
real, intent(in), target :: a(:)
real, intent(in) :: value
real, pointer :: p(:)
integer :: mid, offset
p => a
binarySearch_I = 0
offset = 0
do while (size(p) > 0)
mid = size(p)/2 + 1
if (p(mid) > value) then
p => p(:mid-1)
else if (p(mid) < value) then
offset = offset + mid
p => p(mid+1:)
else
binarySearch_I = offset + mid ! SUCCESS!!
return
end if
end do
end function binarySearch_I
[edit] Haskell
The algorithm itself, parametrized by an "interrogation" predicate p in the spirit of the explanation above:
binarySearch :: Integral a => (a -> Ordering) -> (a, a) -> Maybe a
binarySearch p (low,high)
| high < low = Nothing
| otherwise =
let mid = (low + high) `div` 2 in
case p mid of
LT -> binarySearch p (low, mid-1)
GT -> binarySearch p (mid+1, high)
EQ -> Just mid
Application to an array:
import Data.Array binarySearchArray :: (Ix i, Integral i, Ord e) => Array i e -> e -> Maybe i binarySearchArray a x = binarySearch p (bounds a) where p m = x `compare` (a ! m)
The algorithm uses tail recursion, so the iterative and the recursive approach are identical in Haskell (the compiler will convert recursive calls into jumps).
[edit] Java
[edit] Iterative
... //check will be the number we are looking for //nums will be the array we are searching through int hi = nums.length - 1; int lo = 0; int guess = (hi + lo) / 2; while((nums[guess] != check) && (hi > lo)){ if(nums[guess] > check){ hi = guess - 1; }else if(nums[guess] < check){ lo = guess + 1; } guess = (hi + lo) / 2; } if(hi < lo){ System.out.println(check + " not in array"); }else{ System.out.println("found " + nums[guess] + " at index " + guess); } ...
[edit] Recursive
public static void main(String[] args){ int[] searchMe; int someNumber; ... int index = binarySearch(searchMe, someNumber, 0, searchMe.length); System.out.println(someNumber + ((index == -1) ? " is not in the array" : (" is at index " + index))); ... } public static int binarySearch(int[] nums, int check, int lo, int hi){ if(hi < lo){ return -1; //impossible index for "not found" } int guess = (hi + lo) / 2; if(nums[guess] > check){ return binarySearch(nums, check, lo, guess - 1); }else if(nums[guess]<check){ return binarySearch(nums, check, guess + 1, hi); } return guess; }
[edit] MAXScript
[edit] Iterative
fn binarySearchIterative arr value =
(
lower = 1
upper = arr.count
while lower <= upper do
(
mid = (lower + upper) / 2
if arr[mid] > value then
(
upper = mid - 1
)
else if arr[mid] < value then
(
lower = mid + 1
)
else
(
return mid
)
)
-1
)
arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)
result = binarySearchIterative arr 6
[edit] Recursive
fn binarySearchRecursive arr value lower upper =
(
if lower == upper then
(
if arr[lower] == value then
(
return lower
)
else
(
return -1
)
)
mid = (lower + upper) / 2
if arr[mid] > value then
(
return binarySearchRecursive arr value lower (mid-1)
)
else if arr[mid] < value then
(
return binarySearchRecursive arr value (mid+1) upper
)
else
(
return mid
)
)
arr = #(1, 3, 4, 5, 6, 7, 8, 9, 10)
result = binarySearchRecursive arr 6 1 arr.count
[edit] OCaml
[edit] Recursive
let rec binary_search a value low high = if high = low then if a.(low) = value then low else raise Not_found else let mid = (low + high) / 2 in if a.(mid) > value then binary_search a value low (mid - 1) else if a.(mid) < value then binary_search a value (mid + 1) high else mid
Output:
# let arr = [|1; 3; 4; 5; 6; 7; 8; 9; 10|];; val arr : int array = [|1; 3; 4; 5; 6; 7; 8; 9; 10|] # binary_search arr 6 0 (Array.length arr - 1);; - : int = 4 # binary_search arr 2 0 (Array.length arr - 1);; Exception: Not_found.
[edit] Perl
[edit] Iterative
sub binary_search { ($array_ref, $value, $left, $right) = @_; while ($left <= $right) { $middle = ($right + $left) / 2; if ($array_ref->[$middle] == $value) { return 1; } if ($value < $array_ref->[$middle]) { $right = $middle - 1; } else { $left = $middle + 1; } } return 0; }
[edit] Recursive
sub binary_search { ($array_ref, $value, $left, $right) = @_; if ($right < $left) { return 0; } $middle = ($right + $left) / 2; if ($array_ref->[$middle] == $value) { return 1; } if ($value < $array_ref->[$middle]) { binary_search($array_ref, $value, $left, $middle - 1); } else { binary_search($array_ref, $value, $middle + 1, $right); } }
[edit] PHP
[edit] Iterative
function binary_search( $secret, $start, $end ) { do { $guess = $start + ( ( $end - $start ) / 2 ); if ( $guess > $secret ) $end = $guess; if ( $guess < $secret ) $start = $guess; } while ( $guess != $secret ); return $guess; }
[edit] Recursive
function binary_search( $secret, $start, $end ) { $guess = $start + ( ( $end - $start ) / 2 ); if ( $guess > $secret ) return (binary_search( $secret, $start, $guess )); if ( $guess < $secret ) return (binary_search( $secret, $guess, $end ) ); return $guess; }
[edit] Pop11
[edit] Iterative
define BinarySearch(A, value);
lvars low = 1, high = length(A), mid;
while low <= high do
(low + high) div 2 -> mid;
if A(mid) > value then
mid - 1 -> high;
elseif A(mid) < value then
mid + 1 -> low;
else
return(mid);
endif;
endwhile;
return("not_found");
enddefine;
/* Tests */
lvars A = {2 3 5 6 8};
BinarySearch(A, 4) =>
BinarySearch(A, 5) =>
BinarySearch(A, 8) =>
[edit] Recursive
define BinarySearch(A, value);
define do_it(low, high);
if high < low then
return("not_found");
endif;
(low + high) div 2 -> mid;
if A(mid) > value then
do_it(low, mid-1);
elseif A(mid) < value then
do_it(mid+1, high);
else
mid;
endif;
enddefine;
do_it(1, length(A));
enddefine;
[edit] Python
[edit] Iterative
def binary_search(l, value): low = 0 high = len(l)-1 while low <= high: mid = (low+high)//2 if l[mid] > value: high = mid-1 elif l[mid] < value: low = mid+1 else: return mid return -1
[edit] Recursive
def binary_search(l, value, low = 0, high = -1): if(high == -1): high = len(l)-1 if low == high: if l[low] == value: return low else: return -1 mid = (low+high)//2 if l[mid] > value: return binary_search(l, value, low, mid-1) elif l[mid] < value: return binary_search(l, value, mid+1, high) else: return mid
[edit] Seed7
[edit] Iterative
const func integer: binarySearchIterative (in array elemType: arr, in elemType: aKey) is func
result
var integer: result is 0;
local
var integer: low is 1;
var integer: high is 0;
var integer: middle is 0;
begin
high := length(arr);
while result = 0 and low <= high do
middle := low + (high - low) div 2;
if aKey < arr[middle] then
high := pred(middle);
elsif aKey > arr[middle] then
low := succ(middle);
else
result := middle;
end if;
end while;
end func;
[edit] Recursive
const func integer: binarySearch (in array elemType: arr, in elemType: aKey, in integer: low, in integer: high) is func
result
var integer: result is 0;
begin
if low <= high then
result := (low + high) div 2;
if aKey < arr[result] then
result := binarySearch(arr, aKey, low, pred(result)); # search left
elsif aKey > arr[result] then
result := binarySearch(arr, aKey, succ(result), high); # search right
end if;
end if;
end func;
const func integer: binarySearchRecursive (in array elemType: arr, in elemType: aKey) is
return binarySearch(arr, aKey, 1, length(arr));
[edit] UnixPipes
[edit] Parallel
splitter() {
a=$1; s=$2; l=$3; r=$4;
mid=$(expr ${#a[*]} / 2);
echo $s ${a[*]:0:$mid} > $l
echo $(($mid + $s)) ${a[*]:$mid} > $r
}
bsearch() {
(to=$1; read s arr; a=($arr);
test ${#a[*]} -gt 1 && (splitter $a $s >(bsearch $to) >(bsearch $to)) || (test "$a" -eq "$to" && echo $a at $s)
)
}
binsearch() {
(read arr; echo "0 $arr" | bsearch $1)
}
echo "1 2 3 4 6 7 8 9" | binsearch 6
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