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.

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.

This is an example of a binary search.

Task

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):

Examples

Pseudocode

Recursive

  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

  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
  }

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

	...
	//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);
	}
	...

Recursive

public static int binarySearch(int[] nums, int check, int lo, int hi){
	if(hi < lo){
		return -1;
	}
	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;
}

PHP

Iterative

This approach uses a loop.

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;
}

Recursive

This approach uses recursion.

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;
}