algorithm-analysislisted

# 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_