Every nonempty axis-aligned rectangle has a top-right corner. Enumerate all such corners and retain the greatest area from part (b).
var best = 0
var i = 0
while (i < N) {
  var j = 0
  while (j < N) {
    best = math.max(best, maxRectangleAt(i, j))
    j += 1
  }
  i += 1
}
The loop invariant is that best is the greatest area obtained from the corners processed so far, or zero if there are none. Consequently
(1)
The preprocessing cost from part (a) is included. An entirely false matrix, or an empty one, returns zero. In the printed example, rows through and columns through give area ; exhaustive corner enumeration confirms that no larger all-true rectangle exists.[ref]
Figure 1.
An area-15 rectangle and the row run lengths that certify its width
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