---
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

OCaml reference solutions for the multilingual-LiveCodeBench OCaml problem set, together
with the list of problems the harness cannot score.

- **436** problems in the universe
- **415** are scoreable, and each has a verified reference
- **21** are excluded as unscoreable (see the `errata` config)


## Configs

`references` is one row per problem. `errata` lists the problems the harness cannot score,
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` | from LiveCodeBench's errata list, not independently checked | 8 |

The `float-tolerance` rows are correct solutions. Those problems accept an absolute or
relative error of 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 documented in LiveCodeBench's own `ERRATA.md`. The harness does
not read that file, so these reach every consumer of the dataset. `this-work` entries were
established here by grading a verified reference against the official tests.

Excluded problems still carry a solution, apart from `arc183_d`. The `verification` column
records how far each was checked. For the two interactive problems the solution is included
for completeness and can only be checked against a live judge.

## Feeding stdin

Append a trailing newline to each test input if it lacks one, as the vendored Multi-LCB
executor does. Otherwise OCaml `Scanf` formats ending in a newline raise `End_of_file` on the
last line and a correct program fails every test.

## 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. The `origin_model` column
records which model produced each one.