What is Big-O notation?

Question presented to candidate: "Explain Big-O notation to me as if I had never heard of it. Then look at a few loops written in Python and tell me their Big-O, and explain why we are allowed to drop constants."

What a strong answer should cover:

• Big-O describes how running time (or memory) grows as the input size n grows; it is about the shape of the growth, not seconds.
• Drop constant factors and lower-order terms: 3n² + 5n + 20 is O(n²); 2n is O(n).
• The common classes in order, with an example each: O(1) index, O(log n) binary search, O(n) one pass, O(n log n) good sorting, O(n²) all pairs, O(2ⁿ) all subsets.
• Reading code: sequential steps add, nested loops multiply, halving gives log n; Big-O is an upper bound and usually quoted for the worst case (Theta and Omega for tight and lower bounds).
• Python-specific hidden costs: x in list is O(n) while x in set and dict lookups are O(1) on average; list.pop(0) and slicing are O(n); sort() is O(n log n).

Code / implementation expected: Optional — a few Python functions whose loops the candidate labels O(1), O(log n), O(n), O(n²).