----------------------------------------------------------------------------
--- Computing magic series.
--- A series [a_0,a_1,....,a_(n-1)] is called magic iff there are
--- a_i occurrences of i in this series, for all i=1,...,n-1
---
--- Adapted from an example of the TOY(FD) distribution.
----------------------------------------------------------------------------
import CLP.FD
-- Compute a magic series of length n:
magic :: Int -> [Int]
magic n =
let vs = take n (domain 0 (n-1)) -- FD variables
is = map fd (take n [0..]) -- FD constants: indices of elements
in solveFD [FirstFail] vs $
constrain vs vs is /\
sum vs Equ (fd n) /\
scalarProduct is vs Equ (fd n)
constrain :: [FDExpr] -> [FDExpr] -> [FDExpr] -> FDConstr
constrain [] _ _ = true
constrain (x:xs) vs (i:is) = count i vs Equ x /\ constrain xs vs is
magicfrom :: Int -> [[Int]]
magicfrom n = magic n : magicfrom (n+1)
main :: [[Int]]
main = take 3 (magicfrom 7)
--> [[3,2,1,1,0,0,0],[4,2,1,0,1,0,0,0],[5,2,1,0,0,1,0,0,0]]