N-queens problem: Difference between revisions
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=={{header|Quackery}}==
<code>perms</code> is defined at [[Permutations#Quackery]]. The solution used determines the order of the n-Queen solutions found. The output illustrated here is from the <code>perms</code> solution titled "An Uncommon Ordering".
The method used here stems from the following observations.
* Queens can attach with rook (castle) moves or bishop moves.
* The solutions to the N-rooks problem correspond to the permutations of the numbers 0 to N-1 in a zero-indexed list.
* Two queens are attacking one another with bishop moves to the left (from the appropriate point of view) if the sum of the x-coordinate and the y-coordinate for each of the queens is the same.
* A bishop move to the right is the mirror image of a bishop move to the left.
<syntaxhighlight lang="Quackery"> [ false 0 rot
witheach
[ i + bit
2dup & iff
[ drop dip not
conclude ]
done
| ]
drop ] is l-bishop ( [ --> b )
[ reverse l-bishop ] is r-bishop ( [ --> b )
[ [] swap perms
witheach
[ dup l-bishop iff
drop done
dup r-bishop iff
drop done
nested join ] ] is queens ( n --> [ )
8 queens
dup size echo say " solutions."
cr cr
witheach
[ echo
i^ 1+ 4 mod iff sp else cr ]</syntaxhighlight>
{{out}}
<pre>92 solutions.
[ 4 1 5 0 6 3 7 2 ] [ 5 2 4 6 0 3 1 7 ] [ 5 3 6 0 2 4 1 7 ] [ 2 5 1 6 4 0 7 3 ]
[ 5 2 0 6 4 7 1 3 ] [ 5 1 6 0 2 4 7 3 ] [ 5 3 6 0 7 1 4 2 ] [ 2 5 1 6 0 3 7 4 ]
[ 5 2 6 1 3 7 0 4 ] [ 5 2 6 3 0 7 1 4 ] [ 1 5 0 6 3 7 2 4 ] [ 5 1 6 0 3 7 4 2 ]
[ 5 2 6 1 7 4 0 3 ] [ 4 6 1 5 2 0 3 7 ] [ 4 6 1 5 2 0 7 3 ] [ 3 6 4 2 0 5 7 1 ]
[ 3 6 4 1 5 0 2 7 ] [ 6 4 2 0 5 7 1 3 ] [ 3 1 6 2 5 7 0 4 ] [ 3 1 6 2 5 7 4 0 ]
[ 0 6 3 5 7 1 4 2 ] [ 6 1 5 2 0 3 7 4 ] [ 1 6 2 5 7 4 0 3 ] [ 6 2 0 5 7 4 1 3 ]
[ 4 1 3 6 2 7 5 0 ] [ 2 4 6 0 3 1 7 5 ] [ 4 6 3 0 2 7 5 1 ] [ 4 6 1 3 7 0 2 5 ]
[ 1 4 6 3 0 7 5 2 ] [ 4 6 0 3 1 7 5 2 ] [ 4 2 0 6 1 7 5 3 ] [ 1 4 6 0 2 7 5 3 ]
[ 4 6 0 2 7 5 3 1 ] [ 3 1 6 4 0 7 5 2 ] [ 6 3 1 4 7 0 2 5 ] [ 2 0 6 4 7 1 3 5 ]
[ 1 6 4 7 0 3 5 2 ] [ 0 6 4 7 1 3 5 2 ] [ 3 6 2 7 1 4 0 5 ] [ 3 6 0 7 4 1 5 2 ]
[ 6 1 3 0 7 4 2 5 ] [ 2 6 1 7 4 0 3 5 ] [ 6 2 7 1 4 0 5 3 ] [ 6 3 1 7 5 0 2 4 ]
[ 2 6 1 7 5 3 0 4 ] [ 6 0 2 7 5 3 1 4 ] [ 4 1 3 5 7 2 0 6 ] [ 4 0 3 5 7 1 6 2 ]
[ 4 2 0 5 7 1 3 6 ] [ 3 5 0 4 1 7 2 6 ] [ 5 3 0 4 7 1 6 2 ] [ 5 2 4 7 0 3 1 6 ]
[ 2 5 1 4 7 0 6 3 ] [ 5 0 4 1 7 2 6 3 ] [ 2 5 3 1 7 4 6 0 ] [ 2 5 3 0 7 4 6 1 ]
[ 5 3 1 7 4 6 0 2 ] [ 5 2 0 7 4 1 3 6 ] [ 2 5 7 0 4 6 1 3 ] [ 1 3 5 7 2 0 6 4 ]
[ 3 5 7 2 0 6 4 1 ] [ 3 5 7 1 6 0 2 4 ] [ 2 5 7 1 3 0 6 4 ] [ 2 5 7 0 3 6 4 1 ]
[ 5 2 0 7 3 1 6 4 ] [ 1 5 7 2 0 3 6 4 ] [ 5 7 1 3 0 6 4 2 ] [ 0 5 7 2 6 3 1 4 ]
[ 3 1 4 7 5 0 2 6 ] [ 3 0 4 7 5 2 6 1 ] [ 4 7 3 0 2 5 1 6 ] [ 2 4 1 7 5 3 6 0 ]
[ 0 4 7 5 2 6 1 3 ] [ 4 0 7 5 2 6 1 3 ] [ 3 1 7 5 0 2 4 6 ] [ 7 2 0 5 1 4 6 3 ]
[ 1 7 5 0 2 4 6 3 ] [ 3 7 0 2 5 1 6 4 ] [ 7 3 0 2 5 1 6 4 ] [ 3 0 4 7 1 6 2 5 ]
[ 2 4 7 3 0 6 1 5 ] [ 4 2 7 3 6 0 5 1 ] [ 4 1 7 0 3 6 2 5 ] [ 4 0 7 3 1 6 2 5 ]
[ 4 7 3 0 6 1 5 2 ] [ 2 4 1 7 0 6 3 5 ] [ 3 7 4 2 0 6 1 5 ] [ 3 1 7 4 6 0 2 5 ]
[ 3 7 0 4 6 1 5 2 ] [ 7 1 4 2 0 6 3 5 ] [ 7 1 3 0 6 4 2 5 ] [ 2 7 3 6 0 5 1 4 ]</pre>
=={{header|QBasic}}==
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