derangement (empty) → 0.1.0

raw patch · 4 files changed

+565/−0 lines, 4 filesdep +basedep +fglbuild-type:Customsetup-changed

Dependencies added: base, fgl

Files

• Data/List/Derangement.hs +48/−0
• LICENSE +504/−0
• Setup.lhs +3/−0
• derangement.cabal +10/−0

@@ -0,0 +1,48 @@+-- This program is free software; you can redistribute it and/or modify+-- it under the terms of the GNU General Public License as published by+-- the Free Software Foundation; either version 2 of the License, or+-- (at your option) any later version.+--+-- This program is distributed in the hope that it will be useful,+-- but WITHOUT ANY WARRANTY; without even the implied warranty of+-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the+-- GNU General Public License for more details.+--+-- You should have received a copy of the GNU General Public License+-- along with this program; if not, write to the Free Software+-- Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA++-- | A module for finding derangements of multisets+-- This uses a reduction to the Max Flow problem and then+-- the Edmonds-Karp algorithm provided by "Data.Graph.Inductive.Query.MaxFlow"+-- to find a valid matching.+module Data.List.Derangement (derangement,derangementWRT,derangementBy) where+   import Data.Graph.Inductive.Graph+   import Data.Graph.Inductive.Tree+   import Data.Graph.Inductive.Query.MaxFlow+   import Maybe++   -- | Returns a derangement of a multiset or of a maximal fixed-point free subset represented here as (a,b) where a is paired with b+   derangement :: (Eq a) => [a] -> [a]+   derangement = derangementWRT id++   -- | Like derangement but applies @f :: (Eq b) => (a -> b)@+   derangementWRT :: (Eq b) => (a -> b) -> [a] -> [a]+   derangementWRT f = derangementBy (\x y -> f x == f y)++   -- | Like derangement this returns a zipped derangement but applies @f :: (a -> b)@ before doing equality tests.+   derangementBy :: (a -> a -> Bool) -> [a] -> [a]+   derangementBy cmp xs = map edgeToLab importantEdges+      where g'                    = matchingGraphBy cmp xs+            edgeToLab     (_,b,_) = fromJust $ lab g' b+            importantEdges        = filter isMatch $ labEdges $ maxFlowgraph g' (-1) 0+            isMatch   (u,v,(f,_)) = and [f == 1, u /= -1, v /= 0] -- Note -1 is the source and 0 is the sink++   -- A helper function for generating the G' to run Max flow on+   matchingGraphBy :: (a -> a -> Bool) -> [a] -> Gr a Integer+   matchingGraphBy cmp xs = mkGraph nodeSet edgeSet+      where edgeSet       = concatMap mkEdges zipped+            mkEdges (x,y) = [(-1,x,1), (x+1,0,1)] ++ [(x,a+1,1)| (a,_) <- zipCut y]+            nodeSet       = [(-1,undefined),(0,undefined)] ++ zipped ++ map (\(x,y)-> (x+1,y)) zipped+            zipped        = zip [2,4..] xs+            zipCut      x = filter (\(_,a) -> not $ cmp a x) zipped

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@@ -0,0 +1,3 @@+#!/usr/bin/env runhaskell+> import Distribution.Simple+> main = defaultMain

@@ -0,0 +1,10 @@+Name:                derangement+Version:             0.1.0+Synopsis:            Find derangements of lists+Description:         Find a derangement, a permutation with no fixed points, on a list+License:             GPL+License-file:        LICENSE+Author:              Dennis Griffith+Maintainer:          Dennis Griffith <dgriffi3@uiuc.edu>+Build-Depends:       base,fgl+Exposed-Modules:     Data.List.Derangement