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Solving the Knight's Tour Puzzle In 60 Lines of Python
ttsiod writes "When I was a kid, I used to play the Knight's Tour puzzle with pen and paper: you simply had to pass once from every square of a chess board, moving like a Knight. Nowadays, I no longer play chess; but somehow I remembered this nice little puzzle and coded a 60-line Python solver that can tackle even 100x100 boards in less than a second. Try beating this, fellow coders!"
too bad that your code will break with the next python version.
C-x C-m KnightsPuzzle
He'd hop into KITT and go anywhere he damn well pleases.
Though I have better things to do than actually try, looking over the code FTFA, I have to say that I think a transliteration of this code into Scheme or Lisp would actually look cleaner than Python. And I do know that that would deal with the problem the writer ran into, namely that Python has an absurdly low recursion limit.
I do like Python's syntax (for anything under 100 lines of code) but calling it a model of functional programming is just silly.
Apparently, this isn't NP-complete. There is an algorithm that can solve this in O(n) time, see here: http://mathworld.wolfram.com/KnightsTour.html
This will save a LOT of time for larger boards. Try to implement this.
Marge, get me your address book, 4 beers, and my conversation hat.
wrapper(Size, [X, Y], Path) :- :- :- :-
X == 1,
Y == 1,
Depth is Size * Size - 1,
worker(Size, [X, Y], Depth, [], ReversedPath),
reverse(ReversedPath, Path),
write(Path), nl.
worker(_, State, 0, CurrentPath, [State|CurrentPath]).
worker(Size, State, Depth, CurrentPath, FinalPath)
DepthM1 is Depth - 1,
move_generator(Size, State, NewState),
not(checker(NewState, CurrentPath)),
worker(Size, NewState, DepthM1, [State|CurrentPath], FinalPath).
checker(State, [State|_]).
checker(State, [_|StateList])
checker(State, StateList).
move_generator(Size, [X, Y], [NewX, NewY])
move(MoveX, MoveY),
NewX is X + MoveX, NewX == 1,
NewY is Y + MoveY, NewY == 1.
move(1, 2).
move(2, 1).
move(2, -1).
move(1, -2).
move(-1, -2).
move(-2, -1).
move(-2, 1).
move(-1, 2).
Except you commented out all of the code.
There. I did it in one line of code.
That doesn't look like perl to me...
#!/usr/bin/perl
use Chess;
$knight = Chess::Piece::Knight->new();
$board = Chess::Board->new(100, 100, setup => {
$knight => "a1";
});
$knight->tour()->show();
With the "added intelligence" of the second version, the recursive search devolved into a linear one since the very first attempt at each step will lead to a good solution (add a print to the backtracking part and see if this isn't the case).
So you might as well convert the recursion into a loop and eliminate the stack overflows for large boards.
Is submitter really thinking he is special because he implemented a trivial backtracking algorithm that every first semester CS student has done?
Alas, Python lambdas are very limited, only allowing a single expression. If you need a function that does two things, you can't use lambda anymore. This is not a great hardship as Python allows you to declare inner-scoped functions and you can use that instead, but it's still annoying. I do recommend Python though, as it's a great language even with the occasional shortcoming.
If you mod me Overrated, you are admitting that you have no penis.
Here's a solution in 14 lines of APL. I'm pretty sure they could've made it shorter, but readability would've been even worse. APL has been called a "write-only language".
-- "At Microsoft, quality is job 1.1" -- PC Magazine, Nov. 1994
[
Woosh.
As part of my undergrad education. Taking less than a second on today's hardware is nothing spectacular; the secret is in the algorithm: You rate the squares according to the number of moves available from that square and, when given a choice, pick the square with the least number of moves. This way, you don't work yourself into a dead-end situation as frequently. Combine this with a little backtracking, and you've got a nice example to show how algorithm selection has a much larger impact on runtime performance than language selection.
Incidentally, 200 MHz was considered a fast CPU when I did it, and I remember it taking 8 billion moves and all night without finding a solution. Until, that is, we implemented the preferential choice part of the algorithm. After that, it was pretty much instantaneous.
The society for a thought-free internet welcomes you.
From experience, commenting out the code makes it better. :P
If you can read this, I forgot to post anonymously.
Yes, but a lot of this stuff really isn't worth posting online. Espectially Slashdot I have created many algorithms myself without the need to post it for slashdot acceptance. Some interesting compression algorithms, Memory management algorithms... Whatever that I feel like exploring today. But it is for my own personal knowledge not for public viewing of my code as my method will be to prove some particular point to myself nor will it be efficient or complete, and any attempt to have it posted like the guy who posted this thread will just get critized for anything that is not the best as it could possibly be.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
Well, here's the thing. Perl was used for _everything_ there for a while, sysadmins who thought they were developers were developing full blown applications in Perl and finding, surprise surprise, that it wasn't real maintainable. So I think we're seeing less of that these days. But Perl is not dying, that's silly. If anything Perl is just being relegated to what it's _really_ good at, and that's UNIX automation tasks and quick throw-away scripts, and _sometimes_ smallish applications. There's really no better language for these types of things.
I take the point of the blog plug was that I shouldn't be able to do it in C++ with 60 lines....
//hence the reason I am waiting for c++0x ;
:(
1 #include <set>
2 #include <iostream>
3 #include <cassert>
4 using namespace std;
5
6 int dx[8]={1,1,-1,-1,2,2,-2,-2}, dy[8]={2,-2,2,-2,1,-1,1,-1};
7 int D[50][50];
8 int N,C;
9
10 #define valid(x,y) ((x>=0) && (x<N) && (y>=0) && (y<N) && (D[x][y]==-1 ) )
11
12 bool show()
13 {
14 for (int i=N;i--;)
15 {
16 for (int j=N;j--;)
17 cout<<"\t"<<D[i][j];
18 cout<<"\n";
19 }
20 return true;
21 }
22
23 bool rec(int x, int y)
24 {
25 D[x][y]=C++;
26 if(C==N*N)
27 return show();
28
29 set< pair<int, pair<int,int> > > poss;
30 for (int r=8;r--;)
31 if(valid(x+dx[r], y+dy[r]))
32 {
33 int neighb=0;
34 for (int t=8;t--;)
35 neighb+= valid(x+dx[r]+dx[t],y+dy[r]+dy[t] );
36 poss.insert( make_pair(neighb, make_pair(x+dx[r],y+dy[r] ) ));
37 }
38
39 for (typeof(poss.begin()) q=poss.begin(); q!=poss.end(); q++)
40 if (rec(q->second.first, q->second.second))
41 return true;
42
43 D[x][y]=-1;
44 C--;
45
46 return false;
47 }
48
49 void solve(int n)
50 {
51 N=n, C=0;
52 memset(D,-1,sizeof(D));
53 assert(rec(0,0))
54 }
55
56 int main()
57 {
58 int n;
59 while((cin>>n) && (n>0))
60 solve(n);
61 return 0;
62 }
The bastards! Those darn brackets force me to have 2 extra lines
Copyright infringement is "piracy" in the same way DRM is "consumer rape"
No output, and your font is all wrong.
*ducks*