Algorithm Analysis

Understanding and predicting algorithm performance.

Context

You are analyzing algorithm complexity. Use Big O to compare approaches.

Domain Context

• Big O: Worst-case growth rate; O(1), O(log n), O(n), O(n log n), O(n²)
• Time vs. Space: Tradeoff; faster algorithms often use more memory
• Constant Factors: O(n) with big constant might lose to O(n log n); measure
• Practical: Asymptotic analysis is useful; real data matters too

Instructions

1. Count Operations: How many steps for input size n?
2. Dominant Term: n² + n → O(n²); drop constants and lower terms
3. Compare Algorithms: Which has better complexity for your problem?
4. Consider Constants: O(n) with big constant might lose to O(n log n)
5. Measure: Implement both; benchmark with real data
6. Choose: Pick algorithm with best complexity on expected input sizes

Anti-Patterns

• Obsessing over Big O without measuring; constant factors matter
• Choosing O(n log n) over O(n) without analyzing input distribution
• Not considering space complexity; time-space tradeoffs exist
• Assuming theoretical optimum is practical; real implementation matters
• Ignoring cache effects; access patterns beat asymptotic analysis

Further Reading

• Donald Knuth, TAOCP, Vol 1-3
• MIT OpenCourseWare, Introduction to Algorithms