abstractions listlengths 4 4 | train stringlengths 150 5.95k | test stringlengths 46 6.03k | source stringclasses 4
values | answer stringlengths 9 1.81k | num_tokens int64 299 4.1k |
|---|---|---|---|---|---|
[
"<note1>\n<description>Compare the input and output grid sizes by dividing the number of rows (and columns) in the output by the number of rows (and columns) in the input. This ratio is the uniform scaling factor N that each input cell is blown up into an N×N block. Knowing N lets you plan how big your output will ... | [{"input": [[2, 2, 9, 5, 2, 2, 2, 1], [0, 2, 3, 0, 2, 2, 2, 6]], "output": [[2, 2, 2, 2, 2, 2, 9, 9, 9, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 2, 9, 9, 9, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [2, 2, 2, 2, 2, 2, 9, 9, 9, 5, 5, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1], [0, 0, 0, 2, 2, 2, 3, ... | [{"input": [[6, 2, 6, 2, 2, 6, 2, 2, 6], [2, 6, 6, 6, 2, 2, 2, 2, 6], [2, 2, 2, 6, 2, 2, 2, 6, 2], [2, 2, 6, 6, 2, 6, 6, 2, 2], [2, 2, 6, 7, 2, 6, 2, 2, 6], [2, 2, 2, 2, 6, 2, 2, 6, 2], [6, 6, 2, 2, 2, 6, 2, 6, 6]], "output": [[6, 6, 6, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 6, 6, 6], [6, 6, 6, ... | rearc | ```
6 6 6 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6
6 6 6 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6
6 6 6 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6 2 2 2 2 2 2 6 6 6
2 2 2 6 6 6 6 6 6 6 6 6 2 2 2 2 2 2 2 2 2 2 2 2 6 6 6
2 2 2 6 6 6 6 6 6 6 6 6 2 2 2 2 2 2 2 2 2 2 2 2 6 6 6
2 2 2 6 6 6 6 6 6 6 6 6 2 2 2 2 2 2 2 2 2 2 2 ... | 2,792 |
[
"<note1>\n<description>Try identifying each contiguous region of the same input color (a “connected component”) and computing a simple property of that region—such as its size or its bounding‐box dimensions. Then relabel every cell in that region with a new output value that depends only on that region’s property. ... | [{"input": [[7, 7, 8, 8], [5, 7, 3, 9], [2, 4, 3, 9], [4, 4, 4, 4]], "output": [[1, 3, 5, 6], [1, 1, 6, 6], [1, 4, 4, 9], [1, 8, 8, 9]]}, {"input": [[2, 9, 9, 5, 4], [5, 7, 9, 5, 4], [5, 4, 3, 3, 3], [8, 9, 1, 6, 4], [7, 8, 1, 6, 6]], "output": [[6, 9, 5, 5, 3], [9, 8, 1, 6, 8], [2, 2, 4, 8, 8], [7, 7, 4, 5, 5], [7, 1,... | [{"input": [[6, 1, 8], [1, 1, 4], [1, 6, 2]], "output": [[2, 2, 7], [7, 2, 2], [3, 1, 9]]}] | barc_heavy | ```
2 2 7
7 2 2
3 1 9
``` | 548 |
[
"<note1>\n<description>Scan each input row for nonzero “seed” cells and sort them left to right. Whenever you find two adjacent seeds in the same row, treat them as a pair to be connected by diagonal strokes. This lets you break the problem into independent pairwise connections.</description>\n<example>Suppose a ro... | [{"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], [8, 0, 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, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, ... | [{"input": [[0, 0, 0, 0, 0, 5, 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, 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, 9, 0, 0], [0, 0, 0, 0, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ... | barc_heavy | ```
0 0 0 0 0 5 7 0 0 0 0 0 0 0
0 0 0 0 0 0 5 7 0 0 0 0 0 0
0 0 0 0 0 9 0 7 0 0 0 0 0 0
0 0 0 0 0 0 9 7 0 0 0 0 0 0
0 0 0 0 0 0 0 9 0 0 0 9 0 0
0 0 0 0 6 8 0 9 0 0 9 0 0 0
0 0 0 0 0 6 8 9 0 9 0 0 0 0
0 0 0 0 0 0 6 5 9 9 9 0 0 0
0 0 0 0 0 0 0 6 0 0 4 9 0 0
0 0 0 0 0 0 0 6 0 0 0 0 0 0
0 0 0 0 0 0 0 6 0 0 0 0 0 0
0 0 0 0 ... | 3,030 |
[
"<note1>\n<description>Check whether the input can be tiled into four similar sub-regions (quadrants), each containing the same shape drawn in a different color on a black background. Often a single larger task breaks neatly into four equal or nearly equal rectangles. Splitting the grid this way lets you isolate ea... | [{"input": [[0, 0, 0, 0, 4, 4, 4, 4], [8, 0, 8, 0, 0, 4, 4, 4], [0, 0, 0, 8, 0, 4, 4, 4], [0, 0, 0, 0, 4, 0, 4, 4], [0, 0, 8, 0, 0, 0, 0, 4], [0, 8, 0, 0, 4, 0, 4, 0], [0, 0, 8, 8, 4, 4, 4, 4], [8, 0, 0, 0, 4, 4, 4, 0], [0, 0, 0, 0, 4, 4, 4, 0], [2, 0, 0, 0, 9, 9, 9, 9], [0, 0, 0, 2, 9, 9, 9, 9], [2, 0, 2, 0, 9, 9, 9, ... | [{"input": [[1, 1, 9, 1, 1, 9, 1, 1, 9, 9, 1, 7, 9, 9, 9, 9, 7, 9, 7, 9, 9, 9], [9, 9, 1, 1, 9, 9, 1, 1, 9, 9, 1, 7, 7, 7, 9, 9, 9, 9, 9, 9, 7, 9], [9, 1, 1, 1, 1, 9, 9, 9, 9, 1, 1, 9, 7, 7, 7, 7, 7, 9, 9, 7, 9, 7], [1, 1, 9, 1, 1, 9, 1, 1, 9, 9, 1, 9, 9, 7, 9, 7, 7, 9, 7, 9, 9, 9], [1, 1, 1, 9, 1, 1, 1, 1, 1, 9, 9, 7,... | rearc | ```
7 6 3 3 6 7 6 7 6 3 6
7 7 7 1 6 6 6 6 3 7 6
6 7 7 7 7 7 9 6 7 6 7
3 6 7 6 7 7 6 7 6 6 6
7 6 7 6 6 3 7 6 6 6 6
6 1 7 3 6 6 7 3 6 6 7
7 7 6 9 7 6 6 6 6 6 6
``` | 2,602 |
[
"<note1>\n<description>Scan each row and column for lines that are a single color throughout; these uniform lines often act as separators dividing the grid into meaningful sub‐regions.</description>\n<example>In a 10×10 grid, if column 4 is entirely blue, you can treat column 4 as a vertical divider and analyze the... | [{"input": [[8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 2, 4], [8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 2, 8], [8, 8, 8, 8, 8, 8, 7,... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0]... | rearc | ```
0 0 0
0 0 0
0 0 0
``` | 3,116 |
[
"<note1>\n<description>First identify each distinct non-zero color as a separate object by grouping its connected pixels. This isolates individual shapes in the grid so you can analyze them one by one.</description>\n<example>In a toy grid with blue pixels forming two blobs and red pixels forming one blob, label th... | [{"input": [[6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [6, 6, 6, 6, 0, 0, 0, 0, 0, 0], [6, 0, 0, 0, 4, 0, 0, 0, 0, 0], [6, 6, 6, 4, 4, 4, 0, 0, 0, 0], [0, 0, 4, 4, 4, 4, 4, 0, 6, 0], [0, 0, 0, 4, 4, 4, 0, 0, 6, 6], [0, 9, 0, 0, 4, 0, 0, 6, 6, 6], [0, 9, 9, 0, 0, 6, 6, 6, 6, 6], [0, 0, 9, 9, 8, 6, 6, 0, 0, 0], [0, 0, 0, 8, 8, 0, 0... | [{"input": [[0, 0, 0, 0, 6, 6, 0, 0, 0, 0], [4, 4, 0, 0, 6, 6, 0, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 0, 0, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 4, 4, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 5, 0], [0, 0, 0, 0, 0, 3, 0, 5, 5, 0], [0, 3, 3, 3, 3, 3, 0, 0, 0, 0], [0, 3, 3, 3, 3, 3, 0... | barc_heavy | ```
6 6
6 6
``` | 1,156 |
[
"<note1>\n<description>First isolate the key shape by identifying all connected cells of the standout color (here “2”). Treat 4-connected neighbors (up, down, left, right) as part of the same component. Focusing only on that component simplifies subsequent steps.</description>\n<example>Imagine a grid where several... | [{"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, 0, 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,... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0], ... | barc_heavy | ```
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 8 8 8 8
0 0 0 0 0 8 8 8 8 8 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 0 0
0 0 0 0 ... | 2,486 |
[
"<note1>\n<description>First, scan the grid to find the three “landmark” cells (the ones with colors 2, 3, and 4). These will serve as anchor points for the transformation.</description>\n<example>For instance, if you see a 2 at (5,2), a 3 at (11,7), and a 4 at (3,11), record those three coordinates—they will defin... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 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, 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,... | [{"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, 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, 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,... | arc 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 5 5 5 4 0 0
0 0 0 0 0 0 0 5 0 0 5 0 0
0 0 0 0 0 0 0 5 0 0 5 0 0
0 2 5 5 5 5 5 5 5 5 5 0 0
0 0 0 0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 0 0 5 0 0 0 0 0
0 0 0 0 0 0 0 3 0 0 0 0 0
0 0 ... | 3,325 |
[
"<note1>\n<description>When you see two cells of the same color lying in different rows and different columns, treat them as opposite corners of a rectangle. Completing that rectangle by placing the same color at the other two corner positions often uncovers a symmetry or hidden alignment.</description>\n<example>S... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0, 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, 7, 0, 0, 0], [0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0], [0, 0, 7, 0, 0, 0, 0, 0, 0, 6, 0, 0], [0, ... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, ... | barc_heavy | ```
0 0 0 0 1 0 0 0 0 0 7 0
0 0 0 0 0 0 7 0 0 0 1 0
0 0 0 0 1 0 0 0 0 0 7 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 7 0 0 0
0 0 0 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 7 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 1 0 0 7
0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0
``` | 2,234 |
[
"<note1>\n<description>When a grid contains a background value (here 0) and scattered non-zero pixels, group those non-zero pixels into connected components using orthogonal adjacency. Each component represents a distinct region or “shape.”</description>\n<example>Imagine a grid where you see one 2×2 block of seven... | [{"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, 2, 9, 9, 5, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 7, 9, 5, 4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 3, 3, 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, 7, 8, 2, 4, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 8, 8, 4, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 8, 8, 8, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 5, 7, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 4, 7, 1, 1, 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... | barc_heavy | ```
7 8 2 4 4
7 8 8 8 4
4 8 8 8 8
4 3 5 7 3
4 7 1 1 3
``` | 2,764 |
[
"<note1>\n<description>Identify and preserve a unique “anchor” object that remains unchanged across examples—often a solitary pixel of one color. Treat this anchor as a fixed reference when deciding which components to leave untouched. It can also serve as a pivot for classification of other shapes.</description>\n... | [{"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, 8, 8, 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, 8, 8, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 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_heavy | ```
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 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 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 ... | 3,030 |
[
"<note1>\n<description>First locate the two uniquely colored cells by scanning for their distinct values. Label one as the fixed reference (e.g., color 3) and the other as the mover (e.g., color 1). Knowing which is which clarifies which cell should stay put and which should shift.</description>\n<example>In a grid... | [{"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, 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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "ou... | [{"input": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 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]], "output": [[0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0,... | barc_heavy | ```
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 3 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 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
``` | 1,400 |
[
"<note1>\n<description>To expand a shape uniformly on a grid, use a Manhattan‐distance “dilation”: include every cell whose Manhattan distance to the original shape is at most a chosen radius. This turns isolated points into diamond patterns and thin lines into thick bands.</description>\n<example>For instance, dil... | [{"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, 6], [0, 0, 0, 0, 0, 7, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, 0, 9, 0, 0, 0], [0, 0, 0, 0, 0, 0, 6, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 8], [6, 0, 0, 0, 0, 0, 0... | [{"input": [[0, 0, 0, 0, 0, 0, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 9, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 5, 0, 0, 1, 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, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 7, 0], [0, 0, 0, 0, 0, 0, 0... | barc_heavy | ```
0 0 0 0 0 7 7 7 0 0
0 0 0 0 0 9 7 0 0 0
0 0 0 0 9 9 9 0 0 0
0 0 0 0 0 5 0 0 1 0
0 0 0 0 6 6 5 1 1 1
0 0 0 6 6 6 6 0 1 0
0 0 0 0 6 6 0 0 4 0
0 0 0 0 0 0 0 4 7 4
0 0 0 0 0 0 0 7 7 7
0 0 0 0 0 0 0 0 7 0
``` | 1,666 |
[
"<note1>\n<description>Look for rows or columns filled entirely with one color—they act as natural dividers that segment the large grid into uniform sub-blocks. Finding these “separator” lines tells you both the size and count of the blocks to process individually. Determining the block layout is the first step tow... | [{"input": [[0, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9], [9, 9, 9, 0, 9, 2, 9, 9, 9, 9, 9], [9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 0], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [9, 9, 0, 9, 9, 2, 9, 9, 0, 9, 9], [9, 9, 9, 9, 9, 2, 9, 9, 9, 9, 9], [9, 9, 9, 9, 0, 2, 9, 9, 9, 0, 9], [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], [0, 9, 9, 0, 9, 2, 0, 9, 9, ... | [{"input": [[8, 8, 8, 5, 8, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8], [8, 5, 8, 8, 8, 7, 8, 8, 8, 8, 5, 7, 8, 8, 8, 5, 8, 7, 8, 5, 8, 8, 8], [8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8], [8, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 7, 8, 8, 8, 5, 8, 7, 8, 8, 8, 8, 8], [7, 7, 7, 7, 7, 7, 7, 7,... | rearc | ```
1 8 1 8
1 1 1 1
1 1 8 1
``` | 1,894 |
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