This fills in the deduction feature I mentioned in commit 7acc554805,
of determining the identity by elimination, having ruled out all other
candidates.
In fact, it goes further: as soon as we know that an element can't be
the group identity, we rule out every possible entry in its row and
column which would involve it acting as a left- or right-identity for
any individual element.
This noticeably increases the number of puzzles that can be solved at
Hard mode without resorting to Unreasonable-level recursion. In a test
of 100 Hard puzzles generated with this change, 80 of them are
reported as Unreasonable by the previous solver.
(One of those puzzles is 12i:m12b9a1zd9i6d10c3y2l11q4r , the example
case that exposed the latin.c validation bug described by the previous
two commits. That was reported as ambiguous with the validation bug,
as Unreasonable with the validation bug fixed, and now it's merely
Hard, because this identity-based deduction eliminates the need for
recursion.)
This actually fixes the example game id mentioned in the previous
commit. Now 12i:m12b9a1zd9i6d10c3y2l11q4r is reported as Unreasonable
rather than ambiguous, on the basis that although the solver still
recurses and finds two filled grids, the validator throws out the
nonsense one at the last minute, leaving only one that's actually
legal.
I've only just realised that there's a false-positive bug in the
latin.c solver framework.
It's designed to solve puzzles in which the solution is a latin square
but with some additional constraints provided by the individual
puzzle, and so during solving, it runs a mixture of its own standard
deduction functions that apply to any latin-square puzzle and extra
functions provided by the client puzzle to do deductions based on the
extra clues or constraints.
But what happens if the _last_ move in the solving process is
performed by one of the latin.c built-in methods, and it causes a
violation of the client puzzle's extra constraints? Nothing will ever
notice, and so the solver will report that the puzzle has a solution
when it actually has none.
An example is the Group game id 12i:m12b9a1zd9i6d10c3y2l11q4r . This
was reported by 'groupsolver -g' as being ambiguous. But if you look
at the two 'solutions' reported in the verbose diagnostics, one of
them is arrant nonsense: it has no identity element at all, and
therefore, it fails associativity all over the place. Actually that
puzzle _does_ have a unique solution.
This bug has been around for ages, and nobody has reported a problem.
For recursive solving, that's not much of a surprise, because it would
cause a spurious accusation of ambiguity, so that at generation time
some valid puzzles would be wrongly discarded, and you'd never see
them. But at non-recursive levels, I can't see a reason why this bug
_couldn't_ have led one of the games to present an actually impossible
puzzle believing it to be soluble.
Possibly this never came up because the other clients of latin.c are
more forgiving of this error in some way. For example, they might all
be very likely to use their extra clues early in the solving process,
so that the requirements are already baked in by the time the final
grid square is filled. I don't know!
Anyway. The fix is to introduce last-minute client-side validation:
whenever the centralised latin_solver thinks it's come up with a
filled grid, it should present it to a puzzle-specific validator
function and check that it's _really_ a legal solution.
This commit does the plumbing for all of that: it introduces the new
validator function as one of the many parameters to latin_solver, and
arranges to call it in an appropriate way during the solving process.
But all the per-puzzle validation functions are empty, for the moment.
Applications of the associativity rule were iterating over only n-1 of
the group elements, because I started the loops at 1 rather than 0. So
the solver was a bit underpowered, and would have had trouble with
some perfectly good unambiguous game ids such as 6i:2a5i4a6a1s .
(The latin.c system is very confusing for this, because for historical
reasons due to its ancestry in Solo, grid coordinates run from 0 to
n-1 inclusive, but grid _contents_ run from 1 to n, using 0 as the
'unknown' value. So there's a constant risk of getting confused as to
which kind of value you're dealing with.)
This solver weakness only affects puzzles in 'identity hidden' mode,
because in normal mode, the omitted row and column are those of the
group identity, and applications of associativity involving the
identity never generate anything interesting.
In identity-hidden mode, as soon as you find any table entry that
matches the element indexing its row or column (i.e. a product of
group elements of the form ab=a or ab=b), then you immediately know
which element is the group identity, and you can fill in the rest of
its row and column trivially.
But the Group solver was not actually able to do this deduction.
Proof: it couldn't solve the game id 4i:1d1d1d1, which is trivial if
you take this into account. (a^2=a, so a is the identity, and once you
fill in ax=xa=x for all x, the rest of the grid is forced.)
So I've added dedicated piece of logic to spot the group identity as
soon as anything in its row and column is filled in. Now that puzzle
can be solved.
(A thing that I _haven't_ done here is the higher-level deduction of
determining the identity by elimination. Any table entry that
_doesn't_ match either its row or column rules out both the row and
the column from being the group identity - so as soon as you have
enough table entries to rule out all but one element, you know the
identity must be the remaining one. At the moment, this is just doing
the simple version of the deduction where a single table entry tells
you what _is_ the identity.)
One slightly tricky part is that because this new identity inference
deduction fills in multiple grid entries at a time, it has to be
careful to avoid triggering an assertion failure if the puzzle is
inconsistent - before filling in each entry, it has to make sure the
value it wants to fill in has not been ruled out by something it
filled in already. Without that care, an insoluble puzzle can cause
the solver to crash - and worse, the same can happen on an insoluble
_branch_ of the guesswork-and-backtracking tree in Unreasonable mode.
In both cases, the answer is to make sure you detect the problem
before hitting the assertion, and return -1 for 'inconsistent puzzle'
if you spot it. Then any guesswork branch that ends up in this
situation is cleanly abandoned, and we move on to another one.
I still don't actually have a solver design, but a recent conversation
sent my brain in some more useful directions than I've come up with
before, so I might as well at least note it all down.
A Floret grid of height h usually alternates columns of h hexagonal
florets with columns of h-1. An exception is when h=1, in which case
alternating columns of 1 and 0 florets would leave the grid
disconnected. So in that situation all columns have 1 floret in them,
and the starting y-coordinate oscillates to make the grid tile
sensibly.
However, that special case wasn't taken account of when calculating
the grid height. As a result the anomalous extra florets in the
height-1 tiling fell off the bottom of the puzzle window.
A user pointed out that if you run a GTK 3 puzzles with "GDK_SCALE=2"
in the environment, the main game drawing area is blurred. That's
because we're choosing the size of our backing Cairo surface based on
the number of _logical_ pixels in the window size, not taking into
account the fact that the non-unit scale factor means the number of
physical pixels is larger. Everything 'works' in the basis - Cairo
happily expands the smaller backing surface into the larger window -
but resolution is lost in the process.
Now we detect the window's scale factor, construct the backing surface
appropriately, and compensate for that scaling when drawing to the
surface and when blitting the surface to the window.
This is the contrapositive of the deduction introduced in the previous
commit. Previously I said: a square A can have some edges blocked in
such a way that you know it can't be filled without a particular one
of its neighbours B also being filled. And then, if you know the row
containing A and B only has one filled square left to find, then it
can't be A.
This commit adds the obvious followup: if you know the row only has
one _empty_ square left, then for the same reason, it can't be B!
I'm putting this in at the new Hard difficulty, mostly out of
guesswork rather than rigorous play-testing, because I don't remember
ever having _observed_ myself making this deduction in the past. I'm
open to changing the settings if someone has a good argument for it.
This is another deduction I've known about in principle for ages but
the game didn't implement.
In the simplest case, it's obvious: if you can draw a line across the
grid that separates the track endpoints from each other, and the track
doesn't yet cross that line at all, then it's going to have to cross
it at _some_ point. So when you've narrowed down to only one possible
crossing place, you can fill it in as definite.
IF the track already crosses your line and goes back again, the same
rule still applies: _some_ part of your track is on one side of the
line, and needs to get to the other. A more sensible way of expressing
this is to say that the track must cross the boundary an _odd_ number
of times if the two endpoints are on opposite sides of it.
And conversely, if you've drawn a line across the grid that both
endpoints are on the _same_ side of, then the track must cross it an
_even_ number of times - every time it goes to the 'wrong' side (where
the endpoints aren't), it will have to come back again eventually.
But this doesn't just apply to a _line_ across the grid. You can pick
any subset you like of the squares of the grid, and imagine the closed
loop bounding that subset as your 'line'. (Or the _set_ of closed
loops, in the most general case, because your subset doesn't _have_ to
be simply connected - or even connected at all - to make this argument
valid.) If your boundary is a closed loop, then both endpoints are
always on the same side of that boundary - namely, the outside - and
so the track has to cross the boundary an even number of times. So any
time you can identify such a subset in which all but one boundary edge
is already filled in, you can fill in the last one by parity.
(This most general boundary-based system takes in all the previous
cases as special cases. In the original case where it looks as if you
need odd parity for a line across the grid separating the endpoints,
what you're really doing is drawing a closed loop around one half of
the grid, and considering the actual endpoint itself to be the place
where the track leaves that region again - so, looked at that way, the
parity is back to even.)
The tricky part of implementing this is to avoid having to iterate
over all subsets of the grid looking for one whose boundary has the
right property. Luckily, we don't have to: a nice way to look at it is
to define a graph whose vertices are grid squares, with neighbouring
squares joined by a _graph_ edge if the _grid_ edge between those
squares is not yet in a known state. Then we're looking for an edge of
that graph which if removed would break it up into more separate
components than it's already in. That is, we want a _bridge_ in the
graph - which we can find all of in linear time using Tarjan's
bridge-finding algorithm, conveniently implemented already in this
collection in findloop.c.
Having found a bridge edge of that graph, you imagine removing it, and
find one of the two connected components it's just broken its previous
component up into. That's your subset of grid squares, and now you can
count track crossings around the boundary and fill in the bridge edge
by parity.
When I actually came to implement this, it turned out that the very
first puzzle it generated was actually hard for me to solve, because
as it turns out, this general analysis is much better at identifying
opportunities to use this deduction than I am. A straight line right
across the grid is often obvious: a few squares tucked into a
complicated half-solved piece of the worldl, not so much. So I'm
introducing a new Hard difficulty level, and putting this solution
technique in there.
This is a deduction I've been using in my own head for years: if you
only have one remaining filled square to put in a row, then it can't
be any square that has two adjacent edges blocked, because if that
square contains anything at all then it would have to be a corner
piece, and a corner piece forces the square next to it to be filled as
well.
I ran across a puzzle today that this implementation couldn't solve,
but I solved it fine by hand and found the deduction I was using that
wasn't implemented here. Now it is.
Having one of these makes it much easier to debug what's going on when
the solver can't solve something. Also, now the solver can grade the
difficulty of a puzzle, it's useful to expose that feature in a
command-line tool.
This should speed up game generation, because now we don't have to run
the solver _twice_ whenever we want to check that the grid has exactly
the intended difficulty. Instead, we can just run it once and check
the max_diff output.
Printing is only available in GTK versions >= 2.10. We can only embed
the page setup dialog on GTK >= 2.18, so on a GTK version less than
that, we must use a separate page setup dialog.
In GTK, printing is usually done one page at a time, so also modify
printing.c to allow printing of a single page at a time.
Create a separate drawing API for drawing to the screen and for
printing. Create a vtable for functions which need to be different
depending on whether they were called from the printing or drawing
API.
When a function is called from the printing API, it is passed a
separate instance of the frontend than if it were called from the
drawing API. In that instance of the frontend, an appropriate vtable
is available depending on whether it was called from the printing or
drawing API.
The low-level functions used for printing are enabled even if printing
is not enabled. This is in case we ever need to use them for something
other than printing with GTK. For example, using Cairo as a printing
backend when printing from the command line. Enabling the low-level
functions even when GTK printing is not available also allows them to
be compiled under as many build settings as possible, and thus lowers
the chance of undetected breakage.
Move the definition of ROOT2 from ps.c to puzzles.h so other files can
use it (gtk.c needs it for hatching).
Also add myself to the copyright list.
[Committer's note: by 'printing', this log message refers to the GTK
GUI printing system, which handles selecting a printer, printing to a
file, previewing and so on. The existing facility to generate
printable puzzles in Postscript form by running the GTK binaries in
command-line mode with the --print option is unaffected. -SGT]
Asher Gordon points out that when Michael Quevillon was added to the
LICENCE file in commit 8af0c2961, he didn't also make it in to the
copy of the same list in puzzles.but.
When no icons are available, n_xpm_icons will be 0, and
menu_about_event() will try to access xpm_icons[n_xpm_icons-1]. Since
n_xpm_icons is 0, this becomes xpm_icons[-1] which is an invalid
value, causing a segfault.
Instead, check if n_xpm_icons is 0, and if so, don't pass any icon to
gtk_show_about_dialog().
I had occasion recently to want to take a puzzle screenshot on a
machine that didn't have the GTK3 libraries installed, but is advanced
enough to build the GTK2+Cairo version of the puzzles. That _ought_ to
be good enough to take screenshots using bare Cairo without GTK; I
think the only reason why I didn't bother to support it before is
because on GTK2, frontend_default_colours() queries the widget style
to choose a shade of grey. But we have a fixed fallback shade of grey
to use on GTK3, so it's easy to just use that same fallback in
headless GTK2.
One of these days I should sit down and work out exactly when a run of
autoconf generates an autom4te.cache directory, and why it can
suddenly turn up unexpectedly one day after years of never needing to
put it in .gitignore!
Apparently gcc 9 is clever enough to say 'Hey, runtime field width in
an sprintf targeting a fixed-size buffer!', but not clever enough to
notice that the width was computed earlier as the max of lots of
default-width sprintfs into the same buffer (so _either_ it's safe, or
else - on a hypothetical platform with a 263-bit int - the damage was
already done).
Added a bounds check or two to keep it happy.
This change doesn't alter the overall power of the Dominosa solver; it
just moves the boundary between Hard and Extreme so that fewer puzzles
count as Hard, and more as Extreme. Specifically, either of the two
cases of set analysis potentially involving a double domino with both
squares in the set is now classed as Extreme.
The effects on difficulty are that Hard is now easier, and Extreme is
at least easier _on average_. But the main purpose is the effect on
generation time: before this change, Dominosa Extreme was the slowest
puzzle present to generate in the whole collection, by a factor of
more than three. I think the forcing-chain deductions just didn't make
very many additional grids soluble, so that the generator had to try a
lot of candidates before finding one that could be solved using
forcing chains but not with all the other techniques put together.
This is a technique I've had on the todo list (and been using by hand)
for years: a domino can't be placed if it would divide the remaining
area of the grid into pieces containing an odd number of squares.
The findloop subsystem is already well set up for finding domino
placements that would divide the grid, and the new is_bridge query
function can now tell me the sizes of the area on each side of the
bridge, which makes it trivial to implement this deduction by simply
running findloop and iterating over the output array.
This one tells you if a graph edge _is_ a bridge (i.e. it has inverted
sense to the existing is_loop_edge query). But it also returns
auxiliary data, telling you: _if_ this edge were removed, and thereby
disconnected some connected component of the graph, what would be the
sizes of the two new components?
The data structure built up by the algorithm very nearly contained
enough information to answer that already: because we assign
sequential indices to all the vertices in a traversal of our spanning
forest, and any bridge must be an edge of that forest, it follows that
we already know the size of _one_ of the two new components, just by
looking up the (minindex,maxindex) values for the vertex at the child
end of the edge.
To determine the other subcomponent's size, we subtract that from the
size of the full component. That's not quite so easy because we don't
already store that - but it's trivial to annotate every vertex's data
with a pointer back to the topmost node of the spanning forest in its
component, and then we can look at the (minindex,maxindex) pair of
that. So now we know the size of the original component and the size
of one of the pieces it would be split into, so we can just subtract.
We've already spotted when a domino occurs twice in the _same_ forcing
chain. But now we also spot when it occurs twice in the same _pair_ of
complementary forcing chains, one in each of the two options. Then it
must appear in one of those two places, and hence, can't appear
anywhere else.
This is necessary to solve the following test puzzle that someone sent
me in 2006 and I just recovered from my email archive:
6:65111036543150325534405211110064266620632365204324442053
Without this new deduction, the previous solver can't solve that
puzzle even at full power, but the half-solved state it leaves the
grid in has an obvious move in the top right corner (placing the 6-2
domino vertically in that corner forces two 3-0s to its left). Now
that kind of move can be made too, and the solver can handle this
puzzle (grading it as Hard).
In other front ends, Shift-click is an alternative to the middle
button, and Ctrl-click the right button. Apparently I completely
forgot to implement this in the JS front end. Better late than never.
I realised that even with the extra case for a double domino
potentially using two squares in a set, I'd missed two tricks.
Firstly, if the double domino is _required_ to use two of the squares,
you can rule out any placement in which it only uses one. But I was
only ruling out those in which it used _none_.
Secondly, if you have the same number of squares as dominoes, so that
the double domino _can_ but _need not_ use two of the squares, then I
previously thought there was no deduction you could make at all. But
there is! In that situation, the double does have to use _one_ of the
squares, or else there would be only the n-1 heterogeneous dominoes to
go round the n squares. So you can still rule out placements for the
double which fail to overlap any square in the set, even if you can't
(yet) do anything about the other dominoes involved.
Now we don't just ensure that alloc_try_hard arranged a confounder for
every domino; we also make sure that the full Basic-mode solver can't
place even a single domino with certainty.
Now, as well as grading a puzzle by the highest difficulty it needed
during its solution, I can check _how much_ of a given puzzle is
soluble if you remove the higher difficulty levels.
The new Hard and Extreme difficulty levels allow you to make a start
on a grid even if there is no individual domino that can be easily
placed. So it's more elegant to _enforce_ that, in the same way that
Hard-mode Slant tries to avoid the initial toeholds that Easy mode
depends on.
Hence, I've refactored the domino layout code into several alternative
versions. The new one, enabled at Hard mode and above, arranges that
every domino has more than one possible position, so that you have to
use some kind of hard deduction to even get off the ground.
While I'm at it, the old layout system has had a makeover: in the
course of its refactoring, I've arranged to iterate over the domino
values _and_ locations in random order, instead of going over the
locations in grid order. The idea is that that might eliminate a
directional bias. But more importantly, it changes the previous
meaning of random number seeds.
I decided not to go all the way up to order-9 Extreme, because that
takes a lot of CPU to generate. People can select it by hand if they
don't mind that.
As with several other puzzles, the harder difficulty levels turn out
to be impossible to generate at very small sizes, which I fudge by
replacing them with the hardest level actually feasible.
This technique borrows its name from the Solo / Map deduction in which
you find a path of vertices in your graph each of which has two
possible values, such that a choice for one end vertex of the chain
forces everything along it. In Dominosa, an approximate analogue is a
path of squares each of which has only two possible domino placements
remaining, and it has the extra-useful property that it's
bidirectional - once you've identified such a path, either all the odd
domino placements along it must be right, or all the even ones. So if
you can find an inconsistency in either set, you can rule out the
whole lot and settle on the other set.
Having done that basic analysis (which turns out to be surprisingly
easy with an edsf to help), there are multiple ways you can actually
rule out one of the same-parity chains. One is if the same domino
would have to appear twice in it; another is if the set of dominoes
that the chain would place would rule out all the choices for some
completely different square. There are probably others too, but those
are the ones I've implemented.
I'm about to have a need to sort an array based on auxiliary data held
in a variable that's not globally accessible, so I need a sort routine
that accepts an extra parameter and passes it through to the compare
function.
Sorting algorithm is heapsort, because it's the N log N algorithm I
can implement most reliably.
In particular, reorganise the priorities. I think forcing chains are
the most important thing that still wants adding; the parity search
would be easy enough but I don't know how often it would actually be
_useful_; the extended set analysis would be nice but I don't know how
to make it computationally feasible.
I've always had the vague idea that the usual set analysis deduction
goes wrong when there are two adjacent squares, because they might be
opposite ends of the same domino and mess up the count. But I just
realised that actually you can correct for that by adjusting the
required count by one: if you have four 0 squares which between them
can only be parts of 0-0, 0-1 and 0-2, then the only way this can work
is if two of them are able to be the 0-0 - but in that case, you can
still eliminate those dominoes from all placements elsewhere. So set
analysis _can_ work in that situation; you just have to compensate for
the possible double.
(This enhanced form _might_ turn out to be something that needs
promoting into a separate difficulty level, but for the moment, I'll
try leaving it in Hard and seeing if that's OK.)
This is another thing I've been doing with my own brain for ages as a
more interesting alternative to scouring the grid for the simpler
deduction that must be there somewhere - but now the solver can
understand it too, so it can generate puzzles that _need_ it (or at
least need something beyond the simpler strategies it understands).
Currently, there are just two difficulty levels. 'Basic' is the same
as the old solver; 'Trivial' is the subset that guarantees the puzzle
can be solved using only the two simplest deductions of all: 'this
domino can only go in one place' and 'only one domino orientation can
fit in this square'.
The solver has also acquired a -g option, to grade the difficulty of
an input puzzle using this system.
The new solver should be equivalent to the previous solver's
intelligence level, but it's more usefully split up into basic
data-structure maintenance and separate deduction routines that you
can omit some of. So it's a better basis to build on when adding
further deductions or dividing the existing ones into tiers.
The new solver also produces much more legible diagnostics, when the
command-line solver is run in -v mode.
I've made the existing optional solver diagnostics appear as the
verbose output of the solver program. They're not particularly legible
at the moment, but they're better than nothing.
If you drag an arrow on to a square which is already filled in as part
of a completed region, or whose counterpart is filled in, or whose
counterpart is actually a dot, then the game can't actually place a
double arrow. Previously, it didn't find that out until execute_move
time, at which point it was too late to prevent a no-op action from
being placed on the undo chain.
Now we do those checks in interpret_move, before generating the move
string that tries to place the double arrow in the first place. So
execute_move can now enforce by assertion that arrow-placement moves
it gets are valid.
Fixes an assertion failure in which you move the keyboard cursor to a
peg, press Enter to indicate that you're about to jump it to
somewhere, and then instead execute an undo or redo action which
replaces the peg with a hole. Thanks to Vitaly Ostrosablin for the
report.
I've only just found out that it has the effect of treating the argv
words not as plain filenames, but as arguments to Perl default 'open',
i.e. if they end in | then the text before that is treated as a
command. That's not what was intended!
