How does binary search work with recursion?

Can you explain how binary search works with recursion?

Sure! Binary search is an efficient algorithm for finding an item from a sorted list. It works by repeatedly dividing the search interval in half.

How do you implement it recursively?

In a recursive implementation, you check the middle element of the array. If it matches the target, you return its index. If the target is less than the middle element, you search the left half; otherwise, you search the right half.

Can you show me a code example?

Certainly! Here's a simple Python implementation:

def binary_search(arr, target, low, high):
    if low > high:
        return -1  # Target not found
    mid = (low + high) // 2
    if arr[mid] == target:
        return mid
    elif arr[mid] > target:
        return binary_search(arr, target, low, mid - 1)
    else:
        return binary_search(arr, target, mid + 1, high)

What are the time and space complexities of this algorithm?

The time complexity of binary search is O(log n), and the space complexity is O(log n) due to the recursive call stack.