Finding largest rectangle in 2D array

Question

I need an algorithm which can parse a 2D array and return the largest continuous rectangle. For reference, look at the image I made demonstrating my question.

Answer 1

A straight forward approach would be to do a loop through all the potential rectangles in the grid, figure out their area, and if it is greater than the current highest area, select it as the highest:

var biggestFound
for each potential rectangle:
    if area(this potential rectangle) > area(biggestFound)
        biggestFound = this potential rectangle

Then you simply need to find the potential rectangles.

for each square in grid:
    recursive loop 1:
        if not occupied:
            grow right until occupied, and return a rectangle
            grow down one and recurse (call loop 1)

This will duplicate a lot of work (for example you will re-evaluate a lot of sub-rectangles), but it should give you an answer.

Edit

An alternate approach might be to start with a single square the size of the grid, and "subtract" occupied squares to end up with a final set of potential rectangles. There might be optimization opportunities here using quadtrees, and in ensuring that you keep split rectangles "in order", top to bottom, left to right, in case you need to re-combine rectangles farther down in the algorithm.

If you are actually starting out with rectangular data (for your "populated grid" set), instead of a loose pixel grid, then you could easily get better perf out of a rectangle/region subtracting algorithm.

I'm not going to post pseudo-code for this because the idea is completely experimental, and I have no idea if the perf will be any better for a loose pixel grid ;)

Windows system "regions" and "dirty rectangles", as well as general "temporal caching" might be good inspiration here for more efficiency. There are also a lot of z-buffer tricks if this is for a graphics algorithm...