Learn the basics of how binary search is performed on a give data set (for example an array) with simple and easy to understand example.

1. Data Structure - 1

2. Now as most of you must be knowing a major drawback of
the linear search that it is extremely time consuming for large
data sets .
Consider for Example we have an array with only five numbers
[1,3,0,8,5] and we want to search the number 5 in the array.
Then the maximum time taken to search the array would be
basically five iterations.

3. However , consider a case where you have say 10,000
numbers in an array [i.e. numbers from 1 to 10000 in any
random fashion] and we want to search an element which is
the last number in the array.
Now as you can see here this is extremely time consuming as
it would take 10000 iterations to search the number.
This Is where we use binary search to speed up the operation
significantly.

4. The pre requirement for binary search is that the array should
be in a sorted order.
The following example will give you a better understanding of
the working of the binary search algorithm.

5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Suppose the user wants to find the number 7 in the array of 20 numbers
given below. To find 7, the number would be initially compared with middle
element of the array say 10.
Iteration no - 01

6. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Now as we see the array is sorted and the number 7 is less than 10 the array
after the number 10 is totally discarded thus reducing the array to be
searched by half.

7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Now similar process is done on the rest of the array. Now the array to be
searched is between the numbers 1 to 10. Again in a similar fashion the
middle element of the array is searched and compared with the number 7.
Again since 5 is the middle element it is not the number to be searched.
Iteration no - 02

8. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Now here as we see the number 7 is greater than 5 the array numbers 1 to 4
are discarded and the array to be searched is now from 5 to 10.

9. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Again the same thing is done . The middle element of the array is found out
i.e. the middle element of the array between 5 to 10 which turns out to be 7
the number to be found out.
Iteration no - 03

10. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Thus using binary search we found out the number 7 from an array of 20
numbers in 3 iterations which would have taken 7 iterations using linear
search thus reducing the work by half.

11. Thus we see that binary search is a much more efficient
algorithm for searching in a large list then the linear search
algorithm.
The only drawback of the algorithm being the array on which
the search is being performed should be COMPULSORILY in
the sorted order.