In this Tutorial, we will go through the implementation of **Binary Search Algorithm in Python** and write an efficient python code about it. It is also known as **half search method**,** logarithmic chop**, or** binary chop**. Binary search works on logarithmic time in the worst case scenario making *O(log(n))* comparisons, where n is the number of elements in the array, the O is Big O notation, and the log is the logarithm.

The binary search takes constant *(O(1))* space, meaning that the space taken by the algorithm is the same for any number of elements in the array. It is also faster than Linear search, except small linear arrays.

## Performance

**Worst Case Performance:***O(log(n))***Best Case Performance:***O(1)***Average Case Performance:***O(log(n))***Worst Case Space Complexity:***O(1)*

Binary Search works on sorted arrays. Large data companies like **Twitter, facebook**

**often use binary search on their hash tables to find the data quickly. The binary search algorithm works as follows:**

- Binary search begins by comparing the
**middle element**of the array with the target value. - If the target value matches the
**middle element**, its position in the array is returned. - If the target value is
**less than the middle element**, the search continues in the**lower half**of the array. - If the target value is
**greater than the middle element**, the search continues in the**upper half**of the array. By doing this, the algorithm eliminates the half in which the target value cannot lie in each iteration

## Binary Search Pseudo Code

Let an array **A** with **n** elements with values sorted in ascending order and a target value **T**. The following subroutine will be used to find the index of **T** in **A**.

- Set
**L**to**0**and**R**to**n-1** - If
**L > R**search is Unsuccessful - Set
**m**to the floor of**((L+R) / 2)**, - If
**A[m] < T**, set**L = m + 1**, and goto step 2. - If
**A[m] > T**, set**R = m – 1**, and goto step 2. - If
**A[m] == T**, Voila!! Search is done, return**m**

function binary_search(A, n, T): L := 0 R := n − 1 while L <= R: m := floor((L + R) / 2) if A[m] < T: L := m + 1 else if A[m] > T: R := m - 1 else: return m return unsuccessful

## Binary Search Python Code

from math import floor def binary_search(Array, Search_Term): n = len(Array) L = 0 R = n-1 while L <= R: mid = floor((L+R)/2) if Array[mid] < Search_Term: L = mid + 1 elif Array[mid] > Search_Term: R = mid - 1 else: return mid return -1 # Insert your array here A = [1,2,3,4,7,9,12,14,18] # term to be searched term = 14 index = binary_search(A, term) if index >= 0: print("{} is at index {}".format(A[index], index)) else: print("Search term not found")

Note : Array must be sorted for Binary search to work

## Output

14 is at index 7

If you face any error, Please comment below. I shall be happy to help 😁

Find more variations of binary search on pyblog.in.

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