Find the coordinates of all rectangles of contiguous 1s in a 2D array in Javascript

Question

I have found numerous questions asking about how to find the largest contiguous rectangle in a 2D array, and some that ask for the number of rectangles, but only one that deals with finding the coordinates, width, and height of all of the rectangles required to cover an area of 1s in a 2D of 1s and 0s.

The question (Finding rectangles in a 2d block grid) has a solution but is difficult to follow since it references an external code block.

I am dealing with 2D arrays that make up the pixels of letters:

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0

The desired output here would be something like:

[[4,0,6,17],[7,0,16,2],[7,7,15,9],[7,15,15,17]]

Where each array contains the upper left hand coordinate and lower right hand coordinate (any method that gets upper left and width and height also works).

Could someone provide the psudocode (or Javascript) for either the question previously asked or another algorithm that works, or provide a more in-depth explanation of the steps required?

Answer 1

Here is a way to do it with using a simple algorithm.

1. Calculate the total area covered by rectangles -> A
2. While the area of the rectangles found so far is smaller than A
   1. Find a new rectangle
      1. Find the upper left corner, scan the matrix and stop at the first 1 found
      2. Find the bottom right corner, starting at the upper left corner, scan the matrix and stop at the first 0 found
   2. Mark the rectangle found by setting each cell to something else than 1
   3. Add its area to the accumulated area
   4. Push the rectangle to a list

const mat = [
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],//0
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],//1
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],//2
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//3
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//4
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//5
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//6
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0],//7
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0],//8
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0],//9
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//10
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//11
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//12
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//13
  [0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],//14
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],//15
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0],//16
  [0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0] //17
];

const W = mat[0].length;
const H = mat.length;

// get the area covered by rectangles
let totalRectArea = 0;
for (let i = 0; i < W; ++i) {
  for (let j = 0; j < H; ++j) {
    totalRectArea += mat[j][i] > 0 ? 1 : 0;
  }
}

const rects = [];
let rectArea = 0;

// find all rectangle until their area matches the total
while (rectArea < totalRectArea) {
  const rect = findNextRect();
  rects.push(rect);
  markRect(rect);
  rectArea += (rect.x2 - rect.x1 + 1) * (rect.y2 - rect.y1 + 1);
}

console.log(rects);

function findNextRect() {
  // find top left corner
  let foundCorner = false;
  const rect = { x1: 0, x2: W-1, y1: 0, y2: H-1 };
  for (let i = 0; i < W; ++i) {
    for (let j = 0; j < H; ++j) {
      if (mat[j][i] === 1) {
        rect.x1 = i;
        rect.y1 = j;
        foundCorner = true;
        break;
      }
    }
    if (foundCorner) break;
  }
  // find bottom right corner
  for (let i = rect.x1; i <= rect.x2; ++i) {
    if (mat[rect.y1][i] !== 1) {
      rect.x2 = i-1;
      return rect;
    }
    for (let j = rect.y1; j <= rect.y2; ++j) {
      if (mat[j][i] !== 1) {
        rect.y2 = j-1;
        break;
      }
    }
  }
  return rect;
}

// mark rectangle so won't be counted again
function markRect({ x1, y1, x2, y2 }) {
  for (let i = x1; i <= x2; ++i) {
    for (let j = y1; j <= y2; ++j) {
      mat[j][i] = 2;
    }
  }
}