Binary Search

1. DESIGNANALYSIS AND ALGORITHM
Binary Search

2. Introduction
 Binary Search is a search algorithm that
finds the position of a target value within a
sorted array.
 Binary Search is also known as half-
interval search or logarithmic search.
 Binary Search algorithm works on the
principle of Divide And Conquer.
 Binary Search can be implemented on only
sorted list of elements.

3. Divide And Conquer
 Divide and Conquer is the most-well known
algorithm strategy.
 A Divide and Conquer algorithm works by
recursively breaking down a problem into
two or more sub-problems of the same or
related type, until these become simple
enough to be solved directly.
 The solutions to the sub-problems are then
combined to give a solution to the original
problem.

4. Example
 Consider an Array:
A
0 1 2 3 4 5 6 7 8
min mid=(min + max)/2 max
If(37==a[mid]) return mid
Else if(37<a[mid]) max=mid-1
Else if(37>a[mid]) min=mid+1
20 35 37 40 45 50 51 55 67

5. Algorithm
Input :
A ← sorted array
n ← size of array
key← value to be searched
BinarySearch(a,key,n) :
Set min= 0
Set max= n-1
while (min < max)
Set mid=(min + max)/2

6. Algorithm
if (key ==A[mid])
Return mid
Else if(key<A[mid])
set max= mid - 1
Else
set min= mid + 1
End if
End while
Return (- 1)

7. Time Complexity
 The running time complexity for Binary Search
are of three types :-
 In Worst Case ,Time Complexity : O(log n)
 In Average Case ,Time Complexity : O(log n)
 In Best Case , Time Complexity : O(1)

8. Advantage
 Binary Search is an optimal searching
algorithm using which we can desired
element very efficiently.

9. Disadvantage
 Binary Search algorithm requires the list to
be sorted. Then only method is Applicable.

10. Application
 The Binary Search is an efficient searching
method and used to search desired record
from database.
 For solving non-linear equations with one
unknown this method is used.

11. THANK YOU-------------------------------------