apm-alphacode-pass-3-meta

name	apm - Alphacode Pass 3 Meta
description	Third pass — meta-reasoning about solution correctness, confidence, and robustness. Catches what testing alone misses.
output	{"format":"prose"}

Alphacode Pass 3 Meta

Input: $ARGUMENTS

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Overview

Pass 3 reasons about the solution from outside the solution. Catches bugs testing misses: incorrect problem interpretation, flawed greedy proofs, missed constraints, subtle off-by-one errors. Treats the solution as an artifact to audit.

Prerequisite: Complete Pass 1 (/ape) and ideally Pass 2 (/api).

Steps

Step 1: Re-read the Problem Statement

1. Read problem statement again, fresh
2. Compare your understanding to what's actually written
3. Did you solve the asked problem or a different one?
4. Common misreadings: "at most K" vs "exactly K", "distinct" vs "not necessarily distinct", 0-indexed vs 1-indexed, "non-decreasing" vs "strictly increasing"

Step 2: Audit Algorithm Correctness

1. Greedy: State exchange argument explicitly. Can't state it? Greedy may be wrong.
2. DP: Verify recurrence — base cases, transitions cover all cases, no missing states
3. Graph: Verify assumptions — connected? directed? weighted? negative weights?
4. Any: Construct a case where it would fail IF wrong. Can't? Test harder.

Step 3: Check Off-by-One Errors

1. Array indexing: 0-based vs 1-based consistency
2. Loop bounds: < N vs <= N
3. Binary search: lo < hi vs lo <= hi, mid vs mid+1
4. Interval endpoints: inclusive vs exclusive
5. Modular arithmetic: (a - b) % MOD can be negative

Step 4: Stress Test with Adversarial Inputs

1. All elements equal / sorted / reverse sorted
2. Maximum values on all constraints simultaneously
3. Star graph, chain graph, complete graph
4. Single-character strings
5. Check: within time? Memory? Output format exact?

Step 5: Consider Alternative Approaches

1. Completely different, simpler approach available?
2. Worth implementing as cross-check?
3. Two approaches agree → high confidence. Disagree → find which is wrong.

Step 6: Confidence Assessment

META-REVIEW:
Problem interpretation: [verified / uncertain at X]
Algorithm correctness: [proven / argued / hoped]
Edge cases: [all covered / gaps at X]
Off-by-one audit: [clean / fixed N issues]
Stress test: [passed / failed at X]
Confidence: [high / medium / low]
Action: [submit / fix X first / rethink]

When to Use

• Before submitting a competitive programming solution
• After Wrong Answer, to find the bug
• When solution passes examples but confidence is low

Verification

• Problem re-read after solution written
• Correctness argued (not just tested)
• Off-by-one systematically checked
• Adversarial inputs tested
• Confidence honestly assessed