Python Program for Binary Search (Recursive and Iterative)

In a nutshell, this search algorithm takes advantage of a collection of elements that is already sorted by ignoring half of the elements after just one comparison.

Compare x with the middle element.
If x matches with the middle element, we return the mid index.
Else if x is greater than the mid element, then x can only lie in the right (greater) half subarray after the mid element. Then we apply the algorithm again for the right half.
Else if x is smaller, the target x must lie in the left (lower) half. So we apply the algorithm for the left half.

Recursive :

# Python 3 program for recursive binary search. 
# Modifications needed for the older Python 2 are found in comments. 
  
# Returns index of x in arr if present, else -1 
def binary_search(arr, low, high, x): 
  
    # Check base case 
    if high >= low: 
  
        mid = (high + low) // 2
  
        # If element is present at the middle itself 
        if arr[mid] == x: 
            return mid 
  
        # If element is smaller than mid, then it can only 
        # be present in left subarray 
        elif arr[mid] > x: 
            return binary_search(arr, low, mid - 1, x) 
  
        # Else the element can only be present in right subarray 
        else: 
            return binary_search(arr, mid + 1, high, x) 
  
    else: 
        # Element is not present in the array 
        return -1
  
# Test array 
arr = [ 2, 3, 4, 10, 40 ] 
x = 10
  
# Function call 
result = binary_search(arr, 0, len(arr)-1, x) 
  
if result != -1: 
    print("Element is present at index", str(result)) 
else: 
    print("Element is not present in array") 

Output:

Element is present at index 3

Iterative:

# Iterative Binary Search Function 
# It returns index of x in given array arr if present, 
# else returns -1 
def binary_search(arr, x): 
    low = 0
    high = len(arr) - 1
    mid = 0
  
    while low <= high: 
  
        mid = (high + low) // 2
  
        # Check if x is present at mid 
        if arr[mid] < x: 
            low = mid + 1
  
        # If x is greater, ignore left half 
        elif arr[mid] > x: 
            high = mid - 1
  
        # If x is smaller, ignore right half 
        else: 
            return mid 
  
    # If we reach here, then the element was not present 
    return -1
  
  
# Test array 
arr = [ 2, 3, 4, 10, 40 ] 
x = 10
  
# Function call 
result = binary_search(arr, x) 
  
if result != -1: 
    print("Element is present at index", str(result)) 
else: 
    print("Element is not present in array") 

Output:

Element is present at index 3

Please refer to the article Binary Search for more details!

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