algorithm - find all rectangular areas with certain properties in a matrix -

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given n*m matrix possible values of 1, 2 , null:

  . . . . . 1 . .   . 1 . . . . . 1   . . . 2 . . . .   . . . . 2 . . .   1 . . . . . 1 .   . . . . . . . .   . . 1 . . 2 . .   2 . . . . . . 1

i looking blocks b (containing values between (x0,y0) , (x1,y1)) that:

  • contain @ least 1 '1'
  • contain no '2'
  • are not subset of block above properties

example:

blocks

the red, green , blue area contain '1', no '2', , not part of larger area. there of course more 3 such blocks in picture. want find these blocks.

what fast way find these areas?

i have working brute-force solution, iterating on possible rectangles, checking if fulfill first 2 criteria; iterating on found rectangles, removing rectangles contained in rectangle; , can speed first removing consecutive identical rows , columns. there faster way.

you can somewhere between considering every rectangle, , clever solution.

for example, starting @ each 1 create rectangle , gradually expand edges outwards in 4 directions. stop when hit 2, record rectangle if (a) you've had stop in 4 directions, , (b) haven't seen rectangle before.

then backtrack: need able generate both red rectangle , green rectangle starting 1 near top left.

this algorithm has pretty bad worst cases, though. input consisting of 1s springs mind. need combined other cleverness, or constraints on input.


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