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Talk:Solve a Hidato puzzle: Difference between revisions
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→solved it using constraint programming
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:: (I'd have written about this earlier, but there's some kind of weird proxy stopping me from posting to RC from home.) –[[User:Dkf|Donal Fellows]] 16:33, 6 May 2012 (UTC)
::: I'm not sure Hidato is really equiv to a general Hamiltioian path problem -- is it known to be NP-complete? Hidato is much more constrained in that it has a unique solution requirement; its nodes can have only up to eight neighbors; and more importantly, spatial proximity between nodes are tightly related to the connectivity between them. Although I do agree that if a problem isn't mathematically well understood (as in, having a known effective algorithm), it's generally not worth putting too much effort into it. --[[User:Ledrug|Ledrug]] 17:49, 6 May 2012 (UTC)
:::: I'm also not ''sure'' that is HP, but the suspicion remains. I couldn't find anything in WP on requirements on connectivity for graphs doing HP; maybe there is something, but I couldn't find it. (Graph theory isn't my specialty, not at all.) –[[User:Dkf|Donal Fellows]] 08:55, 7 May 2012 (UTC)
== Short C version ==
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0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 0 0 0 -1 -1 -1
:--[[User:Ledrug|Ledrug]] 17:29, 6 May 2012 (UTC)
== On the algebra of Hidato and Knights's Tour ==
To clarify that the problem is mathmatically well understood lets consider Evil case 1. In the general case for
<pre>
a
b c d
e f g
</pre>
The problem is to find a solution for the following simultaneous equations:
<pre>
a1 .. g7 are binary variables.
a = a1*1 + a2*2 + a3*3 + a4*4 + a5*5 + a6*6 + a7*7
...
g = g1*1 + g2*2 + g3*3 + g4*4 + g5*5 + g6*6 + g7*7
a1 + a2 + a3 + a4 + a5 + a6 + a7 = 1
...
g1 + g2 + g3 + g4 + g5 + g6 + g7 = 1
a1 + b1 + c1 + d1 + e1 + f1 + g1 = 1
...
a7 + b7 + c7 + d7 + e7 + f7 + g7 = 1
b2 + c2 + d2 = a1
...
b7 + c7 + d7 = a6
a2 + c2 + e2 + f2 = b1
...
a7 + c7 + e7 + f7 = b6
a2 + b2 + d2 + e2 + f2 + g2 = c1
...
a7 + b7 + d7 + e7 + f7 + g7 = c6
a2 + c2 + f2 + g2 = d1
...
a7 + c7 + f7 + g7 = d6
b2 + c2 + f2 = e1
...
b7 + c7 + f7 = e6
b2 + c2 + d2 + e2 + g2 = f1
...
b7 + c7 + d7 + e7 + g7 = f6
c2 + d2 + f2 = g2
...
c7 + d7 + f7 = g6
</pre>
In the particular case:
<pre>
4
b 7 d
1 f g
</pre>
Which for this simple case can be resolved by inspection to:
<pre>
b = b2*2 + b3*3
d = d3*3 + d5*5
f = f2*2 + f6*6
g = g3*3 + g6*6
b3 + d3 = 1
b5 + d5 = 1
b2 + f2 = 1
b6 + d6 + f6 + g6 = 1
b3 + b5 = 1
d3 + d5 = 1
f2 + f6 = 1
g6 = 1
</pre>
Putting g6 into the model and resolving again solves the problem by hand.
It is apparent that the number of equations increases rapidly with problem size. A method exists which makes this increase linear see http://en.wikipedia.org/wiki/Tseitin-Transformation.
--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 14:12, 30 December 2013 (UTC)
: if a1 = 0, the equation b2 + c2 + d2 = a1 means "Non of a's neighbors is 2" which is not necessarily true. so this solution does not work. --[[User:Ak|Ak]] ([[User talk:Ak|talk]]) 17:10, 21 March 2014 (UTC)
==extra credit suggestion==
How about adding an extra credit for this task: support Numbrix puzzles as well as Hidato puzzles. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 04:50, 18 December 2013 (UTC)
The REXX programming example only needed a couple of '''if''' statements to solve Numbrix puzzles in addition to Hidato puzzles. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 04:50, 18 December 2013 (UTC)
::Two points. First I think it would be better to add a related task Solve Numbrix Puzzles. I know what Numbrix is but only from external servlets and the press. Explaining it to them what be's satisfaction would further complicate this task. Secondly I had an extra credit for showing that the same logic could solve the Knight's Tour, but them what be made me remove it. The Knight's Tour is exactly the same as Hidato, only the Knight has a different view of which cells are adjacent. Numbrix has only 4 adjacent cells whereas Knight's Tour and Hidato have 8.--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 13:35, 30 December 2013 (UTC)
::: Numbrix puzzles (in my thinking) are just a simpler Hidato puzzle, in the manner of having less possible moves (i.e., being more restrictive). But I have no qualms of someone creating a Rosetta Code task just for Numbrix puzzles. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 16:20, 30 December 2013 (UTC)
::: As regarding the Knights Tour: in fact, I used the same code in the REXX example, I just tweaked/optimized the code a bit for speed. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 16:20, 30 December 2013 (UTC)
== solved it using constraint programming ==
Behold: http://hidoku-solver.appspot.com/
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