The New Sudoku Players' Forum

[JasonLion]

Thanks to denis_berthier we now have PDF files of posts from this topic made between July 2009 and January 2010.

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[yzfwsf]

As I mentioned in the previous post, #187 (SER = 9.4) is one of the two grids in the top1465 collection that can't be solved by nrczt-whips but can by nrczt-braids (as can be verified with a simple T&E procedure).

First tentative solution with whips:
***** SudoRules version 13.7w-bis *****
6.....3...5..9..8...2..6..98.....7...7..5..4......1..51..3..5...4..2..6...8..7..2
hidden-singles ==> r4c3 = 5, r7c2 = 2
interaction row r4 with block b5 for number 4 ==> r6c5 <> 4, r6c4 <> 4
nrczt-whip-cn[11] {n4 n1}r3c7 - {n1 n9}r9c7 - {n9 n8}r8c7 - n8{r8c9 r5c9} - n1{r5c9 r5c3} - n1{r4c2 r1c2} - n9{r1c2 r1c3} - n9{r8c3 r8c1} - {n9 n5}r8c6 - n1{r9c5 r8c4} - {n1r9c5 .} ==> r2c7 <> 4
;;; end common part
nrczt-whip[21] n8{r8c9 r7c9} - n4{r7c9 r9c7} - {n4 n1}r3c7 - n1{r8c7 r8c9} - n7{r8c9 r7c8} - {n7 n5}r3c8 - {n5 n2}r1c8 - n1{r1c8 r4c8} - n1{r4c2 r1c2} - n9{r1c2 r1c3} - {n9 n6}r7c3 - {n6 n4}r7c5 - {n4 n9}r7c6 - {n9 n5}r8c6 - n5{r9c4 r1c4} - n1{r1c4 r2c4} - n2{r2c4 r2c6} - n2{r4c6 r4c4} - n9{r4c4 r4c2} - {n9 n3}r9c2 - {n3r9c8 .} ==> r8c4 <> 8
GRID 187 NOT SOLVED. 55 VALUES MISSING.
Here again, we notice a very long whip (length 21), an indication that this puzzle has few chains.

Let's now solve it with braids:
***** SudoRules version 13.7wbis-B2 *****
6.....3...5..9..8...2..6..98.....7...7..5..4......1..51..3..5...4..2..6...8..7..2
;;; Same resolution path down to "end common part"
;;; We now get braids much shorter than the whip obtained in the previous path:
nrczt-braid-rc[11] n3{r8c9 r9c8} - {n7 n9}r7c8 - {n3 n2}r6c8 - n2{r1c8 r2c7} - n6{r2c7 r2c9} - {n2 n1}r4c8 - n1{r2c9 r1c9} - n1{r1c2 r3c2} - n1{r1c5 r9c5} - n4{r9c7 r7c9} - {n4r9c7 .} ==> r8c9 <> 7
interaction row r8 with block b7 for number 7 ==> r7c3 <> 7
nrczt-braid-cn[4] {n6 n9}r7c3 - n4{r6c3 r6c1} - n9{r9c1 r5c1} - {n2r6c1 .} ==> r6c3 <> 6
nrczt-braid-cn[11] n7{r6c4 r6c5} - n8{r6c5 r6c7} - n6{r6c7 r6c2} - n2{r4c6 r4c8} - n2{r6c7 r2c7} - n6{r2c7 r5c7} - n9{r6c7 r6c8} - n3{r6c8 r9c8} - n2{r6c1 r5c1} - n9{r9c1 r9c2} - {n9r9c1 .} ==> r6c4 <> 2
nrczt-braid-rc[12] n1{r9c4 r9c5} - {n1 n4}r3c7 - n4{r9c5 r9c4} - n6{r9c4 r9c2} - {n6 n9}r7c3 - n9{r1c3 r1c2} - n1{r3c2 r4c2} - n1{r9c8 r1c8} - {n4 n7}r1c9 - {n9 n3}r6c2 - {n1 n4}r1c3 - {n4r6c3 .} ==> r3c4 <> 1
;;; Even with braids activated, the next eliminations use only whips
nrczt-whip-cn[13] {n1 n4}r3c7 - {n4 n9}r9c7 - {n9 n8}r8c7 - n8{r8c9 r5c9} - n1{r5c9 r5c3} - n6{r5c3 r7c3} - n9{r7c3 r7c6} - n8{r7c6 r1c6} - n8{r3c5 r3c2} - n1{r3c2 r3c5} - n3{r3c5 r3c1} - n3{r5c1 r5c6} - {n3r6c5 .} ==> r2c7 <> 1
nrczt-whip-cn[8] n1{r5c9 r5c3} - n1{r2c3 r2c4} - n1{r9c4 r9c5} - n1{r9c8 r8c7} - {n1 n4}r3c7 - n4{r9c7 r9c4} - n6{r9c4 r9c2} - {n6r7c3 .} ==> r4c9 <> 1
nrczt-whip-rc[6] n9{r1c2 r1c3} - {n9 n6}r7c3 - n6{r9c2 r4c2} - {n6 n3}r4c9 - n3{r8c9 r9c8} - {n3r9c2 .} ==> r6c2 <> 9
nrczt-whip-cn[8] n1{r4c8 r4c2} - n1{r3c2 r3c5} - {n1 n4}r3c7 - {n4 n7}r1c9 - {n7 n6}r2c9 - {n6 n3}r4c9 - n3{r4c5 r6c5} - {n7r6c5 .} ==> r1c8 <> 1
nrczt-whip-rn[11] n6{r9c5 r9c4} - n6{r9c2 r4c2} - {n6 n3}r4c9 - n3{r4c6 r5c6} - {n3 n4}r4c5 - n4{r9c5 r7c6} - {n4 n2}r2c6 - n2{r2c7 r1c8} - {n2 n9}r6c8 - {n6 n9}r7c3 - {n6r7c3 .} ==> r6c5 <> 6
;;;; (I checked that a solution with whips only can be obtained from here, which shows that this puzzle needs only a few eliminations to be solvable by whips).
nrczt-braid-bn[11] n6{r9c2 r7c3} - n6{r7c5 r9c5} - {n6 n3}r4c9 - {n6 n3}r6c2 - n3{r6c5 r3c5} - n1{r9c5 r1c5} - n1{r4c2 r3c2} - n3{r5c9 r5c6} - n7{r3c5 r6c5} - n8{r6c4 r3c4} - {n8r6c4 .} ==> r4c2 <> 6
nrczt-braid-rc[8] n6{r5c3 r6c2} - {n6 n3}r4c9 - n3{r8c9 r9c8} - {n6 n9}r9c2 - {n9 n1}r4c2 - n1{r5c9 r5c7} - {n9 n4}r9c7 - {n4r3c7 .} ==> r5c9 <> 6
;;; For shorter computation times, I de-activated braids here. There's nothing new in the sequel (whips of length <= 12). Details can be seen on my Web pages.



As a conclusion of this example and the previous ones:

On the positive side:
- braids can lead to solutions that can't be found when only whips are used (which is not a scoop, as they are more general),
- in all the cases, braids can lead to solutions with much shorter maximum length than whips (in this example braid[13] instead of the whip[21] that didn't even lead to a solution),
- the T&E vs braids theorem is useful in practice as an oracle: using it, we can be confident that there'll be a solution with braids.

On the negative side:
- from a programming POV, useful braids are more difficult to find than whips because there are more useless ones,
- braids are less "beautiful" than whips as there is some branching (although mild compared to some solutions proposed elsewhere with very complex nets),
- from a player POV, I think some strategies of latest branching may make them easier to find than for a computer.

This last idea is the same as the one I explained long ago for t- or z- candidates: these candidates are impurities in what would otherwise be pure xy- or nrc- chains. We use them when we can't do otherwise. This is (conceptually) how rules with t- and/or z- candidates are implemented in SudoRules.
The difference is that for branching, the way I've found for doing this efficiently is still partial.
(I've solved memory oveflow problems but computation times remain very long).

Is there a typo or bug?

[denis_berthier]

.
SudoRules version 13.7wbis dates back to 2007. That was before the rules were made generic and at a time when each rule was written manually. So, there may have been bugs in the large size chains. This is now impossible, as all the chains are created by a generator: a bug in a long whip would also appear in shorter ones and would obviously have appeared after solving tens of millions of puzzles (not only Sudoku).

{n9 n5}r8c6 - n1{r9c5 r8c4}, or better r8c6{n9 n5}- b8n1{r9c5 r8c4}, is impossible in a whip, because n5r8c6 and n1r9c5 are not linked; whether it was a bug or a typo 17 years ago, I can't tell.
As for n8{r8c9 r7c9} - n4{r7c9 r9c7}, I can't see any problem, except that I'd now write it as: b9n8{r8c9 r7c9} - b9n4{r7c9 r9c7}

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 6      189    1479   ! 124578 1478   2458   ! 3      1257   147    !
   ! 347    5      1347   ! 1247   9      234    ! 1246   8      1467   !
   ! 347    138    2      ! 14578  13478  6      ! 14     157    9      !
   +----------------------+----------------------+----------------------+
   ! 8      1369   5      ! 2469   346    2349   ! 7      1239   136    !
   ! 239    7      1369   ! 2689   5      2389   ! 12689  4      1368   !
   ! 2349   369    3469   ! 26789  3678   1      ! 2689   239    5      !
   +----------------------+----------------------+----------------------+
   ! 1      2      679    ! 3      468    489    ! 5      79     478    !
   ! 3579   4      379    ! 1589   2      589    ! 189    6      1378   !
   ! 359    369    8      ! 14569  146    7      ! 149    139    2      !
   +----------------------+----------------------+----------------------+
199 candidates

There is a solution with whips for this puzzle, in W20:

Hidden Text: Show

whip[11]: r3c7{n4 n1} - r9c7{n1 n9} - r8c7{n9 n8} - c9n8{r8 r5} - r5n1{c9 c3} - c2n1{r4 r1} - r1n9{c2 c3} - b7n9{r8c3 r8c1} - r8c6{n9 n5} - r8c4{n5 n1} - b2n1{r1c4 .} ==> r2c7≠4
whip[20]: r3c7{n1 n4} - c9n4{r2 r7} - r9c7{n4 n9} - r9c8{n9 n3} - r9c2{n3 n6} - r7n6{c3 c5} - r7n8{c5 c6} - r7n9{c6 c3} - r1n9{c3 c2} - r6c2{n9 n3} - r4c2{n3 n1} - r5n1{c3 c9} - r5n3{c9 c6} - c5n3{r6 r3} - r3c1{n3 n7} - c3n7{r2 r8} - c3n3{r8 r2} - r2n1{c3 c4} - r2n7{c4 c9} - r1c9{n7 .} ==> r8c7≠1
whip[7]: b9n3{r8c9 r9c8} - b9n1{r9c8 r9c7} - b9n4{r9c7 r7c9} - r1c9{n4 n1} - r8n1{c9 c4} - r2n1{c4 c3} - r5n1{c3 .} ==> r8c9≠7
whip[1]: r8n7{c3 .} ==> r7c3≠7
whip[5]: r7c3{n6 n9} - r1n9{c3 c2} - r6c2{n9 n3} - r4c2{n3 n1} - r5c3{n1 .} ==> r6c3≠6
whip[14]: b9n3{r9c8 r8c9} - b9n1{r8c9 r9c7} - b9n4{r9c7 r7c9} - c9n8{r7 r5} - r5n1{c9 c3} - c3n6{r5 r7} - r7c5{n6 n8} - c6n8{r7 r1} - c2n8{r1 r3} - c2n1{r3 r1} - c5n1{r1 r3} - b2n3{r3c5 r2c6} - b1n3{r2c1 r3c1} - r5n3{c1 .} ==> r9c8≠9
whip[14]: c8n9{r6 r7} - r7n7{c8 c9} - b9n4{r7c9 r9c7} - r3c7{n4 n1} - r1c9{n1 n4} - r2c9{n4 n6} - b6n6{r4c9 r6c7} - b6n8{r6c7 r5c9} - r5n1{c9 c3} - b4n6{r5c3 r4c2} - c2n1{r4 r1} - c5n1{r1 r9} - r9n6{c5 c4} - b5n6{r4c4 .} ==> r5c7≠9
whip[15]: r8n1{c4 c9} - b9n8{r8c9 r7c9} - b9n4{r7c9 r9c7} - r3c7{n4 n1} - b6n1{r5c7 r4c8} - b4n1{r4c2 r5c3} - c3n6{r5 r7} - r7c5{n6 n4} - r7c6{n4 n9} - c8n9{r7 r6} - c8n3{r6 r9} - r9c2{n3 n9} - r4n9{c2 c4} - r4n2{c4 c6} - r4n4{c6 .} ==> r8c4≠8
whip[16]: r3n5{c8 c4} - r1n5{c6 c8} - b3n2{r1c8 r2c7} - r2n6{c7 c9} - c9n7{r2 r7} - r7c8{n7 n9} - c7n9{r9 r6} - c7n6{r6 r5} - b6n8{r5c7 r5c9} - r5n1{c9 c3} - r2n1{c3 c4} - r8c4{n1 n9} - r5c4{n9 n2} - r4n2{c4 c8} - r4n1{c8 c9} - r8n1{c9 .} ==> r3c8≠7
whip[15]: c8n9{r6 r7} - c8n7{r7 r1} - b3n2{r1c8 r2c7} - r2n6{c7 c9} - b6n6{r4c9 r5c7} - b6n8{r5c7 r5c9} - r5n1{c9 c3} - r2n1{c3 c4} - b8n1{r8c4 r9c5} - r9c8{n1 n3} - r6c8{n3 n2} - c1n2{r6 r5} - b4n9{r5c1 r4c2} - b4n6{r4c2 r6c2} - r9c2{n6 .} ==> r6c7≠9
whip[1]: c7n9{r9 .} ==> r7c8≠9
naked-single ==> r7c8=7
whip[8]: r7c9{n4 n8} - r7c5{n8 n6} - r9c5{n6 n1} - r9n4{c5 c7} - r3c7{n4 n1} - c8n1{r1 r4} - b4n1{r4c2 r5c3} - c3n6{r5 .} ==> r7c6≠4
whip[2]: r7n4{c5 c9} - b3n4{r1c9 .} ==> r3c5≠4
whip[10]: r7n9{c6 c3} - r7n6{c3 c5} - b8n4{r7c5 r9c5} - r9c7{n4 n1} - r9c8{n1 n3} - r9c2{n3 n6} - b4n6{r4c2 r5c3} - r5n1{c3 c9} - c9n3{r5 r4} - r4c5{n3 .} ==> r9c4≠9
whip[9]: r7n9{c6 c3} - c3n6{r7 r5} - b4n1{r5c3 r4c2} - r4n9{c2 c8} - c4n9{r4 r8} - r8c7{n9 n8} - b6n8{r5c7 r5c9} - r5c4{n8 n2} - r4n2{c4 .} ==> r5c6≠9
whip[11]: r7c3{n9 n6} - r9c2{n6 n3} - r9c8{n3 n1} - r9c7{n1 n4} - r7n4{c9 c5} - r9c5{n4 n6} - r4c5{n6 n3} - r3n3{c5 c1} - r5c1{n3 n2} - r5c6{n2 n8} - b8n8{r7c6 .} ==> r9c1≠9
whip[7]: c1n2{r6 r5} - b6n2{r5c7 r4c8} - c8n9{r4 r6} - c1n9{r6 r8} - r7c3{n9 n6} - r9c2{n6 n3} - c8n3{r9 .} ==> r6c4≠2
whip[8]: c1n2{r5 r6} - c1n9{r6 r8} - r8c7{n9 n8} - r6c7{n8 n6} - r6c2{n6 n9} - r5n9{c1 c4} - r5n6{c4 c3} - r7c3{n6 .} ==> r5c1≠3
whip[9]: b6n9{r6c8 r4c8} - b5n9{r4c6 r5c4} - c1n9{r5 r8} - r8n7{c1 c3} - r8n3{c3 c9} - b6n3{r4c9 r6c8} - r6c3{n3 n4} - r6c1{n4 n2} - r5c1{n2 .} ==> r6c2≠9
whip[9]: r6n4{c3 c1} - c1n2{r6 r5} - c1n9{r5 r8} - r7c3{n9 n6} - r9c2{n6 n3} - b4n3{r4c2 r5c3} - r5c6{n3 n8} - b6n8{r5c7 r6c7} - r8c7{n8 .} ==> r6c3≠9
whip[11]: r8n1{c9 c4} - b2n1{r1c4 r3c5} - c2n1{r3 r4} - c8n1{r4 r9} - b9n3{r9c8 r8c9} - r4c9{n3 n6} - r5c9{n6 n8} - r6c7{n8 n2} - c1n2{r6 r5} - r5c6{n2 n3} - b2n3{r2c6 .} ==> r1c9≠1
whip[4]: r1n9{c3 c2} - r9n9{c2 c7} - c7n4{r9 r3} - r1c9{n4 .} ==> r1c3≠7
whip[11]: c1n4{r3 r6} - c1n2{r6 r5} - c1n9{r5 r8} - c3n9{r8 r5} - c3n1{r5 r2} - c3n7{r2 r8} - r8n3{c3 c9} - r9c8{n3 n1} - b3n1{r3c8 r3c7} - c7n4{r3 r9} - r9n9{c7 .} ==> r1c3≠4
whip[4]: r1n4{c6 c9} - c9n7{r1 r2} - b1n7{r2c1 r3c1} - r3n4{c1 .} ==> r2c4≠4
whip[4]: r1n4{c6 c9} - c9n7{r1 r2} - b1n7{r2c1 r3c1} - r3n4{c1 .} ==> r2c6≠4
whip[9]: c1n9{r6 r8} - r8c7{n9 n8} - r8c6{n8 n5} - r8c4{n5 n1} - r8c9{n1 n3} - r5n3{c9 c6} - b2n3{r2c6 r3c5} - c5n1{r3 r1} - r1c3{n1 .} ==> r5c3≠9
whip[10]: r7n9{c6 c3} - c3n6{r7 r5} - c2n6{r4 r9} - r9n9{c2 c7} - r8c7{n9 n8} - b6n8{r5c7 r5c9} - r5c4{n8 n2} - r4n2{c4 c8} - r1n2{c8 c6} - c6n4{r1 .} ==> r4c6≠9
whip[1]: c6n9{r8 .} ==> r8c4≠9
whip[9]: c2n6{r6 r9} - r9n9{c2 c7} - r8c7{n9 n8} - b6n8{r5c7 r5c9} - r5n3{c9 c6} - r2c6{n3 n2} - r4c6{n2 n4} - r4c5{n4 n6} - r7n6{c5 .} ==> r5c3≠6
hidden-single-in-a-column ==> r7c3=6
hidden-single-in-a-row ==> r7c6=9
whip[4]: c5n1{r3 r9} - b8n6{r9c5 r9c4} - r9n4{c4 c7} - r3c7{n4 .} ==> r3c4≠1
whip[6]: c5n1{r3 r9} - b8n6{r9c5 r9c4} - r9n4{c4 c7} - r3c7{n4 n1} - c2n1{r3 r4} - c8n1{r4 .} ==> r1c4≠1
whip[6]: b8n6{r9c4 r9c5} - r9n4{c5 c7} - r3c7{n4 n1} - r2n1{c7 c3} - r5n1{c3 c9} - r8n1{c9 .} ==> r9c4≠1
whip[7]: r5c3{n1 n3} - r6c2{n3 n6} - c7n6{r6 r2} - c7n2{r2 r6} - c1n2{r6 r5} - r5c6{n2 n8} - b6n8{r5c7 .} ==> r5c7≠1
whip[4]: c3n9{r1 r8} - r8c7{n9 n8} - b6n8{r5c7 r5c9} - r5n1{c9 .} ==> r1c3≠1
naked-single ==> r1c3=9
whip[7]: r3n5{c8 c4} - c6n5{r1 r8} - r8c4{n5 n1} - b2n1{r2c4 r1c5} - r1c2{n1 n8} - b2n8{r1c4 r3c5} - b8n8{r7c5 .} ==> r3c8≠1
naked-single ==> r3c8=5
whip[6]: r1c8{n2 n1} - r3c7{n1 n4} - b9n4{r9c7 r7c9} - r7n8{c9 c5} - r8c6{n8 n5} - r1n5{c6 .} ==> r1c4≠2
whip[2]: r1n2{c6 c8} - r4n2{c8 .} ==> r5c6≠2
whip[3]: b8n8{r7c5 r8c6} - r5c6{n8 n3} - b2n3{r2c6 .} ==> r3c5≠8
whip[5]: r5n6{c9 c4} - r5n9{c4 c1} - r8n9{c1 c7} - c7n8{r8 r5} - r5n2{c7 .} ==> r6c7≠6
whip[5]: b8n6{r9c4 r9c5} - b8n4{r9c5 r7c5} - b8n8{r7c5 r8c6} - r5c6{n8 n3} - r4c5{n3 .} ==> r9c4≠5
hidden-single-in-a-row ==> r9c1=5
whip[3]: c8n9{r6 r4} - c2n9{r4 r9} - r9n3{c2 .} ==> r6c8≠3
whip[3]: r5n9{c4 c1} - c1n2{r5 r6} - r6c8{n2 .} ==> r6c4≠9
whip[4]: r5c6{n8 n3} - r2c6{n3 n2} - b5n2{r4c6 r4c4} - c4n9{r4 .} ==> r5c4≠8
whip[7]: c4n9{r4 r5} - c4n2{r5 r2} - r2c6{n2 n3} - r5c6{n3 n8} - b6n8{r5c7 r6c7} - c7n2{r6 r5} - r5c1{n2 .} ==> r4c4≠6
whip[7]: c4n9{r4 r5} - c4n2{r5 r2} - r2c6{n2 n3} - r5c6{n3 n8} - b6n8{r5c7 r6c7} - c7n2{r6 r5} - r5c1{n2 .} ==> r4c4≠4
whip[4]: c7n4{r9 r3} - c4n4{r3 r1} - c4n5{r1 r8} - b8n1{r8c4 .} ==> r9c5≠4
whip[5]: r9c2{n9 n3} - r9c8{n3 n1} - r4n1{c8 c9} - r4n6{c9 c5} - r9c5{n6 .} ==> r4c2≠9
singles ==> r9c2=9, r8c7=9, r9c8=3
whip[1]: b9n8{r8c9 .} ==> r5c9≠8
whip[2]: r9c7{n1 n4} - r3c7{n4 .} ==> r2c7≠1
whip[2]: c1n9{r6 r5} - c1n2{r5 .} ==> r6c1≠4, r6c1≠3
hidden-single-in-a-block ==> r6c3=4
whip[2]: r6c1{n2 n9} - r6c8{n9 .} ==> r6c7≠2
singles ==> r6c7=8, r5c6=8, r8c6=5, r8c4=1, r8c9=8, r7c9=4, r1c9=7, r7c5=8, r9c7=1, r3c7=4, r9c5=6, r9c4=4, r2c1=4, r1c4=5, r3c4=8, r1c2=8
whip[2]: r5n3{c9 c3} - r5n1{c3 .} ==> r5c9≠6
whip[2]: r2n1{c9 c3} - r5n1{c3 .} ==> r4c9≠1
whip[3]: c9n1{r2 r5} - b4n1{r5c3 r4c2} - r4n6{c2 .} ==> r2c9≠6
stte

For an example of a puzzle in B but not W, see [PBCS]

[yzfwsf]

HI denis:
As for your whip[20], my solver found this, is it also a whip?

Code: Select all

Memory Chain: Start From 1r8c7 causes cell r1c9 to be empty => r8c7<>1
1r8c7- r3c7(1=4) - 4c9(r12=r7) - r9c7(4=9) - r9c8(9=3) - r9c2(3=6) - 6r7(c3=c5) - 8r7(c5=c6) - 9r7(c6=c3) - 9r1(c3=c2) - r6c2(9=3) - r4c2(3=1) - 1r5(c3=c9) - 3r5(c9=c6) - r5c3(3=6) - r6c3(6=4) - 4c1(r6=r2) - r2c6(4=2) - r2c7(2=6) - r2c9(6=7) - r1c9(7=.)

[denis_berthier]

HI denis:
As for your whip[20], my solver found this, is it also a whip?

Code: Select all

Memory Chain: Start From 1r8c7 causes cell r1c9 to be empty => r8c7<>1
1r8c7- r3c7(1=4) - 4c9(r12=r7) - r9c7(4=9) - r9c8(9=3) - r9c2(3=6) - 6r7(c3=c5) - 8r7(c5=c6) - 9r7(c6=c3) - 9r1(c3=c2) - r6c2(9=3) - r4c2(3=1) - 1r5(c3=c9) - 3r5(c9=c6) - r5c3(3=6) - r6c3(6=4) - 4c1(r6=r2) - r2c6(4=2) - r2c7(2=6) - r2c9(6=7) - r1c9(7=.)

Yes, it seems so. But then, it should be called by its proper name - a whip, not a vague "memory chain".
t-whips, whips, g-whips, braids, g-braids, S-whips, S-braids, all these could be called "memory chains" - plus lots of other chains. This makes the expression quite meaningless in a resolution path where one expects to see precise patterns.

[denis_berthier]

.
As a side note: nrczt-chains/braids were slightly less general than whips/braids: the target was supposed to be linked to a candidate in the last 3D-cell. This may explain why the puzzle was not solved at that time by nrczt-chains and is solved by whips - but I haven't checked.

[yzfwsf]

Release Vesion 625
Gui added Pencile-paper mode
Added patterns game related modules
Added the function of judging whether a puzzle is the smallest puzzle
Added Memory Chain technique, similar to denis_berthier's whip, but I don't know the details and precise definition of whip. In order not to obscure people's understanding of whip, the name Memory Chain is used. And in my solver Like other chains, when searching for Memory Chain, there is no length limit by default, but there are items with length limit in the options, you can try to modify it, but the program will not save this setting, and the default will be unlimited next time.

[denis_berthier]

Release Vesion 625
Gui added Pencile-paper mode
Added patterns game related modules
Added the function of judging whether a puzzle is the smallest puzzle
Added Memory Chain technique, similar to denis_berthier's whip, but I don't know the details and precise definition of whip. In order not to obscure people's understanding of whip, the name Memory Chain is used. And in my solver Like other chains, when searching for Memory Chain, there is no length limit by default, but there are items with length limit in the options, you can try to modify it, but the program will not save this setting, and the default will be unlimited next time.

Does the first part of this remark (with either the word "whip" or my name) appear anywhere in your software, in every place you promote it and in any resolution path it outputs (when they are used)? Did you put it on your chinese forum? I guess not. Proposing (be it in a single place) )something previously existing with a different name (and a notational variant to create pseudo-differences) has a legal name.

As for length, the question is not whether there are length limits on chains or not; what you say here is very ambiguous but (according to previous discussions) it seems you only mean you're not using the simplest first strategy.
But the question is, what's your definition of length of a chain? It seems clear from your notation that you've adopted my definition ( and not the number of inference steps, as done in SE and all the chains defined before whips).
Pretending not to know "the details and precise definition of whip" is not an excuse: they have been publicly available for 17 years, together with 100s of detailed examples and thousands of posts dedicated to them on all the sudoku forums that ever counted.

Other people have implemented whips before (I know at least 3: Paul Isaacson, Mauricio, DEFISE). All those I know had the decency of calling them whips.

[yzfwsf]

If you agree that my implementation satisfies the definition of whip, then I will name it whip instead of Memory chain in the next software update, the implementation is a bit slow now and I still need to improve it.

BTW: I remember you said in a post that P.O.'s chain is his own whip, so I am confused about whether to use whip or not.I tried to find this post, didn't find it, gave up.

[denis_berthier]

If you agree that my implementation satisfies the definition of whip, then I will name it whip instead of Memory chain in the next software update, the implementation is a bit slow now and I still need to improve it.

As I can't use your software, I can't testify about your implementation or its possible bugs. But the intent is clearly whips, so calling them whips seems appropriate.

[yzfwsf]

Can you confirm this?

Code: Select all

.--------------------.-------------------.------------------.
| 678    178   3     | 2578   1578  278  | 1268  4      9   |
| 5      9     168   | 238    138   4    | 7     2368   368 |
| 4      2     178   | 3789   6     3789 | 138   38     5   |
:--------------------+-------------------+------------------:
| 3689   4     56789 | 35789  3578  1    | 368   3568   2   |
| 2389   138   12589 | 6      358   2389 | 4     1358   7   |
| 23678  1378  15678 | 23578  4     2378 | 9     13568  368 |
:--------------------+-------------------+------------------:
| 1      378   278   | 378    9     3678 | 5     23678  4   |
| 23789  6     2789  | 4      378   5    | 238   2378   1   |
| 378    5     4     | 1      2     3678 | 368   9      368 |
'--------------------'-------------------'------------------'

Whip[15]: Start From 7r7c3 causes 3 to disappear in Row 4 => r7c3<>7
7r7c3- 2r7(c3=c8) - 2r2(c8=c4) - 2r1(c46=c7) - 6r1(c7=c1) - 7c1(r1=r6) - 7r9(c1=c6) - 7r3(c6=c4) - 9r3(c4=c6) - 3b2(p9=p5) - r8c5(3=8) - r7c4(8=3) - r7c2(3=8) - r9c1(8=3) - 3c9(r9=r6) - 3r4(c78=.)

[denis_berthier]

.

Code: Select all

(init-sukaku-grid:
   +-------------------+-------------------+-------------------+
   ! 678   178   3     ! 2578  1578  278   ! 1268  4     9     !
   ! 5     9     168   ! 238   138   4     ! 7     2368  368   !
   ! 4     2     178   ! 3789  6     3789  ! 138   38    5     !
   +-------------------+-------------------+-------------------+
   ! 3689  4     56789 ! 35789 3578  1     ! 368   3568  2     !
   ! 2389  138   12589 ! 6     358   2389  ! 4     1358  7     !
   ! 23678 1378  15678 ! 23578 4     2378  ! 9     13568 368   !
   +-------------------+-------------------+-------------------+
   ! 1     378   278   ! 378   9     3678  ! 5     23678 4     !
   ! 23789 6     2789  ! 4     378   5     ! 238   2378  1     !
   ! 378   5     4     ! 1     2     3678  ! 368   9     368   !
   +-------------------+-------------------+-------------------+
)
(try-to-eliminate 773)
whip[15]: r7n2{c3 c8} - r2n2{c8 c4} - r1n2{c6 c7} - r1n6{c7 c1} - c1n7{r1 r6} - r9n7{c1 c6} - r3n7{c6 c4} - r3n9{c4 c6} - b2n3{r3c6 r2c5} - r8c5{n3 n8} - r7n8{c6 c2} - r9c1{n8 n3} - c9n3{r9 r6} - r4n3{c8 c4} - c4n9{r4 .} ==> r7c3≠7

I find a partially different whip, but that's not too surprising.

If you want a large scale test of your whips, there's the cbg collection with all the W ratings already computed (any other rule disabled).

[yzfwsf]

Testing my whip engine,random puzzle skfr 9.2

Code: Select all

..7.6....6....85...8.24....7...5..2..2.4....6..9...1....891.2..3......9..7...6..8

Code: Select all

Hidden Single: 9 in r9 => r9c1=9
Hidden Single: 2 in c1 => r1c1=2
Hidden Single: 2 in r2 => r2c9=2
Grouped AIC Type 1: 4r8c6 = (4-3)r7c6 = r7c89 - (3=4)r9c7 => r8c79<>4
Whip[5]: Supposing 5r8c6 would causes 5 to disappear in Box 9 => r8c6<>5
5r8c6 - 4c6(r8=r7) - r7c1(4=5) - 5r3(c1=c3) - 5r5(c3=c8) - 5b9(p8=.)
Whip[7]: Supposing 8r6c4 would causes 2 to disappear in Box 7 => r6c4<>8
8r6c4 - 6r6(c4=c2) - 6c3(r4=r8) - r8c7(6=7) - r8c4(7=5) - r9c4(5=3) - r9c5(3=2) - 2b7(p9=.)
Whip[10]: Supposing 5r8c3 would cause cell r8c9 to be empty => r8c3<>5
5r8c3 - 2c3(r8=r9) - 1r9(c3=c8) - 1r8(c9=c2) - 6b7(p5=p2) - 6r6(c2=c4) - 6r4(c4=c3) - 4c3(r4=r2) - 1r2(c3=c4) - 7c4(r2=r8) - r8c9(7=.)
Whip[11]: Supposing 7r6c4 would causes 2 to disappear in Box 5 => r6c4<>7
7r6c4 - 6c4(r6=r4) - 6b4(p3=p8) - 6r7(c2=c8) - r8c7(6=7) - 7c5(r8=r2) - 9c5(r2=r5) - 8b5(p5=p8) - 8r4(c4=c7) - r5c7(8=3) - 3r6(c9=c6) - 2b5(p9=.)
Whip[6]: Supposing 1r4c3 would causes 6 to disappear in Column 3 => r4c3<>1
1r4c3 - 1r9(c3=c8) - 1r8(c9=c2) - 1r2(c2=c4) - 7c4(r2=r8) - r8c7(7=6) - 6c3(r8=.)
Whip[8]: Supposing 1r3c8 would causes 1 to disappear in Row 9 => r3c8<>1
1r3c8 - 6r3(c8=c7) - r8c7(6=7) - 7c4(r8=r2) - 7r3(c6=c9) - 9r3(c9=c6) - 9r2(c5=c2) - 1r2(c2=c3) - 1r9(c3=.)
Whip[9]: Supposing 3r4c3 would cause cell r8c7 to be empty => r4c3<>3
3r4c3 - 6c3(r4=r8) - 2c3(r8=r9) - 1r9(c3=c8) - 1r8(c9=c2) - 4r8(c2=c6) - 4c3(r8=r2) - 1r2(c3=c4) - 7c4(r2=r8) - r8c7(7=.)
Whip[12]: Supposing 3r3c8 would causes 3 to disappear in Box 6 => r3c8<>3
3r3c8 - 6r3(c8=c7) - r8c7(6=7) - 7r7(c9=c6) - 7c4(r8=r2) - 7r3(c6=c9) - 9r3(c9=c6) - r2c5(9=3) - 3c3(r2=r5) - r5c6(3=1) - r4c6(1=3) - 3r7(c6=c9) - 3b6(p9=.)
Whip[11]: Supposing 4r4c3 would cause cell r3c8 to be empty => r4c3<>4
4r4c3 - 6c3(r4=r8) - 6r7(c2=c8) - 6r3(c8=c7) - r8c7(6=7) - 7r7(c9=c6) - 3r7(c6=c9) - r4c9(3=9) - 9r3(c9=c6) - 9c5(r2=r5) - 7r5(c5=c8) - r3c8(7=.)
Naked Single: r4c3=6
Hidden Single: 6 in r6 => r6c4=6
Grouped AIC Type 2: (1=5)r3c1 - (5=4)r7c1 - r89c3 = 4r2c3 => r2c3<>1
Whip[11]: Supposing 3r6c6 would causes 7 to disappear in Box 3 => r6c6<>3
3r6c6 - 2c6(r6=r8) - 4c6(r8=r7) - 4c1(r7=r6) - r6c2(4=5) - r6c9(5=7) - 7r7(c9=c8) - 3r7(c8=c9) - 5r7(c9=c1) - 5c3(r9=r3) - 3r3(c3=c7) - 7b3(p7=.)
Whip[11]: Supposing 4r7c8 would causes 4 to disappear in Column 1 => r7c8<>4
4r7c8 - r9c7(4=3) - 3r7(c9=c6) - r9c4(3=5) - r9c8(5=1) - 4r9(c8=c3) - r2c3(4=3) - 3r3(c3=c9) - 1b3(p9=p3) - 9c9(r1=r4) - 4c9(r4=r6) - 4c1(r6=.)
Whip[12]: Supposing 4r1c2 would causes 5 to disappear in Box 8 => r1c2<>4
4r1c2 - 4b4(p8=p7) - r7c1(4=5) - r7c2(5=6) - r8c2(6=1) - 1r9(c3=c8) - 1r2(c8=c4) - 7c4(r2=r8) - 8r8(c4=c5) - 8r6(c5=c8) - r1c8(8=3) - r1c4(3=5) - 5b8(p7=.)
Locked Candidates 2 (Claiming): 4 in r1 => r2c8<>4
Whip[7]: Supposing 4r9c3 would cause cell r2c3 to be empty => r9c3<>4
4r9c3 - 1r9(c3=c8) - 4b9(p8=p3) - r9c7(4=3) - 3r7(c8=c6) - 7r7(c6=c8) - r2c8(7=3) - r2c3(3=.)
Locked Candidates 2 (Claiming): 4 in r9 => r7c9<>4
Whip[7]: Supposing 3r2c3 would cause cell r8c6 to be empty => r2c3<>3
3r2c3 - 4c3(r2=r8) - 2c3(r8=r9) - 1r9(c3=c8) - r2c8(1=7) - 7r3(c9=c6) - r6c6(7=2) - r8c6(2=.)
Naked Single: r2c3=4
Whip[9]: Supposing 1r5c3 would causes 1 to disappear in Box 1 => r5c3<>1
1r5c3 - r8c3(1=2) - r9c3(2=5) - 1r9(c3=c8) - 1r8(c9=c2) - 1r2(c2=c4) - 7c4(r2=r8) - 5c4(r8=r1) - 5r3(c6=c1) - 1b1(p7=.)
Whip[10]: Supposing 8r6c5 would causes 8 to disappear in Column 8 => r6c5<>8
8r6c5 - 8c1(r6=r5) - 1b4(p4=p2) - r4c4(1=3) - r4c6(3=9) - 9c5(r5=r2) - 3c5(r2=r9) - r9c7(3=4) - 4r4(c7=c9) - 4c8(r6=r1) - 8c8(r1=.)
Whip[9]: Supposing 7r8c7 would causes 5 to disappear in Column 9 => r8c7<>7
7r8c7 - 6b9(p4=p2) - r3c8(6=7) - 7r7(c8=c6) - 3r7(c6=c9) - 7c9(r7=r6) - 7r5(c7=c5) - 8c5(r5=r8) - r8c4(8=5) - 5c9(r8=.)
Naked Single: r8c7=6
Hidden Single: 6 in r3 => r3c8=6
Hidden Single: 6 in r7 => r7c2=6
Whip[9]: Supposing 1r3c9 would cause cell r3c6 to be empty => r3c9<>1
1r3c9 - r3c1(1=5) - r3c3(5=3) - r5c3(3=5) - 5c2(r6=r8) - r8c9(5=7) - 7c4(r8=r2) - r2c8(7=3) - r2c5(3=9) - r3c6(9=.)
Grouped AIC Type 2: 9r1c2 = r2c2 - r2c5 = (9-8)r5c5 = (8-1)r4c4 = r12c4 - r3c6 = 1r3c13 => r1c2<>1
Whip[4]: Supposing 1r1c6 would causes 1 to disappear in Box 3 => r1c6<>1
1r1c6 - 1r5(c6=c1) - 1r3(c1=c3) - 1r9(c3=c8) - 1b3(p5=.)
Whip[6]: Supposing 1r4c4 would causes 4 to disappear in Box 3 => r4c4<>1
1r4c4 - 8r4(c4=c7) - 8r1(c7=c8) - 1r1(c8=c9) - 1c8(r2=r9) - 4r9(c8=c7) - 4b3(p1=.)
Locked Candidates 2 (Claiming): 1 in c4 => r3c6<>1
Locked Candidates 2 (Claiming): 1 in r3 => r2c2<>1
AIC Type 2: 3r5c3 = (3-1)r3c3 = r3c1 - r5c1 = 1r4c2 => r4c2<>3
AIC Type 2: 3r5c3 = r3c3 - (3=9)r2c2 - r2c5 = 9r5c5 => r5c5<>3
AIC Type 2: 3r5c3 = (3-1)r3c3 = r3c1 - r5c1 = 1r5c6 => r5c6<>3
AIC Type 2: 2r8c3 = (2-1)r9c3 = r9c8 - r2c8 = (1-7)r2c4 = (7-8)r8c4 = 8r8c5 => r8c5<>2
AIC Type 2: 7r8c4 = (7-1)r2c4 = r2c8 - r9c8 = 1r8c9 => r8c9<>7
Locked Candidates 1 (Pointing): 7 in b9 => r7c6<>7
Grouped AIC Type 1: 4r4c79 = (4-1)r4c2 = r8c2 - r8c9 = (1-4)r1c9 = 4r46c9 => r6c8<>4
AIC Type 2: (3=4)r9c7 - r9c8 = (4-8)r1c8 = 8r1c7 => r1c7<>3
Whip[5]: Supposing 3r1c8 would causes 3 to disappear in Box 8 => r1c8<>3
3r1c8 - 4c8(r1=r9) - r9c7(4=3) - 3r5(c7=c3) - 3r3(c3=c6) - 3b8(p3=.)
Whip[7]: Supposing 3r4c4 would causes 8 to disappear in Box 5 => r4c4<>3
3r4c4 - 8r4(c4=c7) - 8r1(c7=c8) - 4c8(r1=r9) - r9c7(4=3) - 3c5(r9=r2) - 9c5(r2=r5) - 8b5(p5=.)
Naked Single: r4c4=8
Hidden Single: 8 in r8 => r8c5=8
Whip[4]: Supposing 3r5c8 would causes 3 to disappear in Column 3 => r5c8<>3
3r5c8 - 3r4(c9=c6) - 3r7(c6=c9) - 3c7(r9=r3) - 3c3(r3=.)
Finned Jellyfish:3r3457\c3679 fr7c8 => r9c7<>3
Naked Single: r9c7=4
Hidden Single: 4 in c8 => r1c8=4
Hidden Single: 8 in r1 => r1c7=8
ALS Discontinuous Nice Loop: 1r3c1 = (1-3)r3c3 = r5c3 - (3=791)r5c567 - r5c1 = 1r3c1 => r3c1=1
Hidden Single: 1 in r5 => r5c6=1
Hidden Single: 1 in r4 => r4c2=1
Hidden Single: 4 in r4 => r4c9=4
Locked Candidates 1 (Pointing): 9 in b6 => r3c7<>9
Naked Pair: in r7c1,r8c2 => r9c3<>5,
AIC Type 2: 5r9c4 = r9c8 - (5=1)r8c9 - r1c9 = 1r1c4 => r1c4<>5
Locked Candidates 2 (Claiming): 5 in c4 => r7c6<>5
AIC Type 2: 3r4c6 = r4c7 - r5c7 = r5c3 - (3=5)r3c3 - r3c6 = 5r1c6 => r1c6<>3
AIC Type 2: 3r6c5 = r4c6 - (3=4)r7c6 - r7c1 = (4-8)r6c1 = 8r6c8 => r6c8<>3
Grouped Discontinuous Nice Loop: 7r2c45 = (7-1)r2c8 = r9c8 - r9c3 = (1-2)r8c3 = r8c6 - (2=7)r6c6 - r3c6 = 7r2c45 => r2c8,r3c6<>7
Naked Triple: in r1c6,r3c6,r4c6 => r7c6<>3,
Naked Single: r7c6=4
Hidden Single: 4 in r8 => r8c2=4
Hidden Single: 4 in r6 => r6c1=4
Hidden Single: 8 in r6 => r6c8=8
Hidden Single: 8 in r5 => r5c1=8
Full House: r7c1=5
Locked Candidates 2 (Claiming): 3 in r7 => r9c8<>3
Swordfish:3c367\r345  => r3c9<>3
XY-Chain: (3=1)r2c8 - (1=5)r9c8 - (5=3)r9c4 => r2c4<>3
XY-Chain: (9=3)r2c2 - (3=1)r2c8 - (1=5)r9c8 - (5=7)r5c8 - (7=9)r5c5 => r2c5<>9
Hidden Single: 9 in r2 => r2c2=9
Hidden Single: 9 in c5 => r5c5=9
Hidden Single: 9 in r4 => r4c7=9
Full House: r4c6=3
Locked Candidates 2 (Claiming): 7 in r5 => r6c9<>7
XY-Chain: (3=5)r6c2 - (5=3)r6c9 - (3=7)r7c9 - (7=9)r3c9 - (9=5)r3c6 - (5=3)r3c3 => r1c2,r5c3<>3
Hidden Single: 3 in r5 => r5c7=3
Full House: r3c7=7
Hidden Single: 3 in r3 => r3c3=3
Full House: r1c2=5
Full House: r6c2=3
Full House: r5c3=5
Full House: r5c8=7
Full House: r6c9=5
Hidden Single: 5 in r3 => r3c6=5
Full House: r3c9=9
Hidden Single: 9 in r1 => r1c6=9
Hidden Single: 7 in r7 => r7c9=7
Full House: r7c8=3
Hidden Single: 3 in r2 => r2c5=3
Hidden Single: 3 in r1 => r1c9=3
Full House: r1c4=1
Full House: r8c9=1
Full House: r2c4=7
Full House: r2c8=1
Full House: r9c8=5
Hidden Single: 5 in r8 => r8c4=5
Full House: r9c4=3
Hidden Single: 7 in r8 => r8c6=7
Full House: r8c3=2
Full House: r9c3=1
Full House: r9c5=2
Full House: r6c5=7
Full House: r6c6=2


[denis_berthier]

.
Hi yzfwsf,
Generally, a puzzle has many different resolution paths, even using a fixed set of rules. In the present case however, the first half of SudoRules solution and yours are very close, even though you're using different set of rules. This happens when thee are few possibilities at the start.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 2     13459 7     ! 135   6     1359  ! 3489  1348  1349  !
   ! 6     1349  134   ! 137   379   8     ! 5     1347  2     !
   ! 15    8     135   ! 2     4     13579 ! 3679  1367  1379  !
   +-------------------+-------------------+-------------------+
   ! 7     1346  1346  ! 1368  5     139   ! 3489  2     349   !
   ! 158   2     135   ! 4     3789  1379  ! 3789  3578  6     !
   ! 458   3456  9     ! 3678  2378  237   ! 1     34578 3457  !
   +-------------------+-------------------+-------------------+
   ! 45    456   8     ! 9     1     3457  ! 2     34567 3457  !
   ! 3     1456  12456 ! 578   278   2457  ! 467   9     1457  !
   ! 9     7     1245  ! 35    23    6     ! 34    1345  8     !
   +-------------------+-------------------+-------------------+
192 candidates

Code: Select all

t-whip[3]: r9c7{n4 n3} - r7n3{c9 c6} - c6n4{r7 .} ==> r8c7≠4, r8c9≠4
whip[5]: c6n4{r8 r7} - r7c1{n4 n5} - c9n5{r7 r6} - c2n5{r6 r1} - c4n5{r1 .} ==> r8c6≠5
t-whip[7]: c4n6{r6 r4} - c3n6{r4 r8} - r8c7{n6 n7} - r7n7{c9 c6} - c6n4{r7 r8} - r8n2{c6 c5} - r8n8{c5 .} ==> r6c4≠8
whip[10]: c3n2{r8 r9} - r9n1{c3 c8} - r8n1{c9 c2} - b7n6{r8c2 r7c2} - r6n6{c2 c4} - r4n6{c4 c3} - c3n4{r4 r2} - r2n1{c3 c4} - c4n7{r2 r8} - r8c9{n7 .} ==> r8c3≠5
whip[11]: c4n6{r6 r4} - b4n6{r4c3 r6c2} - r7n6{c2 c8} - r8c7{n6 n7} - c5n7{r8 r2} - c5n9{r2 r5} - b5n8{r5c5 r6c5} - c1n8{r6 r5} - r5c7{n8 n3} - r6n3{c9 c6} - r6n2{c6 .} ==> r6c4≠7
whip[6]: c3n6{r4 r8} - b7n1{r8c3 r8c2} - r9n1{c3 c8} - r2n1{c8 c4} - c4n7{r2 r8} - r8c7{n7 .} ==> r4c3≠1
whip[8]: r3n6{c8 c7} - r8c7{n6 n7} - c4n7{r8 r2} - b3n7{r2c8 r3c9} - r3n9{c9 c6} - r2n9{c5 c2} - r2n1{c2 c3} - r9n1{c3 .} ==> r3c8≠1
whip[9]: c3n6{r4 r8} - c3n2{r8 r9} - r9n1{c3 c8} - r8n1{c9 c2} - r8n4{c2 c6} - c3n4{r8 r2} - r2n1{c3 c4} - c4n7{r2 r8} - r8c7{n7 .} ==> r4c3≠3
whip[12]: r3n6{c8 c7} - r8c7{n6 n7} - r7n7{c9 c6} - c4n7{r8 r2} - b3n7{r2c8 r3c9} - r3n9{c9 c6} - r2c5{n9 n3} - c3n3{r2 r5} - r5c6{n3 n1} - r4c6{n1 n3} - c7n3{r4 r9} - c4n3{r9 .} ==> r3c8≠3
whip[12]: c6n2{r6 r8} - c6n4{r8 r7} - c1n4{r7 r6} - r4c3{n4 n6} - r6c2{n6 n5} - r6c9{n5 n7} - r7n7{c9 c8} - r7n3{c8 c9} - r7n5{c9 c1} - b1n5{r3c1 r3c3} - r3n3{c3 c7} - c7n7{r3 .} ==> r6c6≠3
whip[12]: r6n6{c4 c2} - r4c3{n6 n4} - c1n4{r6 r7} - r7c2{n4 n5} - r7n6{c2 c8} - r3n6{c8 c7} - r8c7{n6 n7} - r7c9{n7 n3} - r4c9{n3 n9} - r3n9{c9 c6} - c6n5{r3 r1} - c6n3{r1 .} ==> r6c4≠3
naked-single ==> r6c4=6
whip[11]: r4n6{c3 c2} - r7n6{c2 c8} - r3n6{c8 c7} - r8c7{n6 n7} - b8n7{r8c4 r7c6} - r7n3{c6 c9} - r4c9{n3 n9} - r3n9{c9 c6} - b5n9{r4c6 r5c5} - r5n7{c5 c8} - r3c8{n7 .} ==> r4c3≠4
naked-single ==> r4c3=6
t-whip[3]: r3c1{n1 n5} - r7c1{n5 n4} - c3n4{r9 .} ==> r2c3≠1
whip[11]: r9c7{n4 n3} - r7n3{c9 c6} - r9c4{n3 n5} - r9c8{n5 n1} - r9n4{c8 c3} - r2c3{n4 n3} - r3n3{c3 c9} - c9n1{r3 r1} - c9n9{r1 r4} - c9n4{r4 r6} - c1n4{r6 .} ==> r7c8≠4
whip[12]: b4n4{r6c2 r6c1} - r7c1{n4 n5} - r7c2{n5 n6} - r8c2{n6 n1} - b9n1{r8c9 r9c8} - r2n1{c8 c4} - c4n7{r2 r8} - b8n5{r8c4 r9c4} - r1c4{n5 n3} - r1c8{n3 n8} - r6n8{c8 c5} - r8n8{c5 .} ==> r1c2≠4
whip[1]: r1n4{c9 .} ==> r2c8≠4
whip[7]: r9n1{c3 c8} - b9n4{r9c8 r7c9} - r9c7{n4 n3} - b8n3{r9c4 r7c6} - r7n7{c6 c8} - r2c8{n7 n3} - r2c3{n3 .} ==> r9c3≠4
whip[1]: r9n4{c8 .} ==> r7c9≠4
whip[7]: c3n4{r2 r8} - c3n2{r8 r9} - r9n1{c3 c8} - r2c8{n1 n7} - b2n7{r2c4 r3c6} - r8c6{n7 n2} - r6c6{n2 .} ==> r2c3≠3
naked-single ==> r2c3=4
whip[9]: r8c3{n1 n2} - r9c3{n2 n5} - r9n1{c3 c8} - r8n1{c9 c2} - b1n1{r1c2 r3c1} - r2n1{c2 c4} - c4n7{r2 r8} - b8n5{r8c4 r7c6} - r3n5{c6 .} ==> r5c3≠1
whip[10]: c1n8{r6 r5} - b4n1{r5c1 r4c2} - r4c4{n1 n3} - r4c6{n3 n9} - b2n9{r1c6 r2c5} - c5n3{r2 r9} - r9c7{n3 n4} - r4n4{c7 c9} - r1n4{c9 c8} - c8n8{r1 .} ==> r6c5≠8
whip[9]: b9n6{r8c7 r7c8} - r3c8{n6 n7} - r7n7{c8 c6} - r7n3{c6 c9} - c9n7{r7 r6} - c9n5{r6 r8} - r8c4{n5 n8} - c5n8{r8 r5} - r5n7{c5 .} ==> r8c7≠7
singles ==> r8c7=6, r3c8=6, r7c2=6
whip[9]: r3c1{n1 n5} - r3c3{n5 n3} - r5c3{n3 n5} - b7n5{r9c3 r8c2} - r8c9{n5 n7} - c4n7{r8 r2} - r2n1{c4 c2} - r2n9{c2 c5} - r3c6{n9 .} ==> r3c9≠1
z-chain[4]: b3n1{r1c9 r2c8} - r9n1{c8 c3} - r3n1{c3 c1} - r5n1{c1 .} ==> r1c6≠1
z-chain[5]: r3n1{c3 c6} - r4n1{c6 c4} - b5n8{r4c4 r5c5} - c5n9{r5 r2} - c2n9{r2 .} ==> r1c2≠1
whip[6]: r4n8{c4 c7} - c8n8{r6 r1} - r1n1{c8 c9} - r1n4{c9 c7} - r9n4{c7 c8} - c8n1{r9 .} ==> r4c4≠1
whip[1]: b5n1{r5c6 .} ==> r3c6≠1
whip[1]: r3n1{c3 .} ==> r2c2≠1
biv-chain[3]: c3n3{r5 r3} - r2c2{n3 n9} - c5n9{r2 r5} ==> r5c5≠3
biv-chain[3]: c4n7{r8 r2} - r2n1{c4 c8} - b9n1{r9c8 r8c9} ==> r8c9≠7
whip[1]: r8n7{c6 .} ==> r7c6≠7
biv-chain[3]: b4n1{r4c2 r5c1} - b1n1{r3c1 r3c3} - c3n3{r3 r5} ==> r4c2≠3
biv-chain[3]: r5n1{c6 c1} - b1n1{r3c1 r3c3} - c3n3{r3 r5} ==> r5c6≠3
z-chain[4]: c9n4{r6 r1} - c9n1{r1 r8} - c2n1{r8 r4} - r4n4{c2 .} ==> r6c8≠4
biv-chain[3]: r1n8{c7 c8} - c8n4{r1 r9} - r9c7{n4 n3} ==> r1c7≠3
biv-chain[5]: b8n8{r8c5 r8c4} - c4n7{r8 r2} - c4n1{r2 r1} - c9n1{r1 r8} - r8c3{n1 n2} ==> r8c5≠2
whip[5]: c8n4{r1 r9} - r9c7{n4 n3} - b8n3{r9c4 r7c6} - r3n3{c6 c3} - r5n3{c3 .} ==> r1c8≠3
z-chain[7]: c5n8{r8 r5} - r4c4{n8 n3} - r6c5{n3 n2} - r9n2{c5 c3} - r9n1{c3 c8} - r2n1{c8 c4} - c4n7{r2 .} ==> r8c5≠7
singles ==> r8c5=8, r4c4=8
z-chain[4]: r4n3{c9 c6} - r7n3{c6 c9} - c7n3{r9 r3} - c3n3{r3 .} ==> r5c8≠3
finned-jellyfish-in-columns: n3{c2 c4 c5 c8}{r6 r1 r2 r9} ==> r9c7≠3
singles ==> r9c7=4, r1c8=4, r1c7=8
z-chain[4]: r5n8{c1 c8} - r5n5{c8 c3} - c3n3{r5 r3} - r3n1{c3 .} ==> r5c1≠1
singles ==> r4c2=1,r4c9=4, r5c6=1,> r3c1=1, r3c7≠9
naked-pairs-in-a-column: c3{r3 r5}{n3 n5} ==> r9c3≠5
biv-chain[3]: r9n5{c4 c8} - r8c9{n5 n1} - r1n1{c9 c4} ==> r1c4≠5
whip[1]: c4n5{r9 .} ==> r7c6≠5
biv-chain[4]: b5n3{r4c6 r6c5} - b4n3{r6c2 r5c3} - r3c3{n3 n5} - b2n5{r3c6 r1c6} ==> r1c6≠3
biv-chain[4]: r6n8{c8 c1} - c1n4{r6 r7} - r7c6{n4 n3} - r4n3{c6 c7} ==> r6c8≠3
z-chain[4]: r3n9{c9 c6} - r4c6{n9 n3} - r6n3{c5 c2} - c3n3{r5 .} ==> r3c9≠3
swordfish-in-rows: n3{r3 r4 r5}{c3 c6 c7} ==> r7c6≠3
singles ==> r7c6=4, r7c1=5, r5c1=8, r6c1=4, r8c2=4,r6c8=8
whip[1]: r7n3{c9 .} ==> r9c8≠3
naked-pairs-in-a-column: c6{r6 r8}{n2 n7} ==> r3c6≠7
whip[1]: r3n7{c9 .} ==> r2c8≠7
biv-chain[3]: r2n1{c4 c8} - r9c8{n1 n5} - r9c4{n5 n3} ==> r2c4≠3
biv-chain[3]: r3c7{n7 n3} - c8n3{r2 r7} - c8n7{r7 r5} ==> r5c7≠7
singles ==> r3c7=7, r3c9=9, r6c9≠3
naked-pairs-in-a-row: r1{c4 c9}{n1 n3} ==> r1c2≠3
biv-chain[3]: r8n5{c4 c9} - r6c9{n5 n7} - c6n7{r6 r8} ==> r8c4≠7
stte

[yzfwsf]

I found that the search cost of g-whip is much larger than that of whip. I wonder if SudoRules has the same situation. Searching for g-whip of the same length usually traverses many times more nodes than searching for equal-length whip.