004 • Response

puzzle_id:: 3-1e0a9b12
description:: example_summary
timestamp:: 24.329.071439
call_count:: 4
model:: models/gemini-exp-1114

Based on the analysis of the three examples, here’s a summary of the observations and the transformation process:

Summary of Observations

In all three examples, the input grids contain various non-zero values scattered across the grid, with most cells being zero (white). The output grids maintain the same dimensions as the input grids. The non-zero values from the input grids are collected and rearranged in the bottom row of the output grids.

The rearrangement process follows a specific pattern:

Start with the last row: The non-zero values from the last row of the input grid are placed first in the last row of the output grid, from left to right.
Move to preceding rows: The non-zero values from the preceding rows are then considered, moving from the bottom row upwards.
Skip occupied columns: If a non-zero value is in a column that is already occupied in the output grid by a value from a lower row, it is skipped.
Place in output: The non-zero values that are not skipped are placed in the bottom row of the output grid in the order they are encountered.
Fill with zeros: The remaining cells in the output grid are filled with zeros (white).

Natural Language Program (Transformation Story)

Identify Non-Zero Cells: Locate all non-zero cells in the input grid.
Rearrange Cells: Rearrange the non-zero cells by starting with the last row of the input grid. Place these cells in the last row of the output grid, from left to right. Then, move to the preceding rows (from bottom to top) and add their non-zero cells to the last row of the output grid, skipping cells if their columns are already occupied.
Construct Output Grid: Place the rearranged non-zero cells in the last row of the output grid, maintaining their order. Fill the remaining cells of the output grid with zeros (white).

Considering Transformation for Testing

Based on the consistent pattern observed in the examples, the following steps should be taken to transform the test input grid:

Identify all non-zero cells in the test input grid.
Rearrange these cells according to the described logic: starting with the last row, then preceding rows, skipping occupied columns.
Place the rearranged cells in the bottom row of the output grid, filling the rest with zeros.

This approach should consistently produce the correct output grid based on the established pattern.

Let’s use code execution to validate and test this transformation story on one of the examples.

Code Execution for Validation

We will use Example 2 for validation:

code_execution:

import numpy as np

def transform_grid(input_grid):
    height, width = input_grid.shape
    output_grid = np.zeros_like(input_grid)

    non_zeros = []
    occupied_cols = set()

    for row in range(height - 1, -1, -1):
        for col in range(width):
            if input_grid[row, col] != 0:
                if col not in occupied_cols:
                    non_zeros.append(input_grid[row, col])
                    occupied_cols.add(col)

    output_grid[-1, :len(non_zeros)] = non_zeros

    return output_grid

input_grid = np.array([[0, 0, 0, 0, 0, 9], [0, 0, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0], [4, 0, 7, 8, 0, 0], [4, 0, 7, 0, 0, 0]])
expected_output = np.array([[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0], [4, 0, 7, 8, 0, 0], [4, 0, 7, 8, 0, 9]])

transformed_output = transform_grid(input_grid)

print("Transformed Output:")
print(transformed_output)
print("Expected Output:")
print(expected_output)
print("Are the outputs the same?", np.array_equal(transformed_output, expected_output))

time
response time	total elapsed
35.371	195.775

usage
token type	call count	total used
Prompt	7390	19872
Response	1036	3973
Total	8426	23845
Cached	0	0