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.

1. Compare x with the middle element.
2. If x matches with the middle element, we return the mid index.
3. 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.
4. 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!