understandable snarfable killer cages

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understandable snarfable killer cages

Postby tarek » Wed Jun 04, 2008 11:17 pm

would this be understandable anyone ?
Code: Select all
 v < 16| <20 7 | < 6 < 
17 > > |22 ^ 26| < < ^ 
10 ^ > | 6 ^ 21| < ^13 
-------+-------+------
 ^ ^ ^ |42 > v | ^ ^ ^ 
11 < < | ^ 3 v | > >18 
10 v v | ^ < < |16 v 9 
-------+-------+------
 ^ v > |12 19> | ^ v ^ 
17 > > |31 ^ 23| < <14 
 ^ < 9 | < ^ 7 | < > ^

Dec 29th 2006: SudokuEd's Bullseye 3 (aka Assassin 30V2.1)

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Last edited by tarek on Thu Jun 05, 2008 10:19 am, edited 1 time in total.
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Postby udosuk » Thu Jun 05, 2008 7:19 am

That's a very concise representation of a killer. The only previous text representation I know of is Ruud's one:
Code: Select all
.-----.-----.--.-----.-----.
|17   |16   |20|7    |6    |
|  .--'-----:  :-----'--.  |
|  |22      |  |26      |  |
:--:  .-----:  :-----.  :--:
|10|  |6    |  |21   |  |13|
|  |  |  .--'--'--.  |  |  |
|  |  |  |42      |  |  |  |
:--'--'--:  .--.  :--'--'--:
|11      |  |3 |  |18      |
:--.--.--:  '--'  :--.--.--:
|10|31|12|        |16|23|9 |
|  |  |  '--.--.--'  |  |  |
|  |  |     |19|     |  |  |
:--:  '-----:  :-----'  :--:
|17|        |  |        |14|
|  '--.-----:  :-----.--'  |
|     |9    |  |7    |     |
'-----'-----'--'-----'-----'

... which is a bit more presentable than yours.

Of course there is the PS code:

3x3::k:4353:4353:4098:4098:5123:1796:1796:1541:1541:4353:5638:5638:5638:5123:6663:6663:6663:1541:2568:5638:1545:1545:5123:5386:5386:6663:3339:2568:5638:1545:10764:10764:10764:5386:6663:3339:2830:2830:2830:10764:781:10764:4623:4623:4623:2576:7953:3090:10764:10764:10764:4115:5908:2325:2576:7953:3090:3090:4886:4115:4115:5908:2325:4375:7953:7953:7953:4886:5908:5908:5908:3608:4375:4375:2329:2329:4886:1818:1818:3608:3608:

... which is already the default code among killer solving programs.

Here is the pic:

Image

You ought to be proud of that puzzle. It defies my current version of JSudoku, who is one of the most powerful killer solving software in the market.:!:

Triple click to see the unique solution I wrote:849762531
536491872
712358649
381529764
425637198
967814253
173245986
254986317
698173425

However, it contains a singlet cage, which most killer players frown upon. But of course you can take it away and pose it as a "zero killer".:idea:
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Postby udosuk » Thu Jun 05, 2008 8:13 am

Here is a 162-char text representation of this puzzle:
Code: Select all
17 <16 <20 7 < 6 <
 ^22 < < ^26 < < ^
10 ^ 6 < ^21 < ^13
 ^ ^ ^42 < < ^ ^ ^
11 < < ^ 3 ^18 < <
103112 ^ < ^1623 9
 ^ ^ ^ <19 > ^ ^ ^
17 ^ < < ^ > > ^14
 ^ < 9 < ^ 7 < > ^

To make it more "backward compatible", I suggest the following 2 rules:
  1. All cage sums must appear in the leftmost cell of the topmost row of that cage.
  2. When choosing arrows we always uses the order of preference: ^ < > v.
Of course there are also "diagonal cages". So I suggest we use the 4 symbols: ` ' , . to represent UL,UR,DL,DR arrows respectively, in that order of preference.

And if we use A..Z to represent 10..35, a..j to represent 36..45, we can have an 81-char representation:
Code: Select all
H<G<K7<6<
^M<<^Q<<^
A^6<^L<^D
^^^g<<^^^
B<<^3^I<<
AVC^<^GN9
^^^<J>^^^
H^<<^>>^E
^<9<^7<>^

An 81-char text code for a killer sudoku. Now who'd have thought of that? Genius concept tarek!:D
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Postby tarek » Thu Jun 05, 2008 9:41 am

The good thing is that it could (if a single charachter is used to represent the cage sum) be represented in line format as well.

KiMo is ideal because it only has 0-10:D

There will be some problems with diagonal cages unless there are some arrows that go diagonally:D

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Postby udosuk » Thu Jun 05, 2008 11:02 am

tarek wrote:The good thing is that it could (if a single charachter is used to represent the cage sum) be represented in line format as well.

Yes, exactly.:)

tarek wrote:KiMo is ideal because it only has 0-10:D

More like 0..9, but I get the point. Note for a "zero killer" a sum of 0 can be used to represent a "zero cage" i.e. a cage without a sum.

tarek wrote:There will be some problems with diagonal cages unless there are some arrows that go diagonally:D

But there actually are: ↖↗↙↘:!:

Just not everyone's computer can display them. Therefore I suggest the use of ` ' , . which are also very easily entered. It's just a bit non-intuitive.:idea:
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Postby tarek » Thu Jun 05, 2008 11:48 am

udosuk wrote:
tarek wrote:KiMo is ideal because it only has 0-10:D

More like 0..9, but I get the point.
As you know, I meant 0-9:D

interesting with the diagonal characters.

Code: Select all
H<G<K7<6<^M<<^Q<<^A^6<^L<^D^^^g<<^^^B<<^3^I<<AVC^<^GN9^^^<J>^^^H^<<^>>^E^<9<^7<>^

H<G<K7<6<
^M<<^Q<<^
A^6<^L<^D
^^^g<<^^^
B<<^3^I<<
AVC^<^GN9
^^^<J>^^^
H^<<^>>^E
^<9<^7<>^


so essentially you can get a compact way for representation that is slightly better than what is on offer at the moment, & it should be good for copy & pasting into a solver ... Possibly it can be used for archiving & canonicalizing.

By the way, the puzzle is by SudokuEd "Bullseye 3 (aka Assassin 30V2.1)" ... I used it to demonstrate the idea as it contained small & circular cages. Apologies for not pointing it out from the start (I've added it to the head post too)... I haven't posted any Killer Sudokus .... My coding lags behind my chain of thoughts .... My coding is going next to caged variants the overlapping sudokus.

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Postby tarek » Thu Jun 05, 2008 5:15 pm

to standardize it (returning to udosuk's post):
1. cage sum should occupy the cage cell with the smallest address (leftmost if line format is chosen)
2. cage cell should point towards the cell that contains the sum of that cage (<>^v)
3. looping cages should adopt a clockwise direction.
4. a single character to represent cage sums can be used 0-9 (0 to 9), A-Z (10 to 35), a-j (36 to 45)

udosuk mentioned (,.'`) to represent diagonal directions, if no better suggestion is brought forward then it should be used as standard.

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Postby udosuk » Fri Jun 06, 2008 9:05 am

tarek wrote:2. cage cell should point towards the cell that contains the sum of that cage (<>^v)
3. looping cages should adopt a clockwise direction.

I'm not too sure about this. Looping cages aren't that common in killers, and I don't think these 2 rules run well in the programming aspect.

My view is, since we assume all cages are physically connected, for a non-cage-sum cell of a cage, one or more of its 8 neighbours must be of the same cage. Then the arrow should just point to the neighbour with the smallest address. (If it's not diagonal then the intuitive way is to point to the smallest address of the 4 orthogonal neighbours, thus the order "^ < > v".):idea:

tarek wrote:4. a single character to represent cage sums can be used 0-9 (0 to 9), A-Z (10 to 35), a-j (36 to 45)

JC has raised the concern that people might confuse the capital V (31) with the small v (downward arrow). Any better suggestion to avoid this confusion? Note according to my order of the arrows "v" doesn't appear very often.
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Postby tarek » Fri Jun 06, 2008 1:08 pm

udosuk wrote:
tarek wrote:4. a single character to represent cage sums can be used 0-9 (0 to 9), A-Z (10 to 35), a-j (36 to 45)

JC has raised the concern that people might confuse the capital V (31) with the small v (downward arrow). Any better suggestion to avoid this confusion? Note according to my order of the arrows "v" doesn't appear very often.
We could disregard the captal "V". just like some letters on the telephone numbers as they can be confused with numbers. See: Alphabetic mnemonic system

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Postby tarek » Fri Jun 06, 2008 7:53 pm

I noticed that you carried the idea for discussion to other forums, I thank you for that:D

This method can of course work for overlapping puzzles (Gattai type puzzles) with parts of the cage in the overlapping areas.

it wouldn't work for overlapping cages or remote cages ....

I would still try to push for it to be used a string of 81 characters without even an identifier:!:

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Postby udosuk » Sat Jun 07, 2008 8:51 am

tarek wrote:I would still try to push for it to be used a string of 81 characters without even an identifier:!:

I guess for practical purposes there is a need for an identifier of one or more characters. But it's indeed a very elegant concept to be able to represent a normal killer with non-overlapping, physically connected (orthogonal or diagonal) cages using an 81-char text line!:)
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Postby HATMAN » Tue Jun 10, 2008 10:24 pm

Well guys - weird but magic - I accept that discontinuous cages are impossible to code this way, and given I’m the only one who uses them I’ll sign on.
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Postby Jean-Christophe » Wed Jun 11, 2008 7:45 am

udosuk wrote:
tarek wrote:I would still try to push for it to be used a string of 81 characters without even an identifier:!:

I guess for practical purposes there is a need for an identifier of one or more characters. But it's indeed a very elegant concept to be able to represent a normal killer with non-overlapping, physically connected (orthogonal or diagonal) cages using an 81-char text line!:)


I've added support in JSudoku for the 81 characters format (not released yet).
An identifier would have made the format easier to recognize but is not an absolute necessity. I currently detect this format when it contains at least one '<' and one '^'. When exporting, I follow Udosuk's order of preference which are maybe too restricted. For some cases, it's easier and faster for a program to scan and export if we allow '<' instead of '^' when both are valid.
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Postby tarek » Wed Jun 11, 2008 10:02 am

great news JC:D

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