How does the bisect module work?

Question presented to candidate: "Say you have a big sorted list and you need to find where a value belongs, or count how many values fall in a range. What does Python's bisect module do, how does it work, and when is it the wrong tool?"

What a strong answer should cover:

• bisect is binary search on an already sorted sequence: it halves a [lo, hi) window each step, so it needs about log2(n) comparisons (20 for a million items).
• bisect_left returns the first position where x could go (before equal items), bisect_right / bisect the position after equal items; right - left counts the copies of x.
• insort / insort_left / insort_right keep a list sorted, but the search is O(log n) while the list insert is O(n), so it does not beat a heap or a sorted container for many inserts.
• The key= argument (added in Python 3.10) is applied to the list items, not to x; lo and hi limit the window; only < is used for comparisons.
• Typical uses: membership in a sorted list, range counts, bucketing a score into a grade, and keeping a small sorted list up to date.

Code / implementation expected: Yes — either use bisect for a lookup/range task, or write bisect_left by hand.