Complexity And Invariants Ladder¶
This ladder is not about one algorithm. It is about learning to justify, test, and debug your implementation.
Who This Is For¶
Use this ladder if:
- your sample tests pass but hidden tests fail
- you often cannot explain what a pointer, state, or endpoint means
- you want a repeatable debugging process
Warm-Up¶
- estimate the complexity of a simple loop nest
- explain what each variable means in one accepted solution
- identify one invariant in prefix sums or a running maximum scan
Target skill:
- stop writing code whose state meaning is vague
Core¶
- binary search invariant checks
- prefix-sum correctness arguments
- two-pointer window invariants
- greedy-after-sorting proof sketches
Target skill:
- describe the algorithm as state + invariant + transition
Repo Anchors¶
Retrieval Layer¶
- quick checklists -> Foundations cheatsheet
- tutorial page -> Reasoning And Implementation Discipline
Stretch¶
- write a short proof sketch before coding
- build custom edge cases before running samples
- restate one accepted solution as invariants plus transitions only
Target skill:
- debug by reasoning, not by random edits
Exit Criteria¶
You are ready to move on when:
- you routinely state the invariant before or during coding
- you estimate time complexity before implementation
- you can create small counterexamples for weak ideas quickly