Binary Matrix

[zafstojano]

What does this PR do?

This PR introduces a procedural environment for the 01 Matrix problem. Given an n x n binary matrix, the task is to return the distance of the nearest 0 for each cell. The distance between two cells sharing a common edge is 1.

In order to ensure there exists a solution, I always prepend the generated binary matrix with a 0.

The solution is a level-order BFS traversal starting from the destination (the 0's).

Example

import reasoning_gym 


dataset = reasoning_gym.create_dataset("binary_matrix", size=5, seed=42, max_n=10, p_zero=0.2)

for i, item in enumerate(dataset):
    print(f"Sample {i+1}:")
    print(f"Question: {item['question']}")
    print(f"Answer:\n{item['answer']}\n")
    print(f"Metadata: {item['metadata']}\n")
    print("--------------------------------------------------\n")

Sample 1:
Question: 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:
0 0
1 1

Answer:
0 0
1 1

Metadata: {'matrix': [[0, 0], [1, 1]], 'solution': [[0, 0], [1, 1]]}

--------------------------------------------------

Sample 2:
Question: 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:
0

Answer:
0

Metadata: {'matrix': [[0]], 'solution': [[0]]}

--------------------------------------------------

Sample 3:
Question: 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:
0 1 1 0 1 1 1
1 0 1 1 1 1 1
1 1 1 1 1 0 1
1 1 1 1 1 1 1
0 1 0 0 1 1 0
1 1 1 1 1 1 1
1 1 1 1 0 1 1

Answer:
0 1 1 0 1 2 3
1 0 1 1 2 1 2
2 1 2 2 1 0 1
1 2 1 1 2 1 1
0 1 0 0 1 1 0
1 2 1 1 1 2 1
2 3 2 1 0 1 2

Metadata: {'matrix': [[0, 1, 1, 0, 1, 1, 1], [1, 0, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 0, 1], [1, 1, 1, 1, 1, 1, 1], [0, 1, 0, 0, 1, 1, 0], [1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 0, 1, 1]], 'solution': [[0, 1, 1, 0, 1, 2, 3], [1, 0, 1, 1, 2, 1, 2], [2, 1, 2, 2, 1, 0, 1], [1, 2, 1, 1, 2, 1, 1], [0, 1, 0, 0, 1, 1, 0], [1, 2, 1, 1, 1, 2, 1], [2, 3, 2, 1, 0, 1, 2]]}

--------------------------------------------------

Sample 4:
Question: 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:
0 1 1 1 0
1 0 1 1 1
1 1 0 1 1
0 1 1 1 1
0 0 0 1 1

Answer:
0 1 2 1 0
1 0 1 2 1
1 1 0 1 2
0 1 1 2 3
0 0 0 1 2

Metadata: {'matrix': [[0, 1, 1, 1, 0], [1, 0, 1, 1, 1], [1, 1, 0, 1, 1], [0, 1, 1, 1, 1], [0, 0, 0, 1, 1]], 'solution': [[0, 1, 2, 1, 0], [1, 0, 1, 2, 1], [1, 1, 0, 1, 2], [0, 1, 1, 2, 3], [0, 0, 0, 1, 2]]}

--------------------------------------------------

Sample 5:
Question: 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:
0 1
1 1

Answer:
0 1
1 2

Metadata: {'matrix': [[0, 1], [1, 1]], 'solution': [[0, 1], [1, 2]]}

--------------------------------------------------

[andreaskoepf]

Thanks! I will later add that distance here means "Manhattan or taxicab distance".