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Dominosa: update the to-do list.

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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.
This commit is contained in:
Simon Tatham
2019-04-04 23:51:35 +01:00
parent 453a2c1ca8
commit b0c73d5c58
1 changed files with 47 additions and 25 deletions
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dominosa.c
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@ -5,33 +5,55 @@
*/ */
/* /*
* TODO: * Further possible deduction types in the solver:
* *
* - improve solver so as to use more interesting forms of * * identify 'forcing chains', in the sense of any path of cells
* deduction * each of which has only two possible dominoes to be part of, and
* each of those rules out one of the choices for the next cell.
* Such a chain has the property that either all the odd dominoes
* are placed, or all the even ones are placed; so if either set of
* those introduces a conflict (e.g. a dupe within the chain, or
* using up all of some other square's choices), then the whole set
* can be ruled out, and the other set played immediately.
* *
* * rule out a domino placement if it would divide an unfilled * * rule out a domino placement if it would divide an unfilled
* region such that at least one resulting region had an odd * region such that at least one resulting region had an odd area
* area * + Tarjan's bridge-finding algorithm would be a way to find
* + Tarjan's bridge-finding algorithm would be a way to find * domino placements that split a connected region in two: form
* domino placements that split a connected region in two: * the graph whose vertices are unpaired squares and whose edges
* form the graph whose vertices are unpaired squares and * are potential (not placed but also not ruled out) dominoes
* whose edges are potential (not placed but also not ruled * covering two of them, and any bridge in that graph is a
* out) dominoes covering two of them, and any bridge in that * candidate.
* graph is a candidate. * + Then, finding any old spanning forest of the unfilled squares
* + Then, finding any old spanning forest of the unfilled * should be sufficient to determine the area parity of the
* squares should be sufficient to determine the area parity * region that any such placement would cut off.
* of the region that any such placement would cut off. * + A more advanced form of this: if you have a region with _two_
* ways in and out of it, then you can at least decide on the
* relative parity of the two (either 'these two edges both
* bisect dominoes or neither do', or 'exactly one of these
* edges bisects a domino'). And occasionally that can be enough
* to let you rule out one of the two remaining choices.
* - For example, maybe if both edges bisect a domino then
* those two dominoes would also be both the same.
* - Or perhaps between them they rule out all possibilities
* for some other square.
* - Or perhaps, on purely geometric grounds, they would box in
* a square to the point where it ended up having to be an
* isolated singleton.
* *
* * identify 'forcing chains', in the sense of any path of cells * * possibly an advanced version of set analysis which doesn't have
* each of which has only two possible dominoes to be part of, * to start from squares all having the same number? For example,
* and each of those rules out one of the choices for the next * if you have three mutually non-adjacent squares labelled 1,2,3
* cell. Such a chain has the property that either all the odd * such that the numbers adjacent to each are precisely the other
* dominoes are placed, or all the even ones are placed; so if * two, then set analysis can work just fine in principle, and
* either set of those introduces a conflict (e.g. a dupe within * tells you that those three squares must overlap the three
* the chain, or using up all of some other square's choices), * dominoes 1-2, 2-3 and 1-3 in some order, so you can rule out any
* then the whole set can be ruled out, and the other set played * placements of those elsewhere.
* immediately. * + the difficulty with this is how you avoid it going painfully
* exponential-time. You can't iterate over all the subsets, so
* you'd need some kind of more sophisticated directed search.
* + and the adjacency allowance has to be similarly accounted
* for, which could get tricky to keep track of.
*/ */
#include <stdio.h> #include <stdio.h>