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# Python program to implement Binary Search Algorithm Hello everyone! Welcome back to programminginpython.com. Here in this post am going to show you how to implement a binary search algorithm in Python. In the previous post, I discussed the Linear Search Algorithm which is a very basic search algorithm here I will discuss Binary Search.

Binary Search as the name suggests binary, here the list is divided into halves and then searched in each half. One notable thing about this binary search is that the list should be sorted first before executing the algorithm. The list is divided into two halves by the index, find the mid element of the list and then start to mid-1 is one list and mid+1 to end is another list, check if the element is mid, greater than it, or less than it and return the appropriate position of the key element to be found.

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## Time Complexity

 Best Case O(1) Average Case O(log n) Worst Case O(log n)

## Algorithm

Given a list L of n elements with values or records L0, L1, …, Ln-1, sorted in ascending order, and given key/target value K, binary search is used to find the index of K in L

1. Set a variable `start` to `0` and another variable `end` to `n-1`(size of the list)
2. if `start` > `end` break the algorithm, as it works only on sorted lists
3. calculate `mid` as `(start + end)/2`
4. if the key element is
1. equal to mid, the search is done, returns the position of mid
2. greater than mid, set `start` to `mid + 1` and repeat step 2
3. less than mid, set `end` to `mid - 1` and repeat step 2

## Program

```__author__ = 'Avinash'

def binary_sort(sorted_list, length, key):
start = 0
end = length-1
while start <= end:
mid = int((start + end)/2)
if key == sorted_list[mid]:
print("\nEntered number %d is present at position: %d" % (key, mid))
return -1
elif key < sorted_list[mid]:
end = mid - 1
elif key > sorted_list[mid]:
start = mid + 1
return -1

lst = []

size = int(input("Enter size of list: \t"))

for n in range(size):
numbers = int(input("Enter any number: \t"))
lst.append(numbers)

lst.sort()
print('\n\nThe list will be sorted, the sorted list is:', lst)

x = int(input("\nEnter the number to search: "))

binary_sort(lst, size, x)```