The New Sudoku Players' Forum

[denis_berthier]

Hi DEFISE:
Braid actually uses one or more RLCs to form a complete path. My approach is to number the RLCs in order during BFS, and I realize that the complete path's RLC is a sequence with gradually increasing numbers, so there is no need to exclude duplicate work. My implementation 1 was completely coded according to this idea, but I found that there were very few puzzles that had deviations. Therefore, I corrected the control over the numbering and achieved success, which is implementation 2.

What is a RLC please ?

He means right-linking candidate.

[DEFISE]

My Implementation 1：Found a bias in the scoring of very few (1 in 80,000~160000) puzzles
My Implementation 2：No bias in scoring has been detected.
My Implementation 3: No scoring bias possible.

Code: Select all

3...7.5...9...8.4...72....64......8..1..2...4..38..1.......9.1...53....2....8.3..

SHC: B-Rating = 13;Max buffer filling: 632334/800000;Run time = 52m39s
My Implementation 1:B-Rating = 13; 134 Steps! Time elapsed: 5010.3 ms
My Implementation 2:B-Rating = 13; 134 Steps! Time elapsed: 19442.8 ms
My Implementation 3:B-Rating = 13; 132 Steps! Time elapsed: 3761971.9 ms
Mauricio's js solver: Most difficult rule: NRCZT Braid[13];Time elapsed: 40.684 seconds

Code: Select all

..1.....62.....3...7.....1.7..5......6..8..9..3..42..1..9..4.7....3....48...5.2..

SHC:B-Rating = 13;Max buffer filling: 645137/800000;Run time = 2h11m8s
My Implementation 1:B-Rating = 13;128 Steps! Time elapsed: 5580.6 ms
My Implementation 2:B-Rating = 13;128 Steps! Time elapsed: 28074.5 ms
My Implementation 3:B-Rating = 13;127 Steps! Time elapsed: 2996560.9 ms
Mauricio's js solver: Most difficult rule: NRCZT Braid[13];Time elapsed: 121.045 seconds

Hi yzfwsf,
the new version (SHC 6.1 released last week) is much faster than the old one:
for the 1st puzzle the time is divided by 45.
for the 2nd puzzle the time is divided by 9.

[DEFISE]

another puzzle

Code: Select all

040080903300600020005007000100050200009004001080000090050700080007010600000003009

Hidden Text: Show

Code: Select all



SHC version 5.4 will run under the following conditions:
*******************************************************
Rating category: B
Rating only this puzzle: 040080903300600020005007000100050200009004001080000090050700080007010600000003009
max-length = 40
buffer-size = 800000
max-time = 180mn
*******************************************
braid[2]: r7n1{c3 c7}- r7n3{c7 .} => -6r7c3
braid[2]: r7n1{c3 c7}- r7n3{c7 .} => -2r7c3
braid[2]: r7n1{c3 c7}- r7n3{c7 .} => -4r7c3
braid[2]: r7n1{c7 c3}- r7n3{c3 .} => -4r7c7
braid[12]: r7c7{n1 n3}- r8n3{c8 c2}- c8n1{r1 r9}- r9n7{c8 c7}- r9n5{c7 c4}- c2n1{r9 r3}- c2n9{r3 r2}- r2c5{n9 n4}- r2c6{n9 n5}- r1n5{c6 c8}- r8c8{n5 n4}- c4n4{r
8 .} => -1r2c7
braid[16]: r7c9{n4 n2}- r8c9{n2 n5}- r9n5{c7 c4}- c4n4{r9 r8}- r8c8{n4 n3}- r7c7{n3 n1}- r3c7{n1 n8}- r2c9{n8 n7}- r2c7{n7 n5}- r1n5{c8 c6}- b8n8{r8c4 r8c6}- c6
n2{r8 r6}- r6n1{c6 c4}- r1c4{n1 n2}- c3n2{r1 r9}- r8n2{c1 .} => -4r3c9
braid[13]: c8n3{r5 r8}- c2n3{r8 r4}- b6n8{r5c7 r4c9}- r3c9{n8 n6}- r4n7{c9 c8}- r1n7{c8 c1}- r6n7{c1 c5}- c8n6{r4 r5}- r5c5{n6 n2}- c2n6{r5 r9}- r9c5{n6 n4}- c4
n4{r9 r3}- c8n4{r3 .} => -3r5c7
braid[15]: r9n7{c7 c8}- r1n7{c8 c1}- b9n1{r9c8 r7c7}- r3c7{n1 n8}- r3c9{n8 n6}- r7c3{n1 n3}- r1n6{c8 c3}- r4c3{n6 n4}- r6c3{n4 n2}- r5n8{c7 c4}- r5n2{c4 c5}- r9
c5{n2 n6}- r7n6{c5 c1}- r5c1{n6 n5}- r6c1{n5 .} => -4r9c7
braid[10]: r2n4{c7 c5}- c7n4{r2 r6}- r4n4{c8 c3}- c7n3{r6 r7}- r7c3{n3 n1}- r2c3{n1 n8}- r8c8{n3 n5}- r9n5{c8 c4}- r9n4{c4 c1}- r9n8{c1 .} => -4r3c8
braid[17]: r3c8{n1 n6}- r3c9{n6 n8}- r3n3{c4 c5}- r6n1{c4 c6}- b2n4{r3c5 r2c5}- b2n9{r2c5 r2c6}- r4n9{c6 c4}- r4n8{c4 c6}- c6n6{r4 r7}- r9c5{n6 n2}- c6n2{r7 r1}
- c3n2{r1 r6}- r6c4{n2 n3}- c7n3{r6 r7}- r8n3{c8 c2}- c2n2{r8 r3}- c2n9{r3 .} => -1r3c4
braid[21]: r2c5{n4 n9}- r7c9{n4 n2}- r8c9{n2 n5}- c7n4{r2 r6}- r4n4{c8 c3}- c7n3{r6 r7}- r7c3{n3 n1}- r2c3{n1 n8}- r8n3{c8 c2}- c2n9{r8 r3}- c2n1{r3 r2}- r2c6{n
1 n5}- c3n3{r7 r6}- c7n5{r2 r5}- b6n8{r5c7 r4c9}- r3c9{n8 n6}- r3c1{n6 n2}- c6n8{r4 r8}- r8n2{c6 c4}- r1c4{n2 n1}- r6c4{n1 .} => -4r2c9
braid[1]: b3n4{r2c7 .} => -4r6c7
braid[13]: r1n7{c1 c8}- r2n7{c7 c2}- r4n7{c2 c9}- r9n7{c8 c7}- b6n8{r4c9 r5c7}- r5n5{c7 c8}- r9n5{c8 c4}- c7n5{r9 r2}- r2n4{c7 c5}- r2n9{c5 c6}- r4n9{c6 c4}- c4
n4{r3 r8}- c4n8{r8 .} => -7r5c1
braid[25]: r3c8{n1 n6}- r3c9{n6 n8}- r7c7{n1 n3}- r2n8{c9 c3}- r8n3{c8 c2}- c8n1{r3 r9}- r9n7{c8 c7}- r6c7{n7 n5}- r9n5{c7 c4}- r9n8{c4 c1}- c2n1{r9 r2}- r2n7{c
2 c9}- r1c8{n7 n5}- r8c8{n5 n4}- r1n7{c8 c1}- r2n5{c7 c6}- c2n9{r2 r3}- r3c1{n9 n2}- r8c1{n2 n9}- c4n9{r8 r4}- r4n8{c4 c6}- c6n9{r4 r7}- c6n6{r7 r6}- r6c1{n6 n4
}- r6c9{n4 .} => -1r3c7
braid[1]: c7n1{r9 .} => -1r9c8
braid[7]: c6n8{r8 r4}- r5n8{c4 c7}- r3c7{n8 n4}- r2n4{c7 c5}- r9c5{n4 n6}- r7c5{n6 n9}- r7c6{n9 .} => -2r8c6
braid[9]: r1n7{c1 c8}- r2n7{c7 c2}- r4n7{c2 c9}- c8n1{r1 r3}- r3n6{c8 c9}- c2n1{r3 r9}- c9n8{r3 r2}- c3n8{r2 r9}- b7n6{r9c3 .} => -6r1c1
braid[9]: r1n6{c8 c3}- r9n7{c8 c7}- c1n7{r1 r6}- c7n1{r9 r7}- r7c3{n1 n3}- r4c3{n3 n4}- r6n4{c3 c9}- r6n5{c9 c7}- c7n3{r6 .} => -7r1c8
Single(s): 7r1c1
braid[6]: r2c2{n1 n9}- r7c3{n1 n3}- r8c2{n3 n2}- r3c2{n2 n6}- r3c9{n6 n8}- r2n8{c9 .} => -1r2c3
Single(s): 8r2c3
braid[8]: r1n2{c4 c3}- r1n6{c3 c8}- r3n3{c5 c4}- b2n4{r3c4 r2c5}- r9c5{n4 n6}- r7n6{c5 c1}- r3n6{c1 c2}- r5n6{c2 .} => -2r3c5
braid[8]: c4n1{r6 r1}- r2n1{c6 c2}- b2n2{r1c4 r1c6}- r1n5{c6 c8}- c3n2{r1 r9}- r8n2{c1 c9}- r9n1{c3 c7}- b9n5{r9c7 .} => -2r6c4
braid[9]: r9n8{c1 c4}- r5n8{c4 c7}- r3c7{n8 n4}- r2n4{c7 c5}- r9c5{n4 n6}- r9c2{n6 n1}- r2c2{n1 n9}- r3c1{n9 n6}- r7n6{c1 .} => -2r9c1
braid[10]: r9n7{c8 c7}- r2n7{c7 c9}- c7n1{r9 r7}- r7c3{n1 n3}- r8n3{c2 c8}- c8n4{r8 r4}- r4c3{n4 n6}- r4c9{n6 n8}- r3c9{n8 n6}- r1n6{c8 .} => -5r9c8
braid[10]: c6n8{r8 r4}- r5n8{c4 c7}- r3c7{n8 n4}- r2n4{c7 c5}- c5n9{r2 r3}- r3n3{c5 c4}- r5c4{n3 n2}- r6c4{n3 n1}- r1c4{n1 n5}- c6n5{r1 .} => -9r8c6
braid[9]: r9n8{c1 c4}- r5n8{c4 c7}- r3c7{n8 n4}- r8n8{c4 c1}- c4n4{r3 r8}- r9c5{n4 n2}- r9c2{n2 n1}- r2c2{n1 n9}- r8n9{c2 .} => -6r9c1
braid[10]: r9c8{n7 n4}- r7c9{n4 n2}- r9n5{c7 c4}- c7n1{r9 r7}- c7n3{r7 r6}- r6c4{n3 n1}- r1c4{n1 n2}- c6n2{r1 r6}- c3n2{r6 r9}- r8n2{c1 .} => -7r9c7
Single(s): 7r9c8
braid[6]: r1n6{c3 c8}- r5n6{c8 c5}- r4n6{c6 c9}- r4n7{c9 c2}- r5n7{c2 c7}- b6n8{r5c7 .} => -6r6c3
braid[7]: r7c9{n4 n2}- r8c9{n2 n5}- r9n5{c7 c4}- c8n4{r4 r8}- c4n4{r8 r3}- r3c7{n4 n8}- c9n8{r3 .} => -4r4c9
braid[7]: r8n3{c2 c8}- c2n7{r5 r4}- c8n4{r8 r4}- r4c3{n4 n6}- r4c9{n6 n8}- r3c9{n8 n6}- r1n6{c8 .} => -3r5c2
braid[7]: r7c3{n1 n3}- r8n3{c2 c8}- c8n4{r8 r4}- r4c3{n4 n6}- r1n6{c3 c8}- r5n6{c8 c5}- r9n6{c5 .} => -1r9c2
braid[1]: c2n1{r2 .} => -1r1c3
braid[5]: r1c3{n6 n2}- r9c2{n6 n2}- r9c5{n2 n4}- r3n2{c2 c4}- c4n4{r3 .} => -6r9c3
braid[4]: r1n6{c3 c8}- r9n6{c2 c5}- r5n6{c5 c1}- r7n6{c1 .} => -6r3c2
braid[5]: r4n7{c2 c9}- r9n6{c2 c5}- r5n6{c5 c8}- c9n6{r4 r3}- c9n8{r3 .} => -6r4c2
braid[6]: c2n9{r3 r8}- r8n3{c2 c8}- r7n3{c7 c3}- c8n4{r8 r4}- r4c3{n4 n6}- b1n6{r1c3 .} => -9r3c1
braid[1]: c1n9{r8 .} => -9r8c2
braid[2]: r1c3{n2 n6}- r3c1{n6 .} => -2r3c2
braid[3]: r8n9{c1 c4}- r4n9{c4 c6}- c6n8{r4 .} => -8r8c1
Single(s): 8r9c1
braid[5]: r3c1{n2 n6}- r1c3{n6 n2}- c6n2{r1 r7}- r9n2{c4 c2}- b7n6{r9c2 .} => -2r6c1
braid[5]: r3n2{c1 c4}- r3n3{c4 c5}- r8n9{c1 c4}- c5n9{r7 r2}- b2n4{r2c5 .} => -2r8c1
braid[6]: r3c1{n2 n6}- r3c9{n6 n8}- r8c2{n2 n3}- r4c2{n3 n7}- r4c9{n7 n6}- c3n6{r4 .} => -2r7c1
braid[7]: r6c4{n1 n3}- c7n3{r6 r7}- c3n3{r7 r4}- r4n4{c3 c8}- r8c8{n4 n5}- r1c8{n5 n6}- c3n6{r1 .} => -1r1c4
Single(s): 1r6c4
braid[3]: r1c4{n2 n5}- r8n8{c4 c6}- c6n5{r8 .} => -2r8c4
braid[3]: r7c9{n4 n2}- r8n2{c9 c2}- r8n3{c2 .} => -4r8c8
Single(s): 4r4c8
braid[2]: c9n2{r8 r7}- c9n4{r7 .} => -5r8c9
braid[4]: c7n8{r5 r3}- c7n4{r3 r2}- r2n7{c7 c9}- c9n5{r2 .} => -5r5c7
braid[4]: r4c3{n6 n3}- r5n5{c1 c8}- r8c8{n5 n3}- r7n3{c7 .} => -6r5c1
braid[4]: r9n6{c5 c2}- r5n6{c2 c8}- r1n6{c8 c3}- r4n6{c3 .} => -6r6c5
braid[4]: r2c9{n5 n7}- r8c8{n5 n3}- r4n7{c9 c2}- c2n3{r4 .} => -5r1c8
braid[1]: r1n5{c6 .} => -5r2c6
braid[2]: r2c2{n9 n1}- r2c6{n1 .} => -9r2c5
Single(s): 4r2c5, 4r3c7, 8r3c9, 8r5c7
braid[1]: c9n6{r4 .} => -6r5c8
braid[2]: r4n8{c4 c6}- r4n9{c6 .} => -3r4c4
braid[1]: r4n3{c3 .} => -3r6c3
braid[2]: r4n8{c6 c4}- r4n9{c4 .} => -6r4c6
braid[2]: r5n6{c2 c5}- r5n7{c5 .} => -2r5c2
braid[1]: c2n2{r9 .} => -2r9c3
braid[2]: r5n6{c5 c2}- r5n7{c2 .} => -2r5c5
braid[2]: r3n2{c4 c1}- r5n2{c1 .} => -2r1c4
Single(s): 5r1c4, 5r9c7, 7r2c7, 5r2c9, 3r6c7, 5r5c8, 2r5c1, 6r3c1, 2r1c3, 1r1c6, 6r1c8, 9r2c6, 1r2c2, 9r3c2, 3r3c5, 2r3c4, 1r3c8, 8r4c6, 9r4c4, 3r5c4, 4r6c3, 5r
6c1, 1r7c7, 3r7c3, 6r4c3, 7r4c9, 3r4c2, 7r5c2, 6r5c5, 2r6c6, 7r6c5, 6r6c9, 6r7c6, 2r8c2, 5r8c6, 3r8c8, 4r8c9, 2r7c9, 9r7c5, 4r7c1, 9r8c1, 8r8c4, 6r9c2, 1r9c3, 4
r9c4, 2r9c5

Unique solution found.B-Rating = 25,Max buffer filling: 231998/800000,Run time = 1h36m56s


My Braid Engine 2 give solution path as follow:

Hidden Text: Show

Code: Select all

Whip[2]: => r7c3<>2
2r7c3 - 1r7{r7c3=r7c7} - 3r7{r7c7=.}
Whip[2]: => r7c3<>4
4r7c3 - 1r7{r7c3=r7c7} - 3r7{r7c7=.}
Whip[2]: => r7c3<>6
6r7c3 - 1r7{r7c3=r7c7} - 3r7{r7c7=.}
Whip[2]: => r7c7<>4
4r7c7 - 1r7{r7c7=r7c3} - 3r7{r7c3=.}
Braid[12]: => r2c7<>1
1r2c7 - r7c7{n1=n3} - 1b9{r7c7=r9c8} - 3b7{r7c3=r8c2} - 1c2{r9c2=r3c2} - 7b9{r9c8=r9c7} - 5r9{r9c7=r9c4} - 9c2{r3c2=r2c2} - r2c5{n9=n4} - r2c6{n9=n5} - 4b8{r7c5=r8c4} - r8c8{n4=n5} - 5r1{r1c8=.}
Braid[16]: => r3c9<>4
4r3c9 - r7c9{n4=n2} - r8c9{n2=n5} - 5b8{r8c4=r9c4} - 4c4{r9c4=r8c4} - r8c8{n4=n3} - 8b8{r8c4=r8c6} - r7c7{n3=n1} - r3c7{n1=n8} - r2c9{n8=n7} - r2c7{n7=n5} - 5b2{r2c6=r1c6} - 2c6{r1c6=r6c6} - 1b5{r6c6=r6c4} - r1c4{n1=n2} - 2c3{r1c3=r9c3} - 2r8{r8c1=.}
Braid[13]: => r5c7<>3
3r5c7 - 3b9{r7c7=r8c8} - 8b6{r5c7=r4c9} - 3c2{r8c2=r4c2} - r3c9{n8=n6} - 7r4{r4c2=r4c8} - 7c9{r6c9=r2c9} - 6b6{r4c8=r5c8} - 7c2{r2c2=r5c2} - 6c2{r5c2=r9c2} - r5c5{n7=n2} - r9c5{n2=n4} - 4b2{r2c5=r3c4} - 4c8{r3c8=.}
Braid[15]: => r9c7<>4
4r9c7 - 7b9{r9c7=r9c8} - 1b9{r9c8=r7c7} - r3c7{n1=n8} - r7c3{n1=n3} - r3c9{n8=n6} - 8b6{r5c7=r4c9} - 7r4{r4c9=r4c2} - 7b1{r2c2=r1c1} - 6b1{r1c1=r1c3} - 3b4{r4c2=r5c2} - 6c2{r5c2=r9c2} - r9c5{n6=n2} - 2c3{r9c3=r6c3} - 2b5{r6c4=r5c4} - 8r5{r5c4=.}
Braid[10]: => r3c8<>4
4r3c8 - 4b2{r3c4=r2c5} - 4c7{r2c7=r6c7} - 3c7{r6c7=r7c7} - r7c3{n3=n1} - r8c8{n3=n5} - r2c3{n1=n8} - 5b8{r8c4=r9c4} - 8r9{r9c4=r9c1} - 4r9{r9c1=r9c3} - 4r4{r4c3=.}
Braid[17]: => r3c4<>1
1r3c4 - r3c8{n1=n6} - 1b5{r6c4=r6c6} - 3b2{r3c4=r3c5} - r3c9{n6=n8} - 4b2{r3c5=r2c5} - 9b2{r2c5=r2c6} - 9b5{r4c6=r4c4} - 8r4{r4c4=r4c6} - 6c6{r4c6=r7c6} - r9c5{n6=n2} - 2c6{r8c6=r1c6} - 2c3{r1c3=r6c3} - r6c4{n2=n3} - 3c7{r6c7=r7c7} - 3b7{r7c3=r8c2} - 2c2{r8c2=r3c2} - 9c2{r3c2=.}
Braid[21]: => r2c9<>4
4r2c9 - r2c5{n4=n9} - r7c9{n4=n2} - 4c7{r2c7=r6c7} - r8c9{n2=n5} - 3c7{r6c7=r7c7} - r7c3{n3=n1} - 3b7{r7c3=r8c2} - r2c3{n1=n8} - 9c2{r8c2=r3c2} - 1b1{r3c2=r2c2} - r2c6{n1=n5} - 5c7{r2c7=r5c7} - 8b6{r5c7=r4c9} - r3c9{n8=n6} - r3c1{n6=n2} - 8c6{r4c6=r8c6} - 2r8{r8c6=r8c4} - r1c4{n2=n1} - r6c4{n1=n3} - 3b4{r6c3=r4c3} - 4r4{r4c3=.}
Whip[1]: => r6c7<>4
4r6c7 - 4b3{r2c7=.}
Braid[13]: => r5c1<>7
7r5c1 - 7b5{r5c5=r6c5} - 7b1{r1c1=r2c2} - 7c7{r2c7=r9c7} - 7c9{r2c9=r4c9} - 8b6{r4c9=r5c7} - 5r5{r5c7=r5c8} - 5c7{r6c7=r2c7} - 5r9{r9c8=r9c4} - 4b3{r2c7=r3c7} - 4c4{r3c4=r8c4} - 8c4{r8c4=r4c4} - 9c4{r4c4=r3c4} - 9r2{r2c5=.}
Braid[25]: => r3c7<>1
1r3c7 - r3c8{n1=n6} - r7c7{n1=n3} - 1b9{r7c7=r9c8} - r3c9{n6=n8} - 3b7{r7c3=r8c2} - 1c2{r9c2=r2c2} - 7b9{r9c8=r9c7} - r2c3{n1=n8} - 5r9{r9c7=r9c4} - r6c7{n7=n5} - 7r2{r2c7=r2c9} - 9c2{r2c2=r3c2} - r1c8{n7=n5} - 5b2{r1c6=r2c6} - 8r9{r9c4=r9c1} - r8c8{n5=n4} - r3c1{n9=n2} - r8c1{n2=n9} - 9c4{r8c4=r4c4} - 8r4{r4c4=r4c6} - 9c6{r4c6=r7c6} - 6c6{r7c6=r6c6} - r6c9{n6=n4} - r6c1{n4=n7} - 7r1{r1c1=.}
Whip[1]: => r9c8<>1
1r9c8 - 1c7{r7c7=.}
Whip[7]: => r8c6<>2
2r8c6 - 8c6{r8c6=r4c6} - 8b6{r4c9=r5c7} - r3c7{n8=n4} - 4b2{r3c4=r2c5} - r9c5{n4=n6} - r7c5{n6=n9} - r7c6{n9=.}
Braid[9]: => r1c1<>6
6r1c1 - 7b1{r1c1=r2c2} - 7b3{r2c7=r1c8} - 1b3{r1c8=r3c8} - 6b3{r3c8=r3c9} - 1c2{r3c2=r9c2} - 6b7{r9c2=r9c3} - 8c3{r9c3=r2c3} - 8c9{r2c9=r4c9} - 7r4{r4c9=.}
Braid[9]: => r1c8<>7
7r1c8 - 6r1{r1c8=r1c3} - 7b9{r9c8=r9c7} - 1b9{r9c7=r7c7} - r7c3{n1=n3} - 3c7{r7c7=r6c7} - r4c3{n3=n4} - 4b6{r4c8=r6c9} - 5r6{r6c9=r6c1} - 7c1{r6c1=.}
Hidden Single: 7 in r1 => r1c1=7
Braid[6]: => r2c3<>1
1r2c3 - r2c2{n1=n9} - r7c3{n1=n3} - r8c2{n3=n2} - r3c2{n2=n6} - r3c9{n6=n8} - 8r2{r2c7=.}
Naked Single: r2c3=8
Braid[8]: => r3c5<>2
2r3c5 - 2b1{r3c1=r1c3} - 3b2{r3c5=r3c4} - 4b2{r3c4=r2c5} - r9c5{n4=n6} - 6b7{r9c1=r7c1} - 6b1{r3c1=r3c2} - 6b3{r3c8=r1c8} - 6r5{r5c8=.}
Braid[8]: => r6c4<>2
2r6c4 - 1c4{r6c4=r1c4} - 2b2{r1c4=r1c6} - 1r2{r2c6=r2c2} - 2c3{r1c3=r9c3} - 5r1{r1c6=r1c8} - 1r9{r9c3=r9c7} - 5b9{r9c7=r8c9} - 2r8{r8c9=.}
Whip[9]: => r9c1<>2
2r9c1 - 8r9{r9c1=r9c4} - 8r5{r5c4=r5c7} - r3c7{n8=n4} - 4b2{r3c4=r2c5} - r9c5{n4=n6} - r9c2{n6=n1} - r2c2{n1=n9} - r3c1{n9=n6} - 6r7{r7c1=.}
Braid[10]: => r9c8<>5
5r9c8 - 7b9{r9c8=r9c7} - 1b9{r9c7=r7c7} - r7c3{n1=n3} - 3b9{r7c7=r8c8} - 4c8{r8c8=r4c8} - r4c3{n4=n6} - 6r1{r1c3=r1c8} - r3c9{n6=n8} - r4c9{n8=n7} - r5c8{n7=.}
Braid[10]: => r4c8<>3
3r4c8 - 3b9{r8c8=r7c7} - 1b9{r7c7=r9c7} - 3c3{r7c3=r6c3} - 5r9{r9c7=r9c4} - r6c4{n3=n1} - r1c4{n1=n2} - 2c3{r1c3=r9c3} - 2r8{r8c1=r8c9} - r7c9{n2=n4} - 4c8{r8c8=.}
Braid[8]: => r5c8<>6
6r5c8 - 3b6{r5c8=r6c7} - 6r1{r1c8=r1c3} - 3r7{r7c7=r7c3} - r4c3{n3=n4} - r6c3{n4=n2} - r5c1{n2=n5} - 5b6{r5c7=r6c9} - 4r6{r6c9=.}
Whip[4]: => r4c6<>6
6r4c6 - 6b6{r4c8=r6c9} - r3c9{n6=n8} - 8r4{r4c9=r4c4} - 9r4{r4c4=.}
Braid[5]: => r3c5<>4
4r3c5 - r3c7{n4=n8} - 3b2{r3c5=r3c4} - 8b6{r5c7=r4c9} - r4c4{n8=n9} - r4c6{n9=.}
Braid[8]: => r6c5<>3
3r6c5 - r6c4{n3=n1} - 3b6{r6c7=r5c8} - 7b5{r6c5=r5c5} - 6b5{r5c5=r6c6} - 2b5{r6c6=r5c4} - r1c4{n2=n5} - 5b8{r8c4=r8c6} - 5c8{r8c8=.}
Braid[8]: => r7c6<>2
2r7c6 - r7c9{n2=n4} - 6c6{r7c6=r6c6} - 4b6{r4c9=r4c8} - 1b5{r6c6=r6c4} - 6b6{r4c8=r4c9} - r4c3{n6=n3} - 3r7{r7c3=r7c7} - 3r6{r6c7=.}
Braid[7]: => r8c6<>9
9r8c6 - r4c6{n9=n8} - r7c6{n9=n6} - 8b6{r4c9=r5c7} - r3c7{n8=n4} - 4b2{r3c4=r2c5} - r7c5{n4=n2} - r9c5{n2=.}
Braid[8]: => r1c6<>5
5r1c6 - 2c6{r1c6=r6c6} - 1c6{r6c6=r2c6} - r1c4{n1=n2} - r2c2{n1=n9} - 2c3{r1c3=r9c3} - r2c5{n9=n4} - r9c5{n4=n6} - 6c6{r7c6=.}
Whip[2]: => r2c7<>5
5r2c7 - 5b2{r2c6=r1c4} - 5r9{r9c4=.}
Whip[2]: => r8c8<>5
5r8c8 - 5b8{r8c4=r9c4} - 5r1{r1c4=.}
Whip[4]: => r4c8<>7
7r4c8 - 7c9{r4c9=r2c9} - 5b3{r2c9=r1c8} - 1b3{r1c8=r3c8} - 6c8{r3c8=.}
Whip[3]: => r4c9<>4
4r4c9 - r4c8{n4=n6} - 6b3{r1c8=r3c9} - 8c9{r3c9=.}
Whip[3]: => r4c3<>3
3r4c3 - 3b7{r7c3=r8c2} - r8c8{n3=n4} - 4r4{r4c8=.}
Whip[2]: => r4c2<>6
6r4c2 - r4c3{n6=n4} - r4c8{n4=.}
Whip[2]: => r4c9<>6
6r4c9 - r4c3{n6=n4} - r4c8{n4=.}
Whip[2]: => r3c8<>6
6r3c8 - 6b1{r3c1=r1c3} - 6r4{r4c3=.}
Naked Single: r3c8=1
Whip[2]: => r6c3<>6
6r6c3 - 6b6{r6c9=r4c8} - 6r1{r1c8=.}
Whip[2]: => r6c4<>3
3r6c4 - 3c7{r6c7=r7c7} - 3c3{r7c3=.}
Naked Single: r6c4=1
Whip[2]: => r6c9<>5
5r6c9 - 4b6{r6c9=r4c8} - 6b6{r4c8=.}
Whip[2]: => r6c9<>7
7r6c9 - 4b6{r6c9=r4c8} - 6b6{r4c8=.}
Whip[2]: => r8c4<>5
5r8c4 - 5b2{r1c4=r2c6} - 5c9{r2c9=.}
Whip[2]: => r9c3<>6
6r9c3 - 6r4{r4c3=r4c8} - 6r1{r1c8=.}
Whip[4]: => r1c3<>1
1r1c3 - r1c6{n1=n2} - r6c6{n2=n6} - 6b6{r6c9=r4c8} - 6r1{r1c8=.}
Hidden Single: 1 in r1 => r1c6=1
Hidden Single: 1 in r2 => r2c2=1
Hidden Single: 2 in c6 => r6c6=2
Hidden Single: 6 in c6 => r7c6=6
Whip[1]: => r3c4<>9
9r3c4 - 9r2{r2c5=.}
Whip[1]: => r3c5<>9
9r3c5 - 9r2{r2c5=.}
Naked Single: r3c5=3
Whip[1]: => r8c4<>2
2r8c4 - 2c5{r7c5=.}
Whip[1]: => r9c4<>2
2r9c4 - 2c5{r7c5=.}
Whip[3]: => r5c2<>6
6r5c2 - r9c2{n6=n2} - 2c3{r9c3=r1c3} - 6c3{r1c3=.}
Braid[3]: => r9c3<>2
2r9c3 - 1r9{r9c3=r9c7} - 2r8{r8c1=r8c9} - 5b9{r8c9=.}
stte
108 Steps!Time elapsed: 17562.1 ms


for this puzzle the time is divided by 14.

N.B: V 6.1 still detect duplicate braids but using a hash table.

[yzfwsf]

This is a milestone improvement. Eliminating duplicates is too time-consuming. I think we should give priority to algorithms that do not generate duplicate paths.

[denis_berthier]

Eliminating duplicates is too time-consuming. I think we should give priority to algorithms that do not generate duplicate paths.

The SHC has never generated duplicate paths. Neither does CSP-Rules.
To be precise, the problem is to avoid generating duplicates and that's where computation times have been drastically improved in the DHC (by introducing hash tables).
.

[yzfwsf]

N.B: V 6.1 still detect duplicate braids but using a hash table.

The SHC has never generated duplicate paths. Neither does CSP-Rules.
To be precise, the problem is to avoid generating duplicates and that's where computation times have been drastically improved in the DHC (by introducing hash tables).
.

We are talking about partial braids, not final braids.

[denis_berthier]

N.B: V 6.1 still detect duplicate braids but using a hash table.

The SHC has never generated duplicate paths. Neither does CSP-Rules.
To be precise, the problem is to avoid generating duplicates and that's where computation times have been drastically improved in the DHC (by introducing hash tables).
.

We are talking about partial braids, not final braids.

Of course.
It's all about the meaning of "generating duplicate" (partial braids). All the possible partial braids need to be considered while expanding from length L to length L+1. The expansions to L+1 that would be duplicates are not generated - in the sense that they never enter the L+1 buffer.
.

[yzfwsf]

Of course.
It's all about the meaning of "generating duplicate" (partial braids). All the possible partial braids need to be considered while expanding from length L to length L+1. The expansions to L+1 that would be duplicates are not generated - in the sense that they never enter the L+1 buffer.
.

That's because SHC uses a deduplication checker when processing L+1, and now uses a hash table implementation.What I mean is that it is best not to generate duplicate partial braids, so that we don't need to implement a time-consuming detection procedure.

[denis_berthier]

.
It's exactly what I said. They are not generated.