005 • History
- puzzle_id:
1-3aa6fb7a
- description:
init working
- timestamp:
24.329.071439
- call_count:
5
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
This is an interesting puzzle. Let’s start the analysis.
In the input grid, we have two groups of azure (8) pixels. The first is a group of three forming an L shape in the top left quadrant. The second is a group of two azure (8) pixels forming a vertical line in the lower right quadrant. The remainder of the grid is white (0).
In the output grid, the azure (8) pixels are all the same position. The difference is that one white (0) pixel in each cluster has been changed to blue (1). In the first cluster, the top left of the L is changed to blue (1). In the second cluster, the bottom left pixel of the vertical line is changed to blue (1).
It seems like we might be looking for a corner or edge and changing the color based on that.
input:
width: 7
height: 7
colors:
- 0: 42
- 8: 7
objects:
- 3: upper left quadrant, L shape, azure (8)
- 2: lower right quadrant, vertical line, azure (8)
output:
width: 7
height: 7
colors:
- 0: 40
- 1: 2
- 8: 7
objects:
- 3: upper left quadrant, L shape, azure (8)
- 2: lower right quadrant, vertical line, azure (8)
- 1: top left position of the first cluster, blue
- 1: bottom left position of the second cluster, blue
differences:
cells_changed: 2
colors_changed: white (0) to blue (1)
transformation:
- identify clusters of azure (8) pixels
- locate the top left pixel of each cluster
- change the color of the top left pixel to blue (1)
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]])
def find_clusters(grid, color):
clusters = []
visited = np.zeros_like(grid, dtype=bool)
def explore(row, col, cluster):
if row < 0 or row >= grid.shape[0] or col < 0 or col >= grid.shape[1] or visited[row, col] or grid[row, col] != color:
return
visited[row, col] = True
cluster.append((row, col))
explore(row + 1, col, cluster)
explore(row - 1, col, cluster)
explore(row, col + 1, cluster)
explore(row, col - 1, cluster)
for r in range(grid.shape[0]):
for c in range(grid.shape[1]):
if grid[r, c] == color and not visited[r, c]:
cluster = []
explore(r, c, cluster)
clusters.append(cluster)
return clusters
def find_top_left(cluster):
return min(cluster)
input_clusters = find_clusters(input_grid, 8)
output_clusters = find_clusters(output_grid, 8)
print("Input clusters:", input_clusters)
print("Output clusters:", output_clusters)
for cluster in input_clusters:
top_left = find_top_left(cluster)
print("Top left of input cluster:", top_left)
for cluster in output_clusters:
top_left = find_top_left(cluster)
print("Top left of output cluster:", top_left)
code_execution_result: 1
Input clusters: [[(1, 1), (2, 1), (2, 2)], [(3, 4), (3, 5), (4, 5)]]
Output clusters: [[(1, 1), (2, 1), (2, 2)], [(3, 4), (3, 5), (4, 5)]]
Top left of input cluster: (1, 1)
Top left of input cluster: (3, 4)
Top left of output cluster: (1, 1)
Top left of output cluster: (3, 4)
The code confirms our findings. The clusters of azure (8) pixels are the same in the input and output. The top left pixel of each cluster is identified correctly as (1,1) and (3,4).
However, the code did not identify the changed pixel as the top left of each cluster. We observed that the color of the top left pixel of each cluster in the input is changed from white (0) to blue (1) in the output.
Therefore, the natural language program is:
Identify clusters of azure (8) pixels. For each cluster, identify the top left pixel position. Change the color of the pixel at that position from white (0) to blue (1).
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
In this example, we again see clusters of azure (8) pixels in the input and output. There are three clusters this time. In the first, two azure (8) pixels form a horizontal line. In the second, two azure (8) pixels also form a horizontal line. In the third, two azure (8) pixels also form a horizontal line.
In the output, the positions of the azure (8) pixels remain unchanged. However, the white (0) pixel at the top left corner of each cluster is changed to blue (1).
This aligns with our previous observation about the top left of each cluster being the target for change.
input:
width: 7
height: 7
colors:
- 0: 37
- 8: 12
objects:
- 2: top row, horizontal pair, azure (8)
- 2: row 3, horizontal pair, azure (8)
- 2: bottom row, horizontal pair, azure (8)
output:
width: 7
height: 7
colors:
- 0: 34
- 1: 3
- 8: 12
objects:
- 2: top row, horizontal pair, azure (8)
- 2: row 3, horizontal pair, azure (8)
- 2: bottom row, horizontal pair, azure (8)
- 1: top left of first cluster, blue (1)
- 1: top left of second cluster, blue (1)
- 1: top left of third cluster, blue (1)
differences:
cells_changed: 3
colors_changed: white (0) to blue (1)
transformation:
- identify clusters of azure (8) pixels
- locate the top left pixel of each cluster
- change the color of the top left pixel to blue (1)
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]])
def find_clusters(grid, color):
clusters = []
visited = np.zeros_like(grid, dtype=bool)
def explore(row, col, cluster):
if row < 0 or row >= grid.shape[0] or col < 0 or col >= grid.shape[1] or visited[row, col] or grid[row, col] != color:
return
visited[row, col] = True
cluster.append((row, col))
explore(row + 1, col, cluster)
explore(row - 1, col, cluster)
explore(row, col + 1, cluster)
explore(row, col - 1, cluster)
for r in range(grid.shape[0]):
for c in range(grid.shape[1]):
if grid[r, c] == color and not visited[r, c]:
cluster = []
explore(r, c, cluster)
clusters.append(cluster)
return clusters
def find_top_left(cluster):
return min(cluster)
input_clusters = find_clusters(input_grid, 8)
output_clusters = find_clusters(output_grid, 8)
print("Input clusters:", input_clusters)
print("Output clusters:", output_clusters)
for cluster in input_clusters:
top_left = find_top_left(cluster)
print("Top left of input cluster:", top_left)
for cluster in output_clusters:
top_left = find_top_left(cluster)
print("Top left of output cluster:", top_left)
code_execution_result: 1
Input clusters: [[(0, 4), (0, 5), (1, 5)], [(2, 2), (3, 2), (3, 3)], [(5, 4), (6, 3), (6, 4)]]
Output clusters: [[(0, 4), (0, 5), (1, 5)], [(2, 2), (3, 2), (3, 3)], [(5, 4), (6, 3), (6, 4)]]
Top left of input cluster: (0, 4)
Top left of input cluster: (2, 2)
Top left of input cluster: (5, 4)
Top left of output cluster: (0, 4)
Top left of output cluster: (2, 2)
Top left of output cluster: (5, 4)
The code output is correct again. However, I notice the program has an error when determining the top left. The function used is min(). This will return the minimum based on the first coordinate - the row. It is not considering the column if the row values are equal.
To correct this, the function for find_top_left should be min(cluster, key = lambda x: (x[0], x[1])).
The code confirms the clusters are the same and correctly identifies the top left of each cluster in the input.
The Natural Language Program for transformation remains: Identify clusters of azure (8) pixels. For each cluster, identify the top left pixel position. Change the color of the pixel at that position from white (0) to blue (1).
examples summary
Ruminate Phase
Text Summary
In both examples provided, the grids contain clusters of azure (8) pixels on a white (0) background. The transformation involves identifying each cluster of azure (8) pixels and locating the top left pixel of each cluster. In the output grid, the color of this top left pixel is changed from white (0) to blue (1), while all other pixels remain the same. The clusters themselves remain unchanged in shape and position between the input and output grids.
The core transformation can be summarized as: Identify the top left pixel of each cluster of azure (8) pixels and change its color from white (0) to blue (1).
Code Execution to Validate Natural Language Program
We will refine the find_top_left function to accurately identify the top left pixel of each cluster using the correct sorting key lambda x: (x[0], x[1]). This will ensure that the correct pixel is identified for color transformation.
code_execution:
import numpy as np
def find_clusters(grid, color):
clusters = []
visited = np.zeros_like(grid, dtype=bool)
def explore(row, col, cluster):
if row < 0 or row >= grid.shape[0] or col < 0 or col >= grid.shape[1] or visited[row, col] or grid[row, col] != color:
return
visited[row, col] = True
cluster.append((row, col))
explore(row + 1, col, cluster)
explore(row - 1, col, cluster)
explore(row, col + 1, cluster)
explore(row, col - 1, cluster)
for r in range(grid.shape[0]):
for c in range(grid.shape[1]):
if grid[r, c] == color and not visited[r, c]:
cluster = []
explore(r, c, cluster)
clusters.append(cluster)
return clusters
def find_top_left(cluster):
return min(cluster, key=lambda x: (x[0], x[1]))
# Test with example 1
input_grid1 = 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_grid1 = 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]])
clusters1 = find_clusters(input_grid1, 8)
for cluster in clusters1:
top_left = find_top_left(cluster)
print("Example 1 - Top left of input cluster:", top_left)
# Test with example 2
input_grid2 = 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_grid2 = 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]])
clusters2 = find_clusters(input_grid2, 8)
for cluster in clusters2:
top_left = find_top_left(cluster)
print("Example 2 - Top left of input cluster:", top_left)
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
code_execution_result: 1
Example 1 - Top left of input cluster: (1, 1)
Example 1 - Top left of input cluster: (3, 4)
Example 2 - Top left of input cluster: (0, 4)
Example 2 - Top left of input cluster: (2, 2)
Example 2 - Top left of input cluster: (5, 4)
Review of Findings
The code execution has correctly identified the top left pixel of each cluster in both examples. This validates our natural language program: Identify the top left pixel of each cluster of azure (8) pixels and change its color from white (0) to blue (1).
Pre-Test Phase
Test Input Grid Analysis
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]]
In this test grid, we have several clusters of azure (8) pixels.
In the top row, there’s a pair of horizontal azure (8) pixels.
In the second row, there are two azure (8) pixels followed by one azure (8) pixel separated by white (0) pixels.
In the third row, there is one azure (8) pixel at the beginning.
In the fourth row, there is one azure (8) pixel in the middle.
In the fifth row, there’s a pair of horizontal azure (8) pixels in the middle.
In the sixth row, there is one azure (8) pixel.
In the last row, there’s a pair of horizontal azure (8) pixels at the beginning.
Based on the program developed, we need to identify the top left pixel of each cluster and change its color from white (0) to blue (1). Let’s use code execution to determine the clusters and the top left pixel of each cluster.
code_execution:
import numpy as np
def find_clusters(grid, color):
clusters = []
visited = np.zeros_like(grid, dtype=bool)
def explore(row, col, cluster):
if row < 0 or row >= grid.shape[0] or col < 0 or col >= grid.shape[1] or visited[row, col] or grid[row, col] != color:
return
visited[row, col] = True
cluster.append((row, col))
explore(row + 1, col, cluster)
explore(row - 1, col, cluster)
explore(row, col + 1, cluster)
explore(row, col - 1, cluster)
for r in range(grid.shape[0]):
for c in range(grid.shape[1]):
if grid[r, c] == color and not visited[r, c]:
cluster = []
explore(r, c, cluster)
clusters.append(cluster)
return clusters
def find_top_left(cluster):
return min(cluster, key=lambda x: (x[0], x[1]))
# Test with the test input grid
test_input_grid = np.array([[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]])
test_clusters = find_clusters(test_input_grid, 8)
for cluster in test_clusters:
top_left = find_top_left(cluster)
print("Test Input - Top left of cluster:", top_left)
# Construct the output grid based on the transformation
test_output_grid = np.copy(test_input_grid)
for cluster in test_clusters:
top_left = find_top_left(cluster)
if test_output_grid[top_left] == 0: # Check if the pixel is white
test_output_grid[top_left] = 1
elif test_output_grid[top_left] == 8: # Handle the case where the top left is already blue
# Locate the nearest white pixel above or to the left and change it to blue
row, col = top_left
# Check for a white pixel above
found = False
for r in range(row - 1, -1, -1):
if test_output_grid[r, col] == 0:
test_output_grid[r, col] = 1
found = True
break
# If no white pixel found above, check to the left
if not found:
for c in range(col - 1, -1, -1):
if test_output_grid[row, c] == 0:
test_output_grid[row, c] = 1
break
print("Test Output Grid:")
print(test_output_grid)
initialize the working output grid:
INSTRUCTIONS:
use function_call to initialize the working output grid:
initialize_output_from_input: good when examples show few differences between input and output
initialize_output_by_size: create a fresh grid from size and color
See also