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Binary Search Ladder

Binary search practice should build confidence in monotonicity and boundary control, not just memorization of one loop.

Who This Is For

Use this ladder if:

  • you can code binary search, but still mistrust the final answer
  • lower_bound makes sense but answer-search feels shaky
  • hidden tests often expose endpoint mistakes

Warm-Up

  • search in a sorted array
  • first position >= x
  • last position <= x

Target skill:

  • understand what the returned index means

Core

  • binary search on answer
  • feasibility predicates
  • monotone capacity, time, or threshold questions

Target skill:

  • define one monotone predicate and one stable boundary convention

Repo Anchor

  • Factory Machines: a strong first answer-search note because the predicate is simple and the boundary meaning is easy to explain.

Stretch

  • combine binary search with prefix sums or greedy checking
  • compare lower_bound style search with answer-search
  • rewrite one solution in both “first true” and “last false” style

Target skill:

  • treat binary search as invariant management, not magic

Exit Criteria

You are ready to move on when:

  • you can explain why l and r are initialized the way they are
  • you know whether the final answer is l or r
  • you can spot non-monotone checks before writing the loop

External Practice