Binary search

Binary search
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
  }

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

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

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>

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));