DSA — Binary Search

What is Binary Search?

Efficiently finds an item in a sorted array by repeatedly dividing the search interval.

def binary_search(arr, target):
    left, right = 0, len(arr) - 1
    
    while left <= right:
        mid = (left + right) // 2
        
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    
    return -1

Recursive Version

def binary_search_recursive(arr, target, left=0, right=None):
    if right is None:
        right = len(arr) - 1
    
    if left > right:
        return -1
    
    mid = (left + right) // 2
    
    if arr[mid] == target:
        return mid
    elif arr[mid] < target:
        return binary_search_recursive(arr, target, mid + 1, right)
    else:
        return binary_search_recursive(arr, target, left, mid - 1)

Time Complexity

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

When to Use

• Sorted data
• Large datasets
• Frequent searches

Mini Practice

1. Implement binary search
2. Find first/last occurrence
3. Search in rotated array
4. Find ceiling/floor

Up Next

Continue with Bubble Sort — simple sorting algorithm.