algorithm to find area of largest sub-array(rectangle) consisting entirely of 1's

Question

There is a 2D binary array (2D array of 0 and 1) where m rows and n columns; give an efficient algorithm to find area of largest sub-array (rectangle) consisting entirely of 1s.

public int findMaxRectangleArea(int[][] A,int m,int n);

Can someone please help me with the algorithm part?

Why all the language tags? Do you have to provide a solution in these? You'd might want to tag `language-agnostic` instead — Kos, Feb 06 '13 at 11:00
http://www.drdobbs.com/database/the-maximal-rectangle-problem/184410529 — sotapme, Feb 06 '13 at 12:14
A similar question has been posted for `C#`, with a slightly different condition (equal sums for 0 and 1). You will find the pseudo code in the accepted answer: [Largest submatrix with equal no of 1's and 0's](http://stackoverflow.com/questions/13698298/largest-submatrix-with-equal-no-of-1s-and-0s). — Alex Filipovici, Feb 06 '13 at 10:44
Then you shouldn't get the job until you've done more studying. — Hovercraft Full Of Eels, Feb 06 '13 at 22:11
Meh about this being closed, but who would vote to delete? Are algorithms really off-topic here? Really? — Kos, Feb 19 '13 at 07:21

score 2 · Answer 1 · answered Feb 06 '13 at 10:58

2

I'd try an approach like this:

Iterate left to right row by row until you find a 0.

This 0 may already identify two rectangles of 1s:

all rows above it
from the top left to the position to the left of the 0

One of them is bigger, remember it.

First step

Then recursively descend into the three unknown sectors (two of them partially unknown) that may still contain a rectangle bigger than what you have already found:

Second step

Make sure you don't iterate over the known rows again, that's redundant.

I believe this solution can look at each field at most twice (where a recursion step's sectors overlap), so it should run in θ(x*y).

answered Feb 06 '13 at 10:58

Kos

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not quite there yet... there is a merging step that you omitted that is not trivial. so you've divided the problem after finding a 0, but then after recursively solving the smaller pieces, you need to merge... – thang Feb 06 '13 at 11:06
Is the merging step really not trivial? If a solution is in smaller pieces, it's entirely contained in one of them, so the whole solution is just the greatest of the four. If I'm wrong, please show an example. – Kos Feb 06 '13 at 11:24
i don't know but it's not listed... trivial or not is subjective. my point is the solution is incomplete. i haven't thought about it... – thang Feb 06 '13 at 11:41

score 0 · Answer 2 · answered Feb 06 '13 at 10:44

0

It all depends ion how large your smallest array dimension is. If it's smaller than the maximum word size on your target platform, you could make your array into a 1D array of bitmaps and use a series of sliding bitmask windows to find the rectangle.

answered Feb 06 '13 at 10:44

Simon Elliott

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algorithm to find area of largest sub-array(rectangle) consisting entirely of 1's

2 Answers2