reasoning-gym/reasoning_gym/algorithmic/binary_matrix.py

"""Find the distance to the nearest 0 for each cell in a binary matrix.

A popular Leetcode problem:
https://leetcode.com/problems/01-matrix/description/
"""

from collections import deque
from dataclasses import dataclass
from random import Random
from typing import Any, Optional

from ..coaching import AttributeType, BaseCurriculum, RangeAttributeDefinition, ScalarAttributeDefinition
from ..factory import ProceduralDataset, register_dataset

QUESTION_TEMPLATE = """Given a square matrix, your job is to find the taxicab (Manhattan) distance of the nearest 0 for each cell.

The output should be a matrix of the same size as the input matrix, where each cell contains the distance to the nearest 0.

Find the distance to the nearest 0 for each cell in the matrix below:
{matrix}
"""


@dataclass
class BinaryMatrixConfig:
    """Configuration for Binary Matrix dataset generation"""

    min_n: int = 3  # Minimum size of the matrix
    max_n: int = 10  # Maximum size of the matrix
    p_zero: float = 0.25  # Probability of a cell being 0

    size: int = 500  # Virtual dataset size
    seed: Optional[int] = None

    def validate(self):
        """Validate configuration parameters"""
        assert 1 <= self.min_n, "min_n must be at least 1"
        assert self.min_n <= self.max_n, "min_n must be less than or equal to max_n"
        assert 0 < self.p_zero <= 1, "p_zero must be between 0 and 1"


class BinaryMatrixDataset(ProceduralDataset):
    """Generates Binary Matrix exercises with configurable difficulty"""

    def __init__(self, config: BinaryMatrixConfig):
        super().__init__(config=config, seed=config.seed, size=config.size)

    def _get_binary_matrix(self, rng: Random, n: int) -> list[list[int]]:
        """Generate a random binary matrix"""
        # Ensure at least one 0 in the matrix, so that a solution exists
        numbers = [0] + [0 if rng.random() < self.config.p_zero else 1 for _ in range(n**2 - 1)]
        rng.shuffle(numbers)
        matrix = [numbers[i * n : (i + 1) * n] for i in range(n)]
        return matrix

    def _get_distances(self, matrix: list[list[int]]) -> list[list[int]]:
        """Get the distance to the nearest 0 for each cell in the matrix"""
        n = len(matrix)
        directions = [[1, 0], [-1, 0], [0, 1], [0, -1]]
        visited = set()
        queue = deque()

        output = [[float("inf")] * n for _ in range(n)]

        for r in range(n):
            for c in range(n):
                if matrix[r][c] == 0:
                    output[r][c] = 0
                    visited.add((r, c))
                    queue.append((r, c))

        clock = 1
        while True:
            temp = deque()
            while queue:
                r, c = queue.popleft()
                for dr, dc in directions:
                    new_r, new_c = r + dr, c + dc
                    if (
                        0 <= new_r < n
                        and 0 <= new_c < n
                        and (new_r, new_c) not in visited
                        and matrix[new_r][new_c] == 1
                    ):
                        output[new_r][new_c] = clock
                        visited.add((new_r, new_c))
                        temp.append((new_r, new_c))
            if temp:
                queue = temp
            else:
                break
            clock += 1

        return output

    def _matrix_to_str(self, matrix: list[list[int]]) -> str:
        """Get a string representation of the matrix"""
        return "\n".join(" ".join(str(x) for x in row) for row in matrix)

    def score_answer(self, answer: Optional[str], entry: dict[str, Any]) -> float:
        """Overwrite this method in derived classes if a single oracle answer is not available."""
        oracle_answer = entry["answer"]
        if answer is not None:
            if answer == oracle_answer:
                return 1.0
            else:
                try:
                    # check if answer is python list of lists
                    answer = self._matrix_to_str(eval(answer))
                    if answer == oracle_answer:
                        return 0.1
                except Exception:
                    return 0.0
        return 0.0

    def __getitem__(self, idx: int) -> dict:
        """Generate a single Binary Matrix question"""
        rng = Random(self.seed + idx)

        n = rng.randint(self.config.min_n, self.config.max_n)
        matrix = self._get_binary_matrix(rng, n)
        matrix_str = self._matrix_to_str(matrix)

        answer = self._get_distances(matrix)
        answer_str = self._matrix_to_str(answer)

        return {
            "question": QUESTION_TEMPLATE.format(matrix=matrix_str),
            "answer": answer_str,
            "metadata": {
                "matrix": matrix,
                "solution": answer,
                "difficulty": {
                    "n": n,
                    "p_zero": self.config.p_zero,
                },
            },
        }


class BinaryMatrixCurriculum(BaseCurriculum):
    def __init__(self):
        super().__init__(BinaryMatrixCurriculum.__name__, BinaryMatrixConfig)

        self._define_attributes(
            ScalarAttributeDefinition(
                name="p_zero",
                field_name="p_zero",
                levels=[0.5, 0.25, 0.1, 0.05],
                default_level=0,
                description="Board size",
                attr_type=AttributeType.STATIC,
                min_value=0,
            ),
            RangeAttributeDefinition(
                name="n",
                levels=[10, 50, 250, 1000],
                default_level=0,
                description="Board size",
                attr_type=AttributeType.APPEND,
                min_value=1,
                lower_field_name="min_n",
                upper_field_name="max_n",
            ),
        )


register_dataset("binary_matrix", BinaryMatrixDataset, BinaryMatrixConfig, BinaryMatrixCurriculum)