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module JCombinations
( combinationsIndex
) where
combinationsIndex :: Int -> Int -> [[Int]]
combinationsIndex n m -- return always sorted members and sorted list
| m < n = []
| otherwise =
-- acc room nextId to move
impli [[0 .. (n-1)]] (replicate n (m-n)) (n-1)
where
incrAt idx list = take idx list
++ ((list !! idx) +1) : drop (idx+1) list
dcrAt idx list = take idx list
++ ((list !! idx) -1) : drop (idx+1) list
impli acc roomLs nextCsr =
if roomLs !! nextCsr > 0 -- still current cursor is movable
then impli (acc ++ [newPosLs]) (dcrAt nextCsr roomLs) nextCsr
else -- no more room to move
-- find the next element available to move
case (pointNextCsr nextCsr) of
Nothing -> acc -- if we cannot move any of them which means
-- we found all cases.
Just newCsr -> -- move all cursors
-- and try to move last cursor next time
impli ( acc ++ [updatePosLsFrom newCsr] )
(updateRoomFrom newCsr) (n-1)
where
posLs = last acc
newPosLs = (incrAt nextCsr posLs)
updatePosLsFrom fromCsr = -- move all cursors
take (fromCsr) posLs -- keep until fromCsr
-- and reset others to leftmost part of the elements
++ take (n -fromCsr) [ ((posLs !! fromCsr)+1) .. ]
updateRoomFrom fromCsr =
take (fromCsr) roomLs
-- reduce each room by one
++ replicate (n -fromCsr) ((roomLs !! fromCsr) -1)
pointNextCsr curcsr
| curcsr == 0 = Nothing
| otherwise = if roomLs !! nxtcsr > 0 then Just nxtcsr
else pointNextCsr nxtcsr
where nxtcsr = curcsr - 1
|
