binary matrix

reasoning_gym/algorithmic/binary_matrix.py

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+"""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 copy import deepcopy
+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 distance of the nearest 0 for each cell.
+
+Example:
+
+Input: Rotate the matrix below by 90 degrees clockwise:
+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 = 0.7  # 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)]
+        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)