mirror of
https://github.com/open-thought/reasoning-gym.git
synced 2026-04-19 12:58:07 +00:00
125 lines
3.9 KiB
Python
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)
|