Big O notation helps us analyze the efficiency of algorithms by describing their time or space complexity. It allows developers to predict performance as input sizes grow.

Common Complexities

1. O(1): Constant time, unaffected by input size.
2. O(log n): Logarithmic time, as seen in binary search.
3. O(n): Linear time, common in simple loops.
4. O(n^2): Quadratic time, seen in nested loops.

Example: Linear Search

Here’s an example of O(n) complexity in Python:

python
Copydef linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] == target:
            return i
    return -1
 
numbers = [4, 2, 7, 1, 9]
print(linear_search(numbers, 7))  # Output: 2

Optimizing Algorithms

• Use data structures like hash tables to reduce search times.
• Break down nested loops when possible to improve performance.

Understanding algorithm complexity is critical for building fast and scalable software solutions.