Binary search: Difference between revisions
(Common Lisp recursive version) |
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return -1; // indicate not found |
return -1; // indicate not found |
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}</cpp> |
}</cpp> |
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=={{header|Common Lisp}}== |
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===Recursive=== |
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<pre> |
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(defun binary-search (value array &optional (low 0) (high (1- (length array)))) |
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(if (< high low) |
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nil |
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(let ((middle (floor (/ (+ low high) 2)))) |
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(cond ((> (aref array middle) value) |
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(binary-search value array low (1- middle))) |
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((< (aref array middle) value) |
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(binary-search value array (1+ middle) high)) |
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(t middle))))) |
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</pre> |
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=={{header|D}}== |
=={{header|D}}== |
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Revision as of 20:13, 12 June 2008
You are encouraged to solve this task according to the task description, using any language you may 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
}
C++
Recursive
<cpp>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;
}</cpp>
Iterative
<cpp>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
}</cpp>
Common Lisp
Recursive
(defun binary-search (value array &optional (low 0) (high (1- (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)))))
D
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.
<d>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);
}</d>
Iterative
<d>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
}</d>
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
Fortran
Recursive
In ANSI 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
Iterative
In ANSI 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
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).
Java
Iterative
<java>... //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);
} ...</java>
Recursive
<java>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;
}</java>
MAXScript
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
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
OCaml
Recursive
<ocaml>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</ocaml>
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.
Perl
Iterative
<perl>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 = $middle + 1;
}
}
return 0;
}</perl>
Recursive
<perl>sub binary_search {
($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);
}
}</perl>
PHP
Iterative
<php> 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;
} </php>
Recursive
<php> 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;
} </php>
Pop11
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) =>
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;
Python
Iterative
<python>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</python>
Recursive
<python>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</python>
Seed7
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;
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));
UnixPipes
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