## Binary Search In Data Structure

• Binary search is speedy with compare to sequential search.
• Binary search is apply to the order list.
• In binary search, we first compare the key with the item in the middle position of the array.
• If there’s a match, we can return immediately. If the key is less than the middle key, then the item sought must lie in the lower half of the array; if it’s greater then the item sought must lie in the upper half of the array.
• So we repeat the procedure on the lower (or upper) half of the array

## Algorithm

Algorithm is quite simple. It can be done either recursively or iteratively:

1. get the middle element;
2. if the middle element equals to the searched value, the algorithm stops;
3. otherwise, two cases are possible:
• searched value is less, than the middle element. In this case, go to the step 1 for the part of the array, before middle element.
• searched value is greater, than the middle element. In this case, go to the step 1 for the part of the array, after middle element.

## Example:-

1.)   Data

 11 5 10 35 95 89

2.)Apply Sorting  process

 0 5 1 10 2 11 3 35 4 89 5 95

1.)  Enter key element (Search Element )By User

2.)  Find the middle Index

Middle index = Int (Stating index + Ending Index) /2

=Int (0+5) /2

Middle index = 2

Middle Element is 11.

3.)  Compare search element with the middle element.

• If they are same then search is sucessfuk
• If Search element > middle Element then bottom part of the list maintain
• If search element is > middle element then upper part of list maintain

89  >  11   Search index = Middle index

Si = 2  Ei =5

Step ni 4, 5 are repeated either end of the list for searching is successful.