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README.md

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+---
+configs:
+- config_name: references
+  data_files: references/*.parquet
+- config_name: errata
+  data_files: errata/*.parquet
+language:
+- en
+tags:
+- code
+- ocaml
+- livecodebench
+---
+
+# OCaml reference solutions for LiveCodeBench
+
+A reference solution in OCaml for every problem in the multilingual-LiveCodeBench OCaml
+universe that can be scored at all, plus the list of problems that cannot be.
+
+- **436** problems in the universe
+- **415** are scoreable, and every one of them has a verified reference
+- **21** are excluded as unscoreable (see the `errata` config)
+
+
+## Configs
+
+`references` is one row per problem. `errata` is the subset no correct program can pass,
+with the evidence for each.
+
+```python
+from datasets import load_dataset
+refs = load_dataset("samuki-hf/ocaml-reference-solutions", "references", split="train")
+errata = load_dataset("samuki-hf/ocaml-reference-solutions", "errata", split="train")
+```
+
+## What `verification` means
+
+Every solution was compiled with `ocamlopt` and run against the real hidden tests.
+
+| value | meaning | count |
+|---|---|---|
+| `exact-match` | passes every official test byte for byte | 410 |
+| `float-tolerance` | correct; differs only in float formatting | 5 |
+| `validated-not-exact` | proven correct; the problem accepts several answers | 12 |
+| `unverified` | on LiveCodeBench's errata list, not re-derived here | 8 |
+
+The `float-tolerance` rows are not a defect in the solutions. Those problems state an accepted
+error of "absolute **or** relative at most 1e-6", and no comparator in the LiveCodeBench
+lineage implements that rule: the original grades per line under `Decimal` equality, Multi-LCB
+adds bool aliasing and `math.isclose(abs_tol=1e-5, rel_tol=0)`, and Agnostics compares whole
+outputs under `rstrip()`.
+
+## Why problems are excluded
+
+| problem | reason | source | evidence |
+|---|---|---|---|
+| `abc337_e` | interactive | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc343_a` | multiple-solutions | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc343_e` | multiple-solutions | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc350_c` | erroneous-tests | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc355_e` | interactive | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc362_c` | multiple-solutions | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `abc363_f` | multiple-solutions | this-work | palindromic product string; 3000/3000 consistent |
+| `abc366_g` | multiple-solutions | this-work | XOR labelling; 300/300 valid on random graphs |
+| `abc373_g` | multiple-solutions | this-work | non-crossing matching; 300/300 valid matchings |
+| `abc392_f` | erroneous-tests | this-work | 2 of 42 hidden tests violate the stated 1 <= P_i <= i (P_1 = 3 and P_1 = 5) and their expected outputs contain zeros, though the answer is a permutation of 1..N. |
+| `abc396_e` | multiple-solutions | this-work | ties in the per-bit choice; 400/400 minimum sums |
+| `abc397_d` | multiple-solutions | this-work | x^3-y^3=N can admit several pairs; 0 wrong over N<=200000 |
+| `arc181_c` | multiple-solutions | this-work | 0/1 grid; 200/200 valid on random P,Q |
+| `arc183_d` | multiple-solutions | this-work | asks for any maximum-score removal order, and the two vertices of an operation may be printed in either order, so even the N=4 test with a unique optimal procedure has four correct printings. Exact match accepts one. |
+| `arc185_c` | multiple-solutions | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `arc188_c` | multiple-solutions | this-work | any valid confused set; 250/250 (170 valid, 80 correct -1) |
+| `arc189_a` | erroneous-tests | livecodebench | documented in LiveCodeBench's own ERRATA.md |
+| `arc190_a` | multiple-solutions | this-work | any minimum-cost operation list is accepted; ours is a valid optimum on 43 of 44 hidden tests but byte-identical on only 13. Test 14 is also wrong: it contains the interval [1,10] with N=10, so the minimum cost is 1 not 2. |
+| `arc191_c` | multiple-solutions | this-work | (A,M) with multiplicative order N; 59/59 verified |
+| `arc192_b` | erroneous-tests | this-work | 1 of 43 hidden tests is wrong: test 20 (N=10, A=[7,16,3,3,9,8,16,12,8,3]) expects Snuke but the true answer is Fennec. Exhaustive game search agrees with the expected output on all 25 other searchable tests. |
+| `arc195_c` | multiple-solutions | this-work | asks for any valid cyclic placement. Our construction is valid on every case checked and its Yes/No agrees with exhaustive search for R+B <= 5, yet it fails all 5 hidden tests because it prints a different valid placement. |
+
+`livecodebench` entries are the ones LiveCodeBench documents in its own `ERRATA.md`, which the
+code never reads, so every downstream consumer inherits them. `this-work` entries were found
+here by running a verified reference against the official tests.
+
+Solutions are still shipped for excluded problems so the set is complete, except `arc183_d`,
+which has none. Their `verification` says how far each was checked. The two interactive
+problems keep a solution only for completeness; nothing can validate it offline.
+
+## Feeding stdin
+
+Append a trailing newline to each test input if it lacks one, as the vendored Multi-LCB
+executor does. Without it, OCaml `Scanf` formats ending in a newline raise `End_of_file` on the
+last line and correct programs look broken.
+
+## Provenance
+
+| provenance | model | solutions |
+|---|---|---|
+| model-sample | qwen3-8b-think | 239 |
+| agent | sonnet | 153 |
+| agent | opus | 17 |
+| model-sample | qwen3-14b-think | 17 |
+| agent | fable | 4 |
+| model-sample | qwen3-14b-nothink | 3 |
+| model-sample | llama31-8b-instruct-nothink | 1 |
+| model-sample | qwen3-8b-nothink | 1 |
+
+Solutions were produced by language models and then verified, not written by hand. The
+`origin_model` column records which model produced each one.

errata/data.parquet

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references/data.parquet

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