Binary Search Explained Like You're 5 (With Code Example)

Binary search is a fast way to find a number in a sorted list. Instead of checking every number one by one (which is slow), binary search starts in the middle, checks if your number is bigger or smaller, then searches only the half where your number could be. It keeps dividing the list in half until it finds your number.

Think of it like finding a word in a dictionary: you don't start at page 1 and read every page. Instead, you open to the middle, see if your word comes before or after, then search only that half. You keep doing this until you find your word. That's exactly how binary search works!

Binary search is very fast—it has O(log n) time complexity. With 1 million numbers, binary search needs only about 20 comparisons, while checking every number could need up to 1 million comparisons. Binary search only works on sorted lists, but when it works, it's incredibly efficient.

Binary search involves these key concepts:

Use binary search in these situations:

Follow these steps to understand binary search:

# Binary Search Implementation
def binary_search(arr, target):
    """
    Find target in sorted array using binary search
    Returns index if found, -1 if not found
    """
    left = 0
    right = len(arr) - 1
    
    while left <= right:
        # Find middle index
        mid = (left + right) // 2
        
        # Check if target is at middle
        if arr[mid] == target:
            return mid  # Found!
        
        # If target is smaller, search left half
        elif arr[mid] > target:
            right = mid - 1
        
        # If target is larger, search right half
        else:
            left = mid + 1
    
    return -1  # Not found

# Example Usage
numbers = [1, 3, 5, 7, 9, 11, 13, 15]
result = binary_search(numbers, 11)
print(f"Found at index: {result}")  # Output: Found at index: 5

Binary search is important for these reasons:

Frequently Asked Questions