I am working on a project where the game world is irregularly shaped (Think of the shape of a lake). this shape has a grid with coordinates placed over it. The game world is only on the inside of the shape. (Once again, think Lake)

How can I efficiently represent the game world? I know that many worlds are basically square, and work well in a 2 or 3 dimension array. I feel like if I use an array that is square, then I am basically wasting space, and increasing the amount of time that I need to iterate through the array. However, I am not sure how a jagged array would work here either.

Example shape of gameworld

X
XX
 XX   X XX
 XXX XXX
  XXXXXXX
XXXXXXXX
 XXXXX XX
   XX   X
  X

Edit: The game world will most likely need each valid location stepped through. So I would a method that makes it easy to do so.