004 • Response
- puzzle_id:
1-3aa6fb7a
- description:
test input
- timestamp:
24.329.064813
- call_count:
4
- model:
models/gemini-1.5-flash-002
Here’s an analysis of the test input grid, incorporating lessons learned from the previous examples and improvements to the natural language program and code.
Test Input Grid Analysis:
The test input grid displays multiple clusters of azure (8) pixels. There are several isolated azure pixels and at least two larger clusters. One cluster is at the top right, and another stretches vertically on the left side. The structure is more complex than the previous examples, with clusters of varying sizes and shapes.
Code Execution (Properties of Test Input):
code_execution:
import numpy as np
from collections import deque
test_input = 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]])
def count_clusters(grid):
rows, cols = grid.shape
visited = np.zeros((rows, cols), dtype=bool)
count = 0
for r in range(rows):
for c in range(cols):
if grid[r, c] == 8 and not visited[r, c]:
count += 1
queue = deque([(r,c)])
visited[r,c] = True
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))
return count
print(f"Shape of test input grid: {test_input.shape}")
print(f"Number of azure pixels: {np.count_nonzero(test_input == 8)}")
print(f"Number of clusters: {count_clusters(test_input)}")
code_execution_result: 1
Shape of test input grid: (7, 7)
Number of azure pixels: 12
Number of clusters: 4
Revised Natural Language Program (v2):
The previous version’s select_pixel function was too simplistic. This version incorporates a more sophisticated approach prioritizing the selection of azure pixels based on their position within a cluster.
Cluster Identification: Identify all clusters of connected azure (8) pixels using a breadth-first search (BFS) as before.
Pixel Selection: For each cluster with more than one pixel:
Calculate the centroid (average x and y coordinates) of the cluster.
For each pixel in the cluster, compute its distance from the centroid.
Prioritize selection based on distance from the centroid, favoring pixels farther from the center.
Among the pixels farthest from the centroid, select the one that is closest to the bottom or left boundary of the grid. If there are multiple, choose one arbitrarily.
Change the selected azure pixel to blue (1).
Single-Pixel Clusters: If a cluster contains only one azure pixel, leave it unchanged.
Code Execution (Validation of v2):
The code below implements the refined natural language program (v2).
code_execution:
import numpy as np
from collections import deque
def transform_grid(grid):
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, grid)
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):
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, grid):
# Calculate centroid
x_coords, y_coords = zip(*cluster)
centroid_x = np.mean(x_coords)
centroid_y = np.mean(y_coords)
# Find distances from centroid
distances = [((x - centroid_x)**2 + (y - centroid_y)**2)**0.5 for x, y in cluster]
max_distance = max(distances)
farthest_pixels = [cluster[i] for i, dist in enumerate(distances) if dist == max_distance]
#Prioritize bottom/left among farthest
best_pixel = None
min_dist_to_border = float('inf')
for pixel in farthest_pixels:
r,c = pixel
dist = min(r,c, grid.shape[0]-1-r, grid.shape[1]-1-c)
if dist < min_dist_to_border:
min_dist_to_border = dist
best_pixel = pixel
return best_pixel
test_input = 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]])
transformed_grid = transform_grid(test_input)
print(f"Transformed Test Grid:\n{transformed_grid}")
code_execution_result: 1
Transformed Test Grid:
[[0 0 0 0 0 1 8]
[8 8 0 0 0 0 8]
[1 0 0 0 0 0 0]
[0 0 0 8 0 0 0]
[0 0 0 8 1 0 0]
[0 1 0 0 0 0 0]
[8 8 0 0 0 0 0]]
The code produces a transformed grid. While the algorithm is more sophisticated, without the correct output for the test puzzle, it’s difficult to definitively assess its accuracy. The approach now prioritizes selecting pixels further from the cluster centroid and closer to the edges, which seems to align better with some observed patterns. Further refinement might still be needed, possibly incorporating additional heuristics based on cluster shape or size, which could help it to achieve higher accuracy. More examples would be very beneficial to further improve the algorithm’s performance.
response time |
total elapsed |
|---|---|
21.52 |
45.938 |
token type |
call count |
total used |
|---|---|---|
Prompt |
6545 |
17403 |
Response |
1869 |
5144 |
Total |
8414 |
22547 |
Cached |
0 |
0 |
See also