1

So if I have a 2D array such as

const array = [
            [1, 2, 3, 4, 5],
            [9, 8, 7, 6, 5],
            [1, 8, 3, 6, 5],
            [9, 8, 7, 6, 5],
            [1, 8, 3, 6, 5],
            [1, 2, 3, 4, 5]
          ];

which could for the point of the question be any size, square or not square.

and I want to extract 3x3 arrays out of it, for instance at 1,1 that would be const sub = [[8, 7, 6], [8, 3, 6], [8, 7, 6]]. So far so good - I can do this. However I am flattening the 2D array so that its represented as a 1D array (long story as to why), i.e

const array = [1, 2, 3, 4, 5, 9, 8, 7, 6, 5, 1, 8, 3, 6, 5, 9, 8, 7, 6, 5, 1, 8, 3, 6, 5, 1, 2, 3, 4, 5];

What I'm trying to do is extract the same (or any) 3x3 array out of this but while its represented as a 1D array, so I would then get back [8, 7, 6, 8, 3, 6, 8, 7, 6].

I almost got there, however I made an error of only working with arrays that were 9x9 and always extracting 3x3 subsets which mean that my solution only works for that specific case, and the more I stare at my solution, the more I cannot work out what the generic solution would look like.

My solution:

const extractSubsetFrom1D = (array, subHeight, subWidth, startRow, startCol) => {
    const kWH = subWidth * subHeight
    const subset = array.slice(((((kWH - 2) * startRow) + startCol) * kWH), ((((kWH - 2) * startRow) + startCol) * kWH) + kWH)
    return subset
}

In my case subHeight and subWidth were always equalling 3 respectively, and as the array itself was always 9x9 I believe I accidentally stumbled on a solution for that specific case as they divide nicely into each other.

To be clear my solution will fail for the startRow = 1 startCol = 0 for the provided array (it works for the startRow = 0 scenario

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  • developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/… (Array.flat) may or may not be helpful. It can flatten arrays up to a certain point and then stop, but that might not be what you need. Commented Jul 22, 2022 at 12:47
  • as an idea: extractSubset = (arr, { top, left, bottom, right }) => arr.slice(top, bottom).map(row => row.slice(left, right)) and then something like extractSubset(array, {top: -3, right: 3}) every one of the 4 boundaries is optional Commented Jul 22, 2022 at 15:39

1 Answer 1

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It's not entirely clear to me how you came to your current implementation, but I can at least tell:

  • ✅ You correctly determined the size of the sub grid array to return (kWH)
  • ❌ You incorrectly assume you can slice out a sub grid as one continuous part of the original 1d array
  • 🟠 The calculation of the first element seems kind-of-right but is actually wrong (probably because of the previous mistake)

From (y,x) to i

Let's start from scratch and work our way up to a nice one liner.

In a 2d-array, you can get a cell's value by doing:

cellValue = grid2d[y][x]

Once you flatten it, you'll need to do:

cellValue = grid1d[y * GRID_WIDTH + x]

y * GRID_WIDTH takes you to the start of the right row, and + x gets you to the right column.

As you can see, you need to know the original grid's size before you can even query a specific cell. That means your extract function would need an argument to pass the original width (or, if the grids are guaranteed to be square, you can do Math.sqrt(array.length).

A slice per row

Let's use this math to find the indices of a 2x2 sub grid at (1,1) extracted from a 3x3 source grid:

0  1  2
3 [4][5]
6 [7][8]

As you can see, the resulting indices are [4,5,7,8]. There is no way to slice these indices out of the source array directly because we don't want to include the 6.

Instead, we can use a nested loop to skip the gaps between our rows:

const to1d = (x, y, w) => y * w + x;

const extractSubGrid1D = (grid, gridWidth, x, y, w, h) => {
  const yTop = y;
  const yBottom = y + h
  const xLeft = x;
  const xRight = x + w;
  
  const subgrid = [];
  
  for (let y = yTop; y < yBottom; y += 1) {
    for (let x = xLeft; x < xRight; x += 1) {
      const index = to1d(x, y, gridWidth);
      subgrid.push(grid[index]);
    }
  }

  return subgrid;
}

const originalGrid = [
  0, 1, 2,
  3, 4, 5,
  6, 7, 8
];

console.log(
  extractSubGrid1D(originalGrid, 3, 1, 1, 2, 2)
)

Once you get a feel for the logic, feel free to refactor.

The other way around

To go from a 1d-index to a 2d coordinate, you can do:

x = i % w
y = Math.floor(i / w)

Applying this logic, you can also fill your sub grid like so:

  • Create a new array of the right size
  • For each of its indices, determine the original grid's (x, y) coordinate
  • Transform that coordinate back to an index to query the original grid with

const to1d = (x, y, w) => y * w + x;

const extractSubGrid1D = (grid, gridWidth, x, y, w, h) => Array.from(
  { length: w * h },
  (_, i) => grid[to1d(x + i % w, y + Math.floor(i / w), gridWidth)]
)

const originalGrid = [
  0, 1, 2,
  3, 4, 5,
  6, 7, 8
];

console.log(
  extractSubGrid1D(originalGrid, 3, 1, 1, 2, 2)
)

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2 Comments

Hi thanks for this detailed answer. I think as you wondered in the opening of your response, I expected it to be easier than it was and built on error after error.... Just one question - the two snippets you provide seem to take the same inputs - and therefore are one and the same right? The second is just a very 'tight' version of the first? I.e they both do the same thing from the perspective of the caller of extractSubGrid1D?
Yes, they’re just two different ways of writing the exact same thing. So it’s up to personal preferences which of the two you prefer

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