hackv1.js

function strokesRequired(picture) {
  var strokes = 0;
  while (true) {
    // Find the next truthy cell and extract x and y
    const next = picture.flatMap((row, x) => row.flatMap((char, y) => (char && { char, x, y }))).filter(r => r)[0];
    if (!next) { // None left means the picture is filled
      break;
    }
    const remove = [[next.x, next.y]]; // We will remove the current cell after
    eliminateNeighbours(picture, [], remove, next.char, next.x, next.y);
    remove.forEach(xy => picture[xy[0]][xy[1]] = undefined); // Clean Picture
    ++strokes;
  }
  return strokes;
}

function eliminateNeighbours(picture, checked, remove, char, x, y) {
  check(picture, checked, remove, char, x + 1, y);
  check(picture, checked, remove, char, x - 1, y);
  check(picture, checked, remove, char, x, y + 1);
  check(picture, checked, remove, char, x, y - 1);
}

function check(picture, checked, remove, char, x, y) {
  if (checked.includes(`${x},${y}`)) {
    return;
  }
  checked.push(`${x},${y}`);

  if (picture[x] && picture[x][y] === char) {
    remove.push([x, y]);
    eliminateNeighbours(picture, checked, remove, char, x, y);
  }
}


const picture = `
aaaba
aaaba
aaacb
`.split("\n").filter(r => !!r).map(p => p.split(''));

console.log("Result:", strokesRequired(picture));