Select a random true position in a boolean[][] that is not in a specific rectangle

Select.java

// map can use [y][x] indexing and the names will make sense here,
// or [x][y] indexing and it will work but be named oddly and the
// Vector2 returned will be using (y, x) order.
public static Vector2 selectRandom(boolean[][] map, Random random, int xMinVisible, int xMaxVisible, int yMinVisible, int yMaxVisible)
{
  int ct = 0, height = map.length, width = map[0].length;
  int[] rowCounts = new int[height];
  for(int y = 0; y < height; y++)
  {
    if(y >= yMinVisible && y <= yMaxVisible)
    {
      for(int x = 0; x < xMinVisible && x < width; x++)
      {
        if(map[y][x]) ct++;
      }
      for(int x = xMaxVisible + 1; x < width; x++)
      {
        if(map[y][x]) ct++;
      }
    }
    else
    {
      for(int x = 0; x < width; x++)
      {
        if(map[y][x]) ct++;
      }
    }
    if(y == 0)
      rowCounts[y] = ct;
    else if(y > 0 && ct > rowCounts[y-1])
      rowCounts[y] = ct;
    //otherwise it stays 0
  }
  int pos = random.nextInt(ct);
  if(pos < rowCounts[0])
  {
    for(int x = 0; x < width; x++)
    {
      if(map[y][x] && --ct == pos)
        return new Vector2(x, 0);
    }
  }
  int stopper = 0;
  for(int y = 1; y < height; y++)
  {
    if((ct = rowCounts[y]) > pos)
    {
      stopper = rowCounts[y-1];
      for(int x = 0; x < width && ct > stopper; x++)
      {
        if(map[y][x] && --ct == pos)
        {
          return new Vector2(x, y)
        }
      }
    }
  }
  return null;
}