The largest square sub-matrix

largestSquareSubMatrix.js

/* Casey has a square image made up of black and white pixels
represented as 0 and 1 respectively. As part of an image analysis
process, Casey needs to determine the size of the largest square area
of white pixels. Given a 2-dimensional square matrix that represents
the image, write a function to determine the length of a side of the
largest square area made up of white pixels.
For example, the n x n = 5 x 5 matrix of pixels is represented as arr =
[[1,1,1,1,1], [1,1,1,0,0], [1,1,1,0,0], [1,1,1,0,0], [1,1,1,1,1]. A diagram of
the matrix is:
1 1 1 1 1
1 1 1 0 0
1 1 1 0 0
1 1 1 0 0
1 1 1 1 1
The largest square sub-matrix is 3 x 3 in size starting at position (0, 0),
(1, 0) or (2, 0). The expected return value is 3.
*/

 /**
  * Create a multidimensional array n*m
  * @param {number} n columns
  * @param {number} m rows
  */
function multidimensionalArray(n, m) {
  let sub = new Array(n);
  for (let i = 0; i < sub.length; i++) {
    sub[i] = new Array(m);
  }

  return sub;
}

/**
 * 
 * @param {array} arr 
 */
function largestMatrix(arr) {
  const cols = arr.length;
  const rows = arr[0].length;
  let maxSize = 0;
  // here we need to create a multidimensional array based on the numbers of cols and rows, can be filled of zeros
  let sub = multidimensionalArray(cols, rows);

  // copy the first row
  for (let i = 0; i < cols; i++) {
    sub[0][i] = arr[0][i];
  }

  // copy the first column
  for (let i = 0; i < rows; i++) {
    sub[i][0] = arr[i][0];
  }

  // for the rest of the matrix
  for (let i = 1; i < rows; i++) {
    for (let j = 1; j < cols; j++) {
      if (arr[i][j] === 1) {
        sub[i][j] = Math.min(sub[i - 1][j - 1], Math.min(sub[i][j - 1], sub[i - 1][j])) + 1;
      } else {
        sub[i][j] = 0;
      }
    }
  }

  // find the maximum size of the matrix
  for (let i = 0; i < rows; i++) {
    for (let j = 0; j < cols; j++) {
      if (sub[i][j] > maxSize) {
        maxSize = sub[i][j];
      }
    }
  }

  return maxSize;
}