diff options
Diffstat (limited to 'miralib/ex/queens.m')
| -rw-r--r-- | miralib/ex/queens.m | 22 |
1 files changed, 22 insertions, 0 deletions
diff --git a/miralib/ex/queens.m b/miralib/ex/queens.m new file mode 100644 index 0000000..2ed5734 --- /dev/null +++ b/miralib/ex/queens.m @@ -0,0 +1,22 @@ +||this generates all solutions to the 8 queens problem -- say +|| solns +||and it will print the solutions one per line - all 92 of them. This +||is a good program for testing the garbage collector. Say `/gc' to +||switch on garbage collector diagnostics. + +solns = layn(map show (queens 8)) +queens 0 = [[]] +queens (n+1) = [q:b|b<-queens n;q<-[1..8];safe q b] +safe q b = and[~checks q b i|i<-index b] +checks q b i = q=b!i \/ abs(q-b!i)=i+1 + +||Note that the function `queens n' returns a list of all solutions to +||the n queens problem (placing queens in the first n columns of a chess +||board, so that no queen gives check to another). A board with n +||queens is represented as a list of n numbers, namely the positions of +||the queens in each column + +||This example exhibits a basic technique of lazy functional +||programming, which is to eliminate backtracking from a search problem +||by working at the level of a list of all solutions, rather than a +||single solution. |