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
This generates all solutions to the 8 queens problem -- say
solnsand 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.
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.