How do you work out and explain the time and space complexity of your solution?

A reliable way to do it, out loud:

1. Name the inputs. “n is the number of orders, m is the number of products.” Different inputs get different letters.
2. Cost of each step, including library calls: contains on a list is O(n), sort is O(n log n), a hash map lookup is O(1) on average, removing from the front of an array list is O(n).
3. Combine. Nested loops multiply, steps that follow each other add.
4. Simplify. Drop constants and keep the dominant term: O(2n + n log n) is O(n log n).
5. Space. Count extra memory: sets, maps, copies, and the recursion depth.

Then say it as one sentence with the trade-off: “This is O(n) time and O(n) space because of the hash set; the sort-based version would be O(n log n) time with less extra memory.”

If the interviewer pushes, distinguish worst case (a hash map degrading with collisions), average case, and amortized cost (dynamic-array appends are O(1) amortized because resizes are rare).