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# ARC HINT GENERATOR
## ROLE & GOAL
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your goal is to generate a concise, actionable hint for a user struggling with an ARC problem. You will analyze the problem, the user's incorrect attempt, and the correct solution to produce a single, targeted hint that helps the user discover the core transformation principle on their own without revealing the answer. This hint will be standalone and memoryless (i.e understandable with no information about the user's previous hint and solution).
---
## HINT GENERATION STRATEGY
1. **Identify the Core Principle**: First, analyze the description of the problem and ground-truth solution to fully understand the correct transformation rule. Deconstruct it into its fundamental operations (e.g., object completion, pattern repetition, symmetry, gravity).
2. **Diagnose the User's Error**: Compare the correct logic with the user's attempted solution and current hint. Pinpoint the specific misconception. Did they miss a condition? Misinterpret a shape? Apply the wrong operation?
3. **Craft a Targeted Hint**: Generate a hint tailored to correct the user's specific error identified in the previous step, improving the user's provided hint that lead to the solution, and preserving details from the previous hint that is useful to solve the problem. It should assist the user when they retry the problem.
---
## GUIDELINES
- **Guide, Don't Solve**: Your hint should illuminate the path, not give away the destination. Focus on *what to look for* or *how to think about* the problem.
- **Be Specific but Abstract**: Use concrete details from the grids (e.g., "notice the relationship between the blue and red pixels") to anchor abstract concepts (e.g., "consider one color as a 'container' for another").
- **Understandable in Isolation**: The user will use the new hint to solve the problem again but may not remember the previous hint applied. If there are parts of the current hint, which is still useful or would be helpful to keep around, feel free to incoporate it in the hint that is generated.
- **Match Style of User Hint**: The user will be able to follow the hint better if it is similar to the style of hint they provide.
---
## OUTPUT FORMAT
concepts:
[Key techniques/patterns/operations, comma-separated]
description:
[Include specific details about patterns, directions, colors, or measurements that illustrate the general method].
---
## INPUTS
### Problem Description
**This the full ARC problem, including input/output pairs for training and testing.**
# Task
Provide a program in python that maps an input grid to an output grid, given the examples below.
Your program should be able to take any input grid and output the corresponding output grid.
# Examples
## Example 1
### Input:
```python
[[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 9, 9, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 8, 8, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 2
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 3
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
# Code Format
Format your code as a python program that can be executed to map an input grid to an output grid. The function should be named `map_grid` and take a single argument `grid` which is a 2D list of integers. The function should return a 2D list of integers.
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]: # grid is a 2D list of integers
# Your code here
pass
```
---
### Solution Attempt
**This the grid generated by the user's incorrect solution attempt.**
To solve this problem, we need to map an input grid to an output grid by inverting the colors of the objects while keeping the background (0) unchanged. The key insight is that each non-zero number in the input grid corresponds to a specific color that needs to be mapped to another number based on observed patterns in the provided examples.
### Approach
1. **Problem Analysis**: The problem involves transforming a grid where non-zero numbers represent colored objects. The goal is to map each non-zero number to a complementary number such that the output grid visually inverts the colors of the objects while maintaining the black background (0).
2. **Pattern Recognition**: By analyzing the provided examples, we observe consistent mappings:
- `1` maps to `4`
- `2` maps to `3`
- `3` maps to `2`
- `6` maps to `5`
- `7` maps to `2`
- `8` maps to `9`
- `9` maps to `8`
3. **Implementation**: We create a dictionary to store these mappings. For each cell in the input grid:
- If the cell is `0`, it remains `0`.
- If the cell is a key in the mapping dictionary, it is replaced by the corresponding value.
- Otherwise, the cell remains unchanged (though the examples suggest only the listed numbers appear).
### Solution Code
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]:
mapping = {
1: 4,
2: 3,
3: 2,
6: 5,
7: 2,
8: 9,
9: 8
}
result = []
for row in grid:
new_row = []
for cell in row:
if cell in mapping:
new_row.append(mapping[cell])
else:
new_row.append(cell)
result.append(new_row)
return result
```
### Explanation
1. **Mapping Dictionary**: The dictionary `mapping` defines how each input number (1, 2, 3, 6, 7, 8, 9) should be transformed in the output grid.
2. **Grid Processing**: For each row in the input grid:
- Each cell is checked against the mapping dictionary.
- If the cell's value exists in the dictionary, it is replaced by the corresponding value.
- If not, the cell's value remains unchanged (though the examples ensure only the listed numbers appear).
3. **Output Construction**: The processed rows are collected into a new grid (`result`), which is returned as the output.
This approach efficiently transforms the input grid by applying the predefined mappings, ensuring that the colored objects are inverted while the background remains black (0). The solution handles any input grid by leveraging the consistent mappings observed in the examples.
---
### Current Hint
**This the user's hint corresponding to the incorrect solution attempt.**
concepts:
color inversion, object detection
description:
In the input you will see several colored objects on a black background.
To make the output, invert the colors of the objects (i.e., change each color to its complementary color) while keeping the background black.
---
# GENERATED HINT
|
[{"input": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}]
|
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0, 0, 7, 7, 7, 7, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 9, 9, 6, 6, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 2, 2, 2, 2, 9, 4, 4, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 7, 7, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 6, 7, 7, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 2, 2, 2, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 9, 9, 0], [0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 5, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 3, 3, 3, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 2, 2, 2, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}]
|
barc
|
concepts:
color inversion, object detection
description:
In the input you will see several colored objects on a black background.
To make the output, invert the colors of the objects (i.e., change each color to its complementary color) while keeping the background black.
|
# ARC HINT GENERATOR
## ROLE & GOAL
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your goal is to generate a concise, actionable hint for a user struggling with an ARC problem. You will analyze the problem, the user's incorrect attempt, and the correct solution to produce a single, targeted hint that helps the user discover the core transformation principle on their own without revealing the answer. This hint will be standalone and memoryless (i.e understandable with no information about the user's previous hint and solution).
---
## HINT GENERATION STRATEGY
1. **Identify the Core Principle**: First, analyze the description of the problem and ground-truth solution to fully understand the correct transformation rule. Deconstruct it into its fundamental operations (e.g., object completion, pattern repetition, symmetry, gravity).
2. **Diagnose the User's Error**: Compare the correct logic with the user's attempted solution and current hint. Pinpoint the specific misconception. Did they miss a condition? Misinterpret a shape? Apply the wrong operation?
3. **Craft a Targeted Hint**: Generate a hint tailored to correct the user's specific error identified in the previous step, improving the user's provided hint that lead to the solution, and preserving details from the previous hint that is useful to solve the problem. It should assist the user when they retry the problem.
---
## GUIDELINES
- **Guide, Don't Solve**: Your hint should illuminate the path, not give away the destination. Focus on *what to look for* or *how to think about* the problem.
- **Be Specific but Abstract**: Use concrete details from the grids (e.g., "notice the relationship between the blue and red pixels") to anchor abstract concepts (e.g., "consider one color as a 'container' for another").
- **Understandable in Isolation**: The user will use the new hint to solve the problem again but may not remember the previous hint applied. If there are parts of the current hint, which is still useful or would be helpful to keep around, feel free to incoporate it in the hint that is generated.
- **Match Style of User Hint**: The user will be able to follow the hint better if it is similar to the style of hint they provide.
---
## OUTPUT FORMAT
concepts:
[Key techniques/patterns/operations, comma-separated]
description:
[Include specific details about patterns, directions, colors, or measurements that illustrate the general method].
---
## INPUTS
### Problem Description
**This the full ARC problem, including input/output pairs for training and testing.**
# Task
Provide a program in python that maps an input grid to an output grid, given the examples below.
Your program should be able to take any input grid and output the corresponding output grid.
# Examples
## Example 1
### Input:
```python
[[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 9, 9, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 8, 8, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 2
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 3
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
# Code Format
Format your code as a python program that can be executed to map an input grid to an output grid. The function should be named `map_grid` and take a single argument `grid` which is a 2D list of integers. The function should return a 2D list of integers.
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]: # grid is a 2D list of integers
# Your code here
pass
```
---
### Solution Attempt
**This the grid generated by the user's incorrect solution attempt.**
To solve this problem, we need to map each non-zero number in the input grid to a specific target number based on predefined rules. The key insight is to identify the consistent mapping of each input number to its corresponding output number from the provided examples.
### Approach
1. **Identify Mappings**: By analyzing the given examples, we determine that each non-zero number in the input grid maps to a specific number in the output grid. For instance:
- Input `1` maps to `4`
- Input `2` maps to `3`
- Input `3` maps to `2`
- Input `6` maps to `5`
- Input `7` maps to `2`
- Input `8` maps to `9`
- Input `9` maps to `8`
2. **Handle Background**: The number `0` represents the background and remains unchanged in the output grid.
3. **Apply Mappings**: For each cell in the input grid, if the cell value is a key in the predefined mapping dictionary, replace it with the corresponding mapped value; otherwise, retain the original value (which is `0`).
### Solution Code
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]:
mapping = {
1: 4,
2: 3,
3: 2,
6: 5,
7: 2,
8: 9,
9: 8
}
output = []
for row in grid:
new_row = [mapping.get(cell, cell) for cell in row]
output.append(new_row)
return output
```
### Explanation
1. **Mapping Dictionary**: The dictionary `mapping` defines how each input number (1, 2, 3, 6, 7, 8, 9) should be transformed into the corresponding output number (4, 3, 2, 5, 2, 9, 8 respectively).
2. **Processing Each Cell**: For each row in the input grid, we create a new row where each cell is replaced by its mapped value if it exists in the dictionary; otherwise, the cell remains unchanged (i.e., `0`).
3. **Output Construction**: The processed rows are collected into a new grid (list of lists) which is returned as the output.
This approach efficiently applies the identified mappings to transform the input grid into the desired output grid while preserving the background (`0`) values. The solution is optimal with a time complexity of O(n*m), where n and m are the dimensions of the grid, as it processes each cell exactly once.
---
### Current Hint
**This the user's hint corresponding to the incorrect solution attempt.**
concepts:
color mapping, object detection
description:
In the input, you will see several colored objects on a black background.
To create the output, change each object's color to a specific color based on its original color.
The mapping is as follows:
red -> green, blue -> yellow, pink -> gray, teal -> maroon, orange -> red, green -> red.
---
# GENERATED HINT
|
[{"input": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}]
|
[{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 3, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 3, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 3, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}]
|
barc
|
concepts:
color mapping, object detection
description:
In the input, you will see several colored objects on a black background.
To create the output, change each object's color to a specific color based on its original color.
The mapping is as follows:
red -> green, blue -> yellow, pink -> gray, teal -> maroon, orange -> red, green -> red.
|
# ARC HINT GENERATOR
## ROLE & GOAL
You are an expert ARC (Abstraction and Reasoning Corpus) analyst. Your goal is to generate a concise, actionable hint for a user struggling with an ARC problem. You will analyze the problem, the user's incorrect attempt, and the correct solution to produce a single, targeted hint that helps the user discover the core transformation principle on their own without revealing the answer. This hint will be standalone and memoryless (i.e understandable with no information about the user's previous hint and solution).
---
## HINT GENERATION STRATEGY
1. **Identify the Core Principle**: First, analyze the description of the problem and ground-truth solution to fully understand the correct transformation rule. Deconstruct it into its fundamental operations (e.g., object completion, pattern repetition, symmetry, gravity).
2. **Diagnose the User's Error**: Compare the correct logic with the user's attempted solution and current hint. Pinpoint the specific misconception. Did they miss a condition? Misinterpret a shape? Apply the wrong operation?
3. **Craft a Targeted Hint**: Generate a hint tailored to correct the user's specific error identified in the previous step, improving the user's provided hint that lead to the solution, and preserving details from the previous hint that is useful to solve the problem. It should assist the user when they retry the problem.
---
## GUIDELINES
- **Guide, Don't Solve**: Your hint should illuminate the path, not give away the destination. Focus on *what to look for* or *how to think about* the problem.
- **Be Specific but Abstract**: Use concrete details from the grids (e.g., "notice the relationship between the blue and red pixels") to anchor abstract concepts (e.g., "consider one color as a 'container' for another").
- **Understandable in Isolation**: The user will use the new hint to solve the problem again but may not remember the previous hint applied. If there are parts of the current hint, which is still useful or would be helpful to keep around, feel free to incoporate it in the hint that is generated.
- **Match Style of User Hint**: The user will be able to follow the hint better if it is similar to the style of hint they provide.
---
## OUTPUT FORMAT
concepts:
[Key techniques/patterns/operations, comma-separated]
description:
[Include specific details about patterns, directions, colors, or measurements that illustrate the general method].
---
## INPUTS
### Problem Description
**This the full ARC problem, including input/output pairs for training and testing.**
# Task
Provide a program in python that maps an input grid to an output grid, given the examples below.
Your program should be able to take any input grid and output the corresponding output grid.
# Examples
## Example 1
### Input:
```python
[[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 9, 9, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 8, 8, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 5, 5, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 2
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
## Example 3
### Input:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[2, 2, 2, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
### Output:
```python
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[3, 3, 3, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
```
# Code Format
Format your code as a python program that can be executed to map an input grid to an output grid. The function should be named `map_grid` and take a single argument `grid` which is a 2D list of integers. The function should return a 2D list of integers.
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]: # grid is a 2D list of integers
# Your code here
pass
```
---
### Solution Attempt
**This the grid generated by the user's incorrect solution attempt.**
To solve this problem, we need to map an input grid to an output grid by transforming each non-zero number in the input grid according to a specific color inversion rule. The key observation from the provided examples is that each non-zero number in the input grid is mapped to a unique number in the output grid following a consistent pattern.
### Approach
1. **Problem Analysis**: The problem requires transforming each non-zero number in the input grid to a corresponding number in the output grid. The examples show that specific numbers (1, 2, 3, 6, 7, 8, 9) are mapped to other numbers (4, 3, 2, 5, 2, 9, 8) respectively, while zeros remain unchanged.
2. **Insight**: By analyzing the examples, we can derive a fixed mapping for each number:
- `0` maps to `0`
- `1` maps to `4`
- `2` maps to `3`
- `3` maps to `2`
- `6` maps to `5`
- `7` maps to `2`
- `8` maps to `9`
- `9` maps to `8`
3. **Algorithm Selection**: The solution involves creating a dictionary that defines the mapping for each relevant number. For each cell in the input grid, we replace its value with the corresponding value from the dictionary. This ensures that the output grid adheres to the color inversion rule observed in the examples.
### Solution Code
```python
def map_grid(grid: list[list[int]]) -> list[list[int]]:
mapping = {
0: 0,
1: 4,
2: 3,
3: 2,
6: 5,
7: 2,
8: 9,
9: 8
}
return [[mapping[cell] for cell in row] for row in grid]
```
### Explanation
1. **Mapping Dictionary**: The dictionary `mapping` is defined to specify how each non-zero number in the input grid should be transformed. For instance:
- Input `1` becomes `4`
- Input `2` becomes `3`
- Input `3` becomes `2`
- Input `6` becomes `5`
- Input `7` becomes `2`
- Input `8` becomes `9`
- Input `9` becomes `8`
- Input `0` remains `0`
2. **Grid Transformation**: The function processes each row of the input grid. For each cell in the row, it looks up the corresponding value in the `mapping` dictionary and constructs a new row. This process is repeated for all rows to form the output grid.
3. **Efficiency**: The solution efficiently transforms each cell in the grid in linear time relative to the grid size (O(n*m) for an n x m grid), making it optimal for the given problem constraints.
This approach ensures that the output grid correctly applies the color inversion rule observed in the examples, transforming each non-zero number to its corresponding value while leaving zeros unchanged. The solution is both concise and effective for any input grid that adheres to the observed number patterns.
---
### Current Hint
**This the user's hint corresponding to the incorrect solution attempt.**
concepts:
color inversion, shape detection
description:
In the input you will see a grid with several colored shapes.
To make the output, invert the color of each shape (change red to green, blue to yellow, etc.).
---
# GENERATED HINT
|
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0, 0, 7, 7, 7, 7, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 9, 9, 6, 6, 0, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 2, 2, 2, 2, 9, 4, 4, 0, 0], [0, 0, 0, 0, 8, 8, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 7, 7, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 6, 7, 7, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 6, 6, 6, 2, 2, 2, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 9, 9, 0], [0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 1, 1, 1, 1, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 5, 2, 2, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0], [0, 5, 5, 5, 3, 3, 3, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0], [0, 0, 0, 0, 2, 2, 2, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 4, 4, 4, 4, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 5, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 5, 5, 5, 0, 0, 0, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 9, 9, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 3, 3, 3, 3, 0, 0], [0, 0, 0, 4, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 2, 2, 2, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 6, 6, 6, 0, 0, 0, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 8, 8, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 2, 2, 2, 2, 0, 0], [0, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 3, 3, 3, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}, {"input": [[0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 9, 9, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "output": [[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}]
|
barc
|
concepts:
color inversion, shape detection
description:
In the input you will see a grid with several colored shapes.
To make the output, invert the color of each shape (change red to green, blue to yellow, etc.).
|
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor inversion, shape detection\n\ndescription:\nIn the input, you will see a grid with(...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\nobject detection, color transformation, bounding box\n\ndescription:\nIn the input you w(...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor transformation, object detection\n\ndescription:\nIn the input, you will see a gri(...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor mapping, object detection, counting\n\ndescription:\nThe input consists of a grid (...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor inversion, object detection\n\ndescription:\nIn the input, you will see a grid wit(...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor transformation, object detection\n\ndescription:\nIn the input, you will see a gri(...TRUNCATED) |
"# ARC HINT GENERATOR\n\n## ROLE & GOAL\nYou are an expert ARC (Abstraction and Reasoning Corpus) an(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 9, 9, 0, 0, 0, 0, 6(...TRUNCATED) | "[{\"input\": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0], [0, 0, 0,(...TRUNCATED) |
barc
| "concepts:\ncolor mapping, object detection\n\ndescription:\nIn the input, you will see a grid with (...TRUNCATED) |
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