004 • History
- puzzle_id:
1-3aa6fb7a
- description:
test input
- timestamp:
24.329.064813
- call_count:
4
Begin puzzle: 1-3aa6fb7a
example_1
input
[[0 0 0 0 0 0 0]
[0 8 0 0 0 0 0]
[0 8 8 0 0 0 0]
[0 0 0 0 8 8 0]
[0 0 0 0 0 8 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]]
output
[[0 0 0 0 0 0 0]
[0 8 1 0 0 0 0]
[0 8 8 0 0 0 0]
[0 0 0 0 8 8 0]
[0 0 0 0 1 8 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]]
images
observations
The input grid shows a cluster of azure (8) pixels. The output grid is identical except one azure pixel has changed to blue (1). The blue pixel is adjacent to, and below, a cluster of azure pixels.
code_execution:
import numpy as np
input_grid = np.array([[0, 0, 0, 0, 0, 0, 0],
[0, 8, 0, 0, 0, 0, 0],
[0, 8, 8, 0, 0, 0, 0],
[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 0, 8, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
output_grid = np.array([[0, 0, 0, 0, 0, 0, 0],
[0, 8, 1, 0, 0, 0, 0],
[0, 8, 8, 0, 0, 0, 0],
[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 1, 8, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
diff = np.where(input_grid != output_grid)
print(f"Differences found at coordinates: {diff}")
print(f"Input grid shape: {input_grid.shape}")
print(f"Number of azure pixels in input: {np.count_nonzero(input_grid == 8)}")
print(f"Number of blue pixels in output: {np.count_nonzero(output_grid == 1)}")
code_execution_result: 1
Differences found at coordinates: (array([1, 4]), array([2, 4]))
Input grid shape: (7, 7)
Number of azure pixels in input: 6
Number of blue pixels in output: 2
input:
width: 7
height: 7
colors:
- 0: 43
- 8: 6
objects:
- size: 6, position: scattered, color: azure
output:
width: 7
height: 7
colors:
- 0: 43
- 8: 4
- 1: 2
objects:
- size: 4, position: scattered, color: azure
- size: 2, position: scattered, color: blue
differences:
cells_changed: 2
colors_changed: Two azure pixels changed to blue. The blue pixels are adjacent to the remaining cluster of azure pixels.
transformation:
- A subset of azure pixels change to blue. Specifically, azure pixels adjacent to other azure pixels are transformed. The transformation might depend on the location and size of the cluster.
Based on the analysis, a possible natural language program for the transformation is: “Identify clusters of azure pixels. Change one azure pixel in each cluster to blue, selecting a pixel adjacent to other azure pixels within the cluster. If there’s only one azure pixel, leave it unchanged.” This needs further validation with more examples.
example_2
input
[[0 0 0 0 8 8 0]
[0 0 0 0 0 8 0]
[0 0 8 0 0 0 0]
[0 0 8 8 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 8 0 0]
[0 0 0 8 8 0 0]]
output
[[0 0 0 0 8 8 0]
[0 0 0 0 1 8 0]
[0 0 8 1 0 0 0]
[0 0 8 8 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 1 8 0 0]
[0 0 0 8 8 0 0]]
images
observations
The input grid for example 2 shows several clusters of azure (8) pixels. The output grid is almost identical, but several azure pixels have been replaced with blue (1) pixels. Each blue pixel appears adjacent to, and below or to the left of, a remaining azure pixel within the same cluster.
code_execution:
import numpy as np
input_grid = np.array([[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 0, 8, 0],
[0, 0, 8, 0, 0, 0, 0],
[0, 0, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 8, 0, 0],
[0, 0, 0, 8, 8, 0, 0]])
output_grid = np.array([[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 1, 8, 0],
[0, 0, 8, 1, 0, 0, 0],
[0, 0, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 8, 0, 0],
[0, 0, 0, 8, 8, 0, 0]])
diff = np.where(input_grid != output_grid)
print(f"Differences found at coordinates: {diff}")
print(f"Input grid shape: {input_grid.shape}")
print(f"Number of azure pixels in input: {np.count_nonzero(input_grid == 8)}}")
print(f"Number of blue pixels in output: {np.count_nonzero(output_grid == 1)}")
code_execution_result:
Differences found at coordinates: (array([1, 2, 5]), array([4, 3, 3]))
Input grid shape: (7, 7)
Number of azure pixels in input: 10
Number of blue pixels in output: 3
input:
width: 7
height: 7
colors:
- 0: 40
- 8: 10
objects:
- size: 10, position: scattered, color: azure
output:
width: 7
height: 7
colors:
- 0: 40
- 8: 7
- 1: 3
objects:
- size: 7, position: scattered, color: azure
- size: 3, position: scattered, color: blue
differences:
cells_changed: 3
colors_changed: Three azure pixels changed to blue. Each blue pixel is below or to the left of a cluster of azure pixels.
transformation:
- Similar to example 1, a subset of azure pixels changes to blue. The transformation seems to target azure pixels that are adjacent to other azure pixels, but the selection is more complex and might be based on the overall cluster's shape.
Based on the two examples, the transformation appears to select a subset of azure pixels within each cluster to change to blue. The selection criteria seem to favor pixels adjacent to other azure pixels, and potentially also considers positional relationships within the cluster (below or to the left). More examples would help refine the natural language program and clarify any ambiguities in the selection process.
examples summary
The transformation consistently involves changing a subset of azure (8) pixels to blue (1) pixels. The changed pixels are always adjacent to other azure pixels, suggesting a rule based on adjacency and cluster proximity. The selection of which adjacent azure pixel to change appears to be somewhat arbitrary, but there’s a tendency to select pixels that are below or to the left of other azure pixels within a cluster. This needs more examples to confirm.
Let’s summarize the observations and develop a natural language program that attempts to capture the transformation:
Natural Language Program (v1):
Identify all clusters of connected azure (8) pixels. Two azure pixels are considered connected if they are adjacent (horizontally or vertically).
For each cluster:
If the cluster contains more than one azure pixel, select one azure pixel within the cluster that is adjacent to at least one other azure pixel. Prioritize selecting a pixel that is located below or to the left of other azure pixels within the cluster (if such a pixel exists).
Change the selected azure pixel to blue (1).
If a cluster contains only one azure pixel, leave it unchanged.
Code Execution (Validation of v1):
The following code implements the natural language program (v1) and attempts to replicate the transformations in the provided examples. It uses a breadth-first search (BFS) to identify connected components (clusters).
code_execution:
import numpy as np
from collections import deque
def transform_grid(grid):
"""Transforms the input grid according to the natural language program."""
rows, cols = grid.shape
visited = np.zeros((rows, cols), dtype=bool)
new_grid = np.copy(grid)
for r in range(rows):
for c in range(cols):
if grid[r, c] == 8 and not visited[r, c]:
cluster = find_cluster(grid, r, c, visited)
if len(cluster) > 1:
pixel_to_change = select_pixel(cluster)
if pixel_to_change:
new_grid[pixel_to_change[0], pixel_to_change[1]] = 1
return new_grid
def find_cluster(grid, r, c, visited):
"""Finds a cluster of connected azure pixels using BFS."""
rows, cols = grid.shape
queue = deque([(r, c)])
visited[r, c] = True
cluster = [(r, c)]
while queue:
row, col = queue.popleft()
for dr, dc in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
nr, nc = row + dr, col + dc
if 0 <= nr < rows and 0 <= nc < cols and grid[nr, nc] == 8 and not visited[nr, nc]:
visited[nr, nc] = True
queue.append((nr, nc))
cluster.append((nr, nc))
return cluster
def select_pixel(cluster):
"""Selects a pixel to change, prioritizing below/left."""
# Simple selection for now - choose the first pixel adjacent to another
for r, c in cluster:
for dr, dc in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
nr, nc = r + dr, c + dc
if (nr, nc) in cluster:
return (r,c) #Could be more sophisticated here
return None
# Test with example 1:
example1_input = np.array([[0, 0, 0, 0, 0, 0, 0],
[0, 8, 0, 0, 0, 0, 0],
[0, 8, 8, 0, 0, 0, 0],
[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 0, 8, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]])
transformed_grid = transform_grid(example1_input)
print(f"Transformed grid for Example 1:\n{transformed_grid}")
# Test with example 2:
example2_input = np.array([[0, 0, 0, 0, 8, 8, 0],
[0, 0, 0, 0, 0, 8, 0],
[0, 0, 8, 0, 0, 0, 0],
[0, 0, 8, 8, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 8, 0, 0],
[0, 0, 0, 8, 8, 0, 0]])
transformed_grid = transform_grid(example2_input)
print(f"Transformed grid for Example 2:\n{transformed_grid}")
code_execution_result: 1
Transformed grid for Example 1:
[[0 0 0 0 0 0 0]
[0 1 0 0 0 0 0]
[0 8 8 0 0 0 0]
[0 0 0 0 1 8 0]
[0 0 0 0 0 8 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]]
Transformed grid for Example 2:
[[0 0 0 0 1 8 0]
[0 0 0 0 0 8 0]
[0 0 1 0 0 0 0]
[0 0 8 8 0 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 1 0 0]
[0 0 0 8 8 0 0]]
The code’s output for Example 1 is different from the provided output. The algorithm’s pixel selection isn’t perfectly aligned with the example. Example 2 also shows some discrepancies. The current select_pixel function is too simplistic. It needs refinement to better capture the selection priority (below/left). More examples are crucial for further improvement. Additional heuristics, potentially based on cluster shape or size, might be needed for a more robust solution.
test
input
[[0 0 0 0 0 8 8]
[8 8 0 0 0 0 8]
[8 0 0 0 0 0 0]
[0 0 0 8 0 0 0]
[0 0 0 8 8 0 0]
[0 8 0 0 0 0 0]
[8 8 0 0 0 0 0]]
image
observations
INSTRUCTIONS:
generate report as per instructions
use code_execution to investigate properties
See also