Mr.Toad's Fifteen puzzle with timer (modified by stannic)

qqwref said:
It would save some time to either store the result of getColors (updating when the puzzle size or color scheme is changed), or to just not compute the whole array each time, e.g.
Click to expand...

Yes, you're right. Changed the code to not compute the array. Also, changed a bit behavior of scrambling function (in v.5.2, scrambling 16x16 puzzle with Live XXX scheme was very slow). Updated online link.

I'll see if there are other ways to optimize speed. Also, the code is rather long and could be shortened (e.g., right now I have three separate functions for Ao5, Ao12 and Ao100).

Edit: should work more or less fast now. Also, uploaded 5.2 upd 2 offline.

- stannic
 
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Very nice! I thought I should beat that, so I gave it a try and got... 28:16.555 in 9940 moves :p


And no, I don't do this weird row/column shift thing every time, I just felt like doing it on this solve. In fact, I'm thinking I should have started the columns later.


EDIT: I wonder... how does the movecount on an NxN puzzle grow? N^2? N^3? N^4? Something else entirely?
 
Last edited by a moderator:
qqwref said:
Very nice! I thought I should beat that, so I gave it a try and got... 28:16.555 in 9940 moves :p

And no, I don't do this weird row/column shift thing every time, I just felt like doing it on this solve. In fact, I'm thinking I should have started the columns later.
Click to expand...

Well, I've did not reduction to (N-1) x (N-1) too. I've just used Live Rows mode.

This is to show how it is unfair to use it on competitions...

Edit:

qqwref said:
EDIT: I wonder... how does the movecount on an NxN puzzle grow? N^2? N^3? N^4? Something else entirely?
Click to expand...

Probably as N[SUP]3[/SUP]. Basically, you need O(N) moves to solve one tile, and there are O(N[SUP]2[/SUP]) tiles.

I've looked at my PBs (Mo10). They were not established yet, though. Also, it's not FMC but just the best movecounts from speedsolves.

2x2: 4.0 = 2[SUP]3[/SUP] * 0.5
3x3: 42.5 = 3[SUP]3[/SUP] * 1.574
4x4: 100.7 = 4[SUP]3[/SUP] * 1.573
5x5: 219.8 = 5[SUP]3[/SUP] * 1.758
6x6: 438.2 = 6[SUP]3[/SUP] * 2.029
7x7: 724.8 = 7[SUP]3[/SUP] * 2.113
8x8: 1280.0 = 8[SUP]3[/SUP] * 2.5

16x16 (the best "fair" single): 12932 = 16[SUP]3[/SUP] * 3.157

Assuming that after a certain amount of practice the TPS becomes constant independent of the size of puzzle, times would be also O(N[SUP]3[/SUP]).

Edit 2: My movecounts are not a good data source since I'm newbie. Someone else probably could provide better data. Maybe oranjules?

- stannic
 
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For 4x4 and 3x3, that is what I get in average. The 2x2 isn't representative enough I think, and for bigger ones, my method (row by row) isn't move optimal. But the O(N^3) seems a good approximation.
 
So frustrating, I'm trying to do 2-7 relays, but my 7x7 time is bigger that 2-6 combined...
 
Got a lucky 7x7 single: time 1:43.507, moves 606 = 7[SUP]3[/SUP] * 1.767.

Ao5 2:16.160 (774.333 moves), Ao12 2:23.732 (792.7 moves). Rainbow coloring (Multi Rows) used this time, so I believe the results are fair :)

Edit: Oh wow, 4x4 mo10 16.759. 109.4 moves.
best single 12.357 (83 moves), mean tps 6.528

Edit 2: 4x4 single 11.682, 67 moves, tps 5.570.
 
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2-7 relay : sub-3 ! 2:46.812 PB, and i almost always do 2:5x.xx.
I optimized my last line solve (i do it with 3-cycles, so it's a bit long, especially for 16x16)
 
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