Lesson 063
Time Complexity
Big O & Growth Rates
1:00How to classify and compare the scalability of algorithms using Big-O notation and the standard growth-rate hierarchy.
By the end, you can
- Explain why time complexity uses operation counts rather than seconds.
- Apply the two simplification rules to reduce any polynomial expression to its Big-O class.
- Recite the canonical growth-rate order: O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!).
- Classify a short code snippet (single loop, nested loops, halving loop) by inspecting its structure.
- Distinguish best, average, and worst case from Big-O notation and explain why people conflate them.
- Identify the complexity class for common operations: array index read, linear scan, binary search, merge sort, nested loop.
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