# Implementation of Binary Search in Python

Binary Search is also known as logarithmic search and half-interval search. Unlike Linear search, it works on sorted arrays or list. Binary search begins by comparing the middle element of the array with the target value. If the target value (element to be found) matches the middle element, its position in the array is returned. If the target value is less than or greater than the middle element, the search continues in the lower or upper half of the array, respectively, eliminating the other half from consideration.

Time complexity of Binary Search is O(log n) where n is the number of elements in the array.

For example:

arr[]=  { 24, 45, 67, 89, 90, 92, 94, 96 }
Let the element to be found = x = 45
Now,
end = 8
beg = 1
mid = (beg+end)/2 =  4 (floor value)  //During implementation please take care of index '0'

Now, we will check if arr=x. Since, arr=89 which is greater than
Therefore we will update end and now end will become 3 (end=mid - 1). Now we will check for the
target element in the first half and second half of the array will be eliminated.

Now in first half, mid=(beg+end)/2 = (1+3)/3 = 2 . Since arr[mid] = arr = 45= x, it will return true.

Algorithm

set: beg=1, set: end=len(listing)   /*n is the number of elements in the array */
set: mid=(beg+end)/2
If element<arr[beg] or element>arr[end]:
return false
Else:
do While beg<=end:
If arr[mid]=element:
return true
Else:
If arr[mid]>element:
set: end=mid-1
Else:
set: beg=mid+1
End IfElse
End IfElse
End While loop
End IfElse
Program:

```def binary_search(element):
beg=0
end=len(listing)-1
mid=(beg+end)//2
while beg<=end:
if listing[mid]==element:
return mid
else:
if listing[mid]>element:
end=mid-1
else:
beg=mid+1
mid=(beg+end)//2
return -1
global listing
listing=[]
print("\nEnter the elements: \n")
listing=list(map(int,raw_input().split()))
print("Enter the element you want to search: ");
element=int(input())
result=binary_search(element)
if result==-1:
print("\nElement is not present in the array")
else:
print('\nElement '+str(element)+' is present at index '+str(result))```

OUTPUT: