Big O Notation: Performance Analysis

Purpose

• Big O notation describes algorithm performance as input size increases.
• Two main complexities:
  • Time complexity: Time taken to run the algorithm.
  • Space complexity: Memory required by the algorithm.

Key Concepts

• n: Represents the number of inputs.
• As n scales to infinity, the algorithm's performance is determined by how rapidly the result grows.
• In technical interviews, estimating time or space complexity is common.

Types of Complexity

Linear Complexity (O(n))

• Example: Looping over an array.
• Time grows linearly with the number of inputs.

Logarithmic Complexity (O(log n))

• Example: Binary search on a sorted array.
• More efficient than linear time, especially for large datasets.

Constant Time (O(1))

• Example: Accessing an element by index in an array.
• Execution time remains constant regardless of input size.

Quadratic Complexity (O(n^2))

• Example: Nested loops (loop within a loop).
• Time grows with the square of the number of inputs.

Exponential Complexity (O(2^n) or similar)

• Example: Evaluating every possible combination in an array.
• Grows extremely fast, inefficient for large datasets.

Simplification

• Multiple growth rates can exist in an algorithm.
• Simplify to the fastest growing, worst-case scenario notation.

Conclusion

• Understanding Big O is crucial for evaluating and optimizing algorithm performance.
• Focus on worst-case scenarios for a concise complexity estimate.