Re: [Haskell-cafe] Extension for "Pearls of Functional Algorithm Design" by Richard Bird, 2010, page 25 #Haskell

21 May 2011


      Do you have some sort of link aggregator that auto-posts to haskell-cafe?

On Sat, May 21, 2011 at 12:09 AM, KC  wrote:
...
Extension for "Pearls of Functional Algorithm Design" by Richard Bird,
2010, page 25 #Haskell
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
module SelectionProblem where
import Data.Array
import Data.List
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-- Question: is there a way to get the type signature as the following:
-- smallest :: (Ord a) => Int -> [Array Int a] -> a
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-- Works on 2 finite ordered disjoint sets represented as sorted arrays.
smallest :: (Ord a) => Int -> (Array Int a, Array Int a) -> a
smallest k (xa,ya) =
   search k (xa,ya) (0,m+1) (0,n+1)
       where
       (0,m) = bounds xa
       (0,n) = bounds ya
-- Removed some of the "indexitis" at the cost of calling another function.
search :: (Ord a) => Int -> (Array Int a, Array Int a) -> (Int,Int) ->
(Int,Int) -> a
search k (xa,ya) (lx,rx) (ly,ry)
   | lx == rx  = ya ! (k+ly)
   | ly == ry  = xa ! (k+lx)
   | otherwise = case (xa ! mx < ya ! my) of
                     (True)    -> smallest2h k (xa,ya)
((lx,mx,rx),(ly,my,ry))
                     (False)   -> smallest2h k (ya,xa)
((ly,my,ry),(lx,mx,rx))
                 where
                     mx = (lx+rx) `div` 2
                     my = (ly+ry) `div` 2
-- Here the sorted arrays are in order by their middle elements.
-- Only cutting the leading or trailing array by half.
-- Here xa is the first array and ya the second array by their middle
elements.
smallest2h :: (Ord a) => Int -> (Array Int a, Array Int a) ->
((Int,Int,Int),(Int,Int,Int)) -> a
smallest2h k (xa,ya) ((lx,mx,rx),(ly,my,ry)) =
   case (k<=mx-lx+my-ly) of
     (True)    -> search k (xa,ya) (lx,rx) (ly,my)
     (False)   -> search (k-(mx-lx)-1) (xa,ya) (mx+1,rx) (ly,ry)
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
-- Works on 3 finite ordered disjoint sets represented as sorted arrays.
smallest3 :: (Ord a) => Int -> (Array Int a, Array Int a, Array Int a) -> a
smallest3 k (xa,ya,za) =
   -- On each recursive call the order of the arrays can switch.
   search3 k (xa,ya,za) (0,bx+1) (0,by+1) (0,bz+1)
       where
       (0,bx) = bounds xa
       (0,by) = bounds ya
       (0,bz) = bounds za
-- Removed some of the "indexitis" at the cost of calling another function.
search3 :: (Ord a) => Int -> (Array Int a, Array Int a, Array Int a) ->
           (Int,Int) -> (Int,Int) -> (Int,Int) -> a
search3 k (xa,ya,za) (lx,rx) (ly,ry) (lz,rz)
   | lx == rx && ly == ry  = za ! (k+lz)
   | ly == ry && lz == rz  = xa ! (k+lx)
   | lx == rx && lz == rz  = ya ! (k+ly)
| lx == rx  = search k (ya,za) (ly,ry) (lz,rz)
   | ly == ry  = search k (xa,za) (lx,rx) (lz,rz)
   | lz == rz  = search k (xa,ya) (lx,rx) (ly,ry)
| otherwise = case (xa ! mx < ya ! my, xa ! mx < za ! mz, ya ! my
< za ! mz) of
                     (True, True, True)    -> smallest3h k (xa,ya,za)
((lx,mx,rx),(ly,my,ry),(lz,mz,rz)) -- a smallest3h k (xa,za,ya)
((lx,mx,rx),(lz,mz,rz),(ly,my,ry)) -- a smallest3h k (ya,xa,za)
((ly,my,ry),(lx,mx,rx),(lz,mz,rz)) -- b smallest3h k (ya,za,xa)
((ly,my,ry),(lz,mz,rz),(lx,mx,rx)) -- b smallest3h k (za,xa,ya)
((lz,mz,rz),(lx,mx,rx),(ly,my,ry)) -- c smallest3h k (za,ya,xa)
((lz,mz,rz),(ly,my,ry),(lx,mx,rx)) -- c
where
                     mx = (lx+rx) `div` 2
                     my = (ly+ry) `div` 2
                     mz = (lz+rz) `div` 2
-- Here the sorted arrays are in order by their middle elements.
-- Only cutting the leading or trailing array by half.
-- Here xa is the first array, ya the second array, and za the third
array by their middle elements.
smallest3h :: (Ord a) => Int -> (Array Int a, Array Int a, Array Int a) ->
       ((Int,Int,Int),(Int,Int,Int),(Int,Int,Int)) -> a
smallest3h k (xa,ya,za) ((lx,mx,rx),(ly,my,ry),(lz,mz,rz)) =
   case (k<=mx-lx+my-ly+mz-lz) of
     (True)    -> search3 k (xa,ya,za) (lx,rx) (ly,ry) (lz,mz)
     (False)   -> search3 (k-(mx-lx)-1) (xa,ya,za) (mx+1,rx) (ly,ry)
(lz,rz)
--
--
Regards,
KC
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Re: [Haskell-cafe] Extension for "Pearls of Functional Algorithm Design" by Richard Bird, 2010, page 25 #Haskell

Daniel Peebles