module ProposalMatcher where
import Data.Array.IArray
import Data.Graph.Inductive.Graph
import Data.Graph.Inductive.Tree
import Data.List

import PMInstance
import PMConfig

prefBoringness cfg p = if prefIsVeryBoring cfg p then 2
	else if prefIsBoring cfg p then 1 else 0
prefExpertness cfg p = if prefIsExpert cfg p then 2
	else if prefIsKnowledgeable cfg p then 1 else 0

data REdge = REdge {
	reIdx  :: Int,
	reCap  :: Int,
	reCost :: Wt
}

instance Show REdge where
	show (REdge idx cap cost) = "#" ++ (show idx) ++ ": "
		++ (show cap) ++ " @ " ++ (show cost)

data ReductionResult = ReductionResult {
	rrGraph      :: Gr () REdge,
	rrSource     :: Node,
	rrSink       :: Node,
	rrEIdxBounds :: (Int, Int),
	rrEDIdx      :: (Int, Int) -> Int
}

-- Hack: show as much of the reduction result as we easily can
data RR1 = RR1 (Gr () REdge) Node Node (Int, Int) deriving Show
instance Show ReductionResult where
	show (ReductionResult g so si eib _) = show (RR1 g so si eib)

indexEdges :: Int -> [(Int, Int, REdge)] -> (Int, [(Int, Int, REdge)])
indexEdges i [] = (i, [])
indexEdges i ((v1, v2, re):es) =
	let (imax, ies) = indexEdges (i+1) es in
	(imax, (v1, v2, re{ reIdx = i }) : ies)

doReduction :: PMConfig -> PMInstance -> ReductionResult
doReduction cfg (PMInstance numRvrs numProps rloadA prefA) =
	let
		source = 0
		sink = 1
		rvrNode i boringness = 2 + 3*i + boringness
		propNode j expertness = 2 + 3*numRvrs + 3*j + expertness
		numNodes = 2 + 3*numRvrs + 3*numProps
		edIdx (i, j) = i*numProps + j
		in
	let
		totalReviews = (reviewsEachProposal cfg) * numProps
		totalRelativeLoad = foldl (+) 0 (map (rloadA !) [0 .. numRvrs - 1])
		targetLoad i = ceiling (widenInteger totalReviews * (rloadA ! i) / totalRelativeLoad)
		-- Edge groups A through H are indicated in the figure in the paper.
		edgesABC = do
			i <- [0 .. numRvrs - 1]
			let tl = targetLoad i
			let freeEdgeA = (source, rvrNode i 0, REdge undefined tl 0)
			let nonfreeEdgesA = do
				l <- [tl .. tl + (loadTolerance cfg) - 1]
				let costA = marginalLoadCost cfg ((widenInteger (l - tl) + 1/2) / widenInteger (loadTolerance cfg))
				[(source, rvrNode i 0, REdge undefined 1 costA)]
			let edgesBC = do
				l <- [0 .. tl + (loadTolerance cfg) - 1]
				let costB = marginalBoringCost cfg ((widenInteger l + 1/2) / widenInteger tl)
				let edgeB = (rvrNode i 0, rvrNode i 1, REdge undefined 1 costB)
				let costC = marginalVeryBoringCost cfg ((widenInteger l + 1/2) / widenInteger tl)
				let edgeC = (rvrNode i 1, rvrNode i 2, REdge undefined 1 costC)
				[edgeB, edgeC]
			[freeEdgeA] ++ nonfreeEdgesA ++ edgesBC
		edgesD = do
			i <- [0 .. numRvrs - 1]
			j <- [0 .. numProps - 1]
			let pref = prefA ! (i, j)
			-- We must generate an edge even if there is a conflict
			-- of interest; otherwise we'll fail to read its flow
			-- value in doMatching.
			[(rvrNode i (prefBoringness cfg pref),
				propNode j (prefExpertness cfg pref),
				REdge (edIdx (i, j))
					(if prefIsConflict cfg pref then 0 else 1)
					(assignmentCost cfg pref))]
		edgesEFGH = do
			j <- [0 .. numProps - 1]
			let edgeE = (propNode j 2, propNode j 0, REdge undefined 1 (-(expertBonus cfg)))
			let edgeF = (propNode j 2, propNode j 1, REdge undefined (reviewsEachProposal cfg) 0)
			let edgeGFirst = (propNode j 1, propNode j 0, REdge undefined 1 (-(knowledgeableBonus cfg)))
			let edgeGRest = (propNode j 1, propNode j 0, REdge undefined (reviewsEachProposal cfg - 1) 0)
			let edgeH = (propNode j 0, sink, REdge undefined (reviewsEachProposal cfg) 0)
			[edgeE, edgeF, edgeGFirst, edgeGRest, edgeH]
		theNodes = [(x, ()) | x <- [0 .. numNodes - 1]]
		-- Index the non-D edges
		unindexedEdges = edgesABC ++ edgesEFGH
		(imax, reindexedEdges) = indexEdges (numRvrs*numProps) unindexedEdges
		theEdges = edgesD ++ reindexedEdges
		in
	ReductionResult (mkGraph theNodes theEdges) source sink (0, imax-1) edIdx

-- Returns a list of reviews as ordered pairs (reviewer#, proposal#).
doMatching :: PMConfig -> PMInstance -> PMatching
doMatching cfg inst@(PMInstance numRvrs numProps _ _) =
	let ReductionResult graph source sink idxBounds edIdx = doReduction cfg inst in
	let flowArray = minCostFlow cfg idxBounds reIdx reCap reCost graph (source, sink) in
	let pairs = do
		i <- [0 .. numRvrs - 1]
		j <- [0 .. numProps - 1]
		if flowArray ! edIdx (i, j) == 1
			then [(i, j)]
			else []
		in
	PMatching (sort pairs) -- for prettiness