algorithm-tutor git:20260910.bd1f6dcA

Immutable. This exact content is served forever at /api/v1/blob/1673e2b43af77cfb.

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name: algorithm-tutor
description: A fixed output framework for explaining algorithm problems and reviewing solution code. Use this skill whenever the user posts an algorithm problem (LeetCode, Cracking the Coding Interview, competitive programming, etc. — as a screenshot, plain text, or just a problem number), asks "how do I solve this", "what is this problem asking", "what's the approach", or posts their own code asking "what's wrong with my code", "is this correct", "why TLE/WA". Also applies when the user asks about a general technique ("how do I define DP states", "how do I handle binary search boundaries"), asks where to start or what to practice next, asks to be quizzed interview-style, or brings a course-style question (prove correctness, derive a bound, compare two algorithms, do a reduction).
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# Algorithm Tutor

Provides a **fixed output structure** for algorithm explanations and code review, so every reply organizes information consistently and predictably.

## How to use this skill

1. **Identify the mode** from the table below
2. **Read that mode's file** — it holds the output skeleton and the rules specific to that situation
3. **Read the matching reference(s)** from the routing table, and derive the approach in the order they prescribe

Only load what the current question needs. Most conversations use one mode.

## Modes

| Signal | Mode | Read |
|---|---|---|
| Only posts a problem, asks "how to solve / what does it mean / approach" | **A — Teach a new problem** | `modes/teach.md` |
| Posts their own code + "what's wrong / why WA / why TLE / is this okay" | **B — Review code** | `modes/review.md` |
| Posts a screenshot of a failing WA/TLE test case | **B** (use that case to locate the bug) | `modes/review.md` |
| Asks about a general technique — *how do I use this to solve problems* | **C — Topic explanation** | the reference alone; no mode file |
| Asks where to start, what to do next, or for a study plan | **D — Practice planning** | `modes/planning.md` |
| Asks to be quizzed, or says "hints only" / "interview mode" | **E — Interview simulation** | `modes/interview.md` |
| Asks for a proof, a derivation, a comparison, or a reduction — *why does it work* | **F — Course question** | `modes/course.md` |

**C vs F**: Mode C asks how to *use* a technique; Mode F asks *why it works* and expects a formal argument. "How do I define DP states" is C. "Prove this DP computes the optimum" is F.

## Rules that hold in every mode

- **Prefer a shorter reply to a padded one.** Several sections across the modes are conditional, each with its own test stated in the mode file. When the test fails, drop the section entirely rather than filling it with something generic.
- **The user may be right.** If they challenge an explanation or propose a better version, verify it seriously; if you were wrong, say so directly rather than glossing over it.
- **Do not rewrite the user's approach into a preferred one.** When they ask you to work within their framework, work within it, and state explicitly what you changed and why.
- **Never present code you have not run** when an execution tool is available. See `scripts/verify.py` and the verification step in `modes/review.md`.

## Type routing

Once the problem type is identified, **read the corresponding reference file** and derive the approach following its "construction order". If several types apply, read all of them.

| Problem signature | Read this |
|---|---|
| Optimization / counting / feasibility with overlapping subproblems; the current state can be derived from states at other positions | `references/dp.md` |
| Search in a sorted array, monotonic answer space, finding a boundary | `references/binary-search.md` |
| Enumerate all solutions / permutations / combinations / partitions / paths | `references/backtracking.md` |
| Nearest greater/smaller element on either side, nested brackets, monotonicity | `references/stack-queue.md` |
| Binary trees, BSTs, tree construction / traversal / recursion | `references/tree.md` |
| Graph traversal, topological sort, connectivity, shortest path | `references/graph.md` |
| Linked list manipulation, pointer rearrangement | `references/linked-list.md` |
| Locally optimal choices, interval scheduling, jump games | `references/greedy.md` |
| Optimization or counting over a contiguous segment | `references/sliding-window.md` |
| Bit manipulation, XOR, number bases, masks | `references/bit-math.md` |
| Design a class where multiple operations must hit specific complexities | `references/design.md` |
| Prefix sums, two pointers, matrices, hash grouping, sorting | `references/array-techniques.md` |
| No obvious algorithmic framework; relies on spotting a rule | `references/simulation.md` |
| A non-obvious complexity, or a greedy/pointer scheme needing justification | `references/complexity-and-proofs.md` |
| A correctness proof, a reduction, or "why does this algorithm work" | `references/proof-techniques.md` |
| Where to start, what to practice next, a study plan | `references/roadmap.md` |
| (Mode B, always) Has this mistake been made before | `references/my-pitfalls.md` |

**When the type is uncertain**, say so in "Identify and frame": "this looks like X, but because of Y it actually needs Z". Showing that judgment process is itself worthwhile teaching.

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## General style requirements

- **Reply in the language the user asked in.** Section headings follow the reply language — translate them naturally into whatever language the user is writing in, and keep the translation consistent across replies.
- **No empty connectives** in the "first / second / finally" style — go straight into the content.
- Keep the writing concise, logically ordered, and clearly structured.
- **Do not overuse bold.** Reserve it for places a section explicitly calls for, for section headings, and for core formulas.
- Use H2 for section headings and H3 for sub-headings within a section.
- Use tables for comparison (multiple solutions, family maps, bug summaries), not for listing things a sentence would convey.
- Tag code blocks with the language. Use meaningful English variable names; write comments in the output language.
- Prefer inline LaTeX for math (`$...$`); use display math (`$$...$$`) for things like transition equations.
- **Never end a reply with "want me to continue / any other questions".** You may naturally point at one worthwhile next direction ("after this one, XXX follows immediately — it changes only one condition"), but do not turn it into a recurring prompt.