reasoning-gym/reasoning_gym/algorithmic/binary_matrix.py
2025-02-09 20:05:56 +01:00

125 lines
3.9 KiB
Python

"""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 Optional
from ..factory import ProceduralDataset, register_dataset
QUESTION_TEMPLATE = """Given a square matrix, your job is to find the taxicab distance of the nearest 0 for each cell.
Example:
Input: Find the distance to the nearest 0 for each cell in the matrix below:
0 0 0
0 1 0
1 1 1
Output:
0 0 0
0 1 0
1 2 1
Find the distance to the nearest 0 for each cell in the matrix below:
{matrix}
"""
@dataclass
class BinaryMatrixConfig:
"""Configuration for Binary Matrix dataset generation"""
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.max_n, "max_n must be at least 1"
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) -> list[list[int]]:
"""Generate a random binary matrix"""
n = rng.randint(1, self.config.max_n)
# 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 __getitem__(self, idx: int) -> dict:
"""Generate a single Binary Matrix question"""
rng = Random(self.seed + idx)
matrix = self._get_binary_matrix(rng)
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},
}
register_dataset("binary_matrix", BinaryMatrixDataset, BinaryMatrixConfig)