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| PSBlake
| Joined: 18 Jan 2006 | Posts: 8 | : | | Items |
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Posted: Sat Jan 28, 2006 5:10 am Post subject: |
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gsf wrote: |
so to decode you would need a dictionary of 5,472,730,538 canonical puzzles
or a function that produces a canonical puzzle given its label |
This is always the tradeoff in computer science: Space or speed. Do you want a smaller app, or a quicker one? In this case, I'm examining the intellectual challenge of a smaller app. In fact, the smallest.
gsf wrote: | but that would only give you a puzzle equivalent to the original
to get the exact original you would also need the row/col permutations
and the cell label permutation |
I'm missing the distinction here: Are you saying that (in simpler terms) for a 2x2 sudoku:
is not distinct from:
Because the 2 groupings are of the same shape?
I wasn't aware of this, if it is the case.
If it is, by my reasoning (of which I am by no means certain) then for any 9x9 Sudoku, there should be 9! (362880) essentially identical Sudoku differing in numbers, but sharing identically shaped groupings. That means I need 19 bits to represent them. I've already got 9 spare bits from the previous algorithm. Rounded to the nearest byte makes 2 bytes, making my representation 16 bytes, with some non-contiguous data fields. Messy, but small.
As for competing with existing compression formats, I'm beating them. |
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| gsf
| Joined: 18 Aug 2005 | Posts: 411 | : | Location: NJ USA | Items |
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Posted: Sat Jan 28, 2006 2:46 pm Post subject: |
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PSBlake wrote: | gsf wrote: |
so to decode you would need a dictionary of 5,472,730,538 canonical puzzles
or a function that produces a canonical puzzle given its label |
This is always the tradeoff in computer science: Space or speed. Do you want a smaller app, or a quicker one? In this case, I'm examining the intellectual challenge of a smaller app. In fact, the smallest.
gsf wrote: | but that would only give you a puzzle equivalent to the original
to get the exact original you would also need the row/col permutations
and the cell label permutation |
I'm missing the distinction here: Are you saying that (in simpler terms) for a 2x2 sudoku:
is not distinct from:
Because the 2 groupings are of the same shape?
I wasn't aware of this, if it is the case.
If it is, by my reasoning (of which I am by no means certain) then for any 9x9 Sudoku, there should be 9! (362880) essentially identical Sudoku differing in numbers, but sharing identically shaped groupings. |
read up on sudoku counting
there are 6670903752021072936960 completed grids
but only 5472730538 up to isomorphism
encoding a grid in the 5472730538 only gets a member of a class of possibly >1 grids
along with that encoding must be encoded the row/col cell-value permutations
that transform the class member to the original grid that was to be encoded |
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| gypsy fly
| Joined: 06 Mar 2006 | Posts: 18 | : | Location: Portland OR USA | Items |
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Posted: Tue Mar 14, 2006 9:43 pm Post subject: |
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I can see that this discussion is several months old. Nevertheless, I'll bump it up. Here's a txt format that I decided to implement for a sudoku worksheet program.
This is a 9x9. The first character defines data type. C for citing the source, D for difficulty, Period (.) for puzzle in column sequence with each new line being the rows.
After the second "." separator is a relative boolean string for change/no change (i.e. 0 means a given, 1 is player input). The player saves versions with a "Save As" and any valid naming convension of their choice.
CThe Oregonian 03/10
D5
.000409670.111010001
.000076900.111100011
.000000003.111111110
.000001740.111110001
.640000018.001111100
.021600000.100011111
.100000000.011111111
.004320000.110001111
.062904000.100010111
A partially completed puzzle is saved thusly:
CThe Oregonian 03/10
D5
.218439675.111010001
.400076902.111100011
.006002403.111111110
.000201746.111110001
.640000128.001111100
.021640009.100011111
.100060294.011111111
.004320061.110001111
.062914007.100010111
I'm going to add more data type as the need arises. |
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