AbigailII: It's not that difficult to determine which ones must be zero.  If you shoot in square S1 and get zero, then you need to check

for each unlabled square S2 next to S1

  mustBeZero  = false

  for each labeled square S3 next to S2

     if S3 is labeled with 0

       mustBeZero = true;

     endif

  endfor
  if (mustBeZero)
     label(S2, "0")
  endif

endfor

This would cause the "barren plains" where there are no frogs at all to be quickly filled in.  It also means that if there's a 1 two squares away that's next to a known frog, that won't fill in the square, which might be reasonable, since you might not want to do too much thinking for the players.  If you wanted to also fill in those squares, replace "if S3 is labeled with 0" with "if S3 is labeled with the number of known frogs in neighboring squares".