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In computer science, a binary search or half-interval search algorithm finds the position of a specified value (the input "key") within a sorted array. In each step, the algorithm compares the input key value with the key value of the middle element of the array. If the keys match, then a matching element has been found so its index, or position, is returned. Otherwise, if the sought key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the input key is greater, on the sub-array to the right. If the remaining array to be searched is reduced to zero, then the key cannot be found in the array and a special "Not found" indication is returned.

If the list to be searched contains more than a few items (a dozen, say) a binary search will require far fewer comparisons than a linear search, but it imposes the requirement that the list be sorted. Similarly, a hash search can be faster than a binary search but imposes still greater requirements. If the contents of the array are modified between searches, maintaining these requirements may even take more time than the searches. And if it is known that some items will be searched for much more often than others, and it can be arranged that these items are at the start of the list, then a linear search may be the best.

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Example Code

The binary search algorithm can also be expressed iteratively with two index limits that progressively narrow the search range

int binary_search(int A[], int key, int imin, int imax)
{
  // continue searching while [imin,imax] is not empty
  while (imax >= imin)
    {
      /* calculate the midpoint for roughly equal partition */
      int imid = midpoint(imin, imax);
 
      // determine which subarray to search
      if      (A[imid] <  key)
        // change min index to search upper subarray
        imin = imid + 1;
      else if (A[imid] > key )
        // change max index to search lower subarray
        imax = imid - 1;
      else
        // key found at index imid
        return imid;
    }
  // key not found
  return KEY_NOT_FOUND;
}

Reference: Wikipedia