Synnefo » snf-ganeti » ganeti-local

{-| Implementation of cluster-wide logic.

This module holds all pure cluster-logic; I\/O related functionality

goes into the "Main" module for the individual binaries.

-}

module Ganeti.HTools.Cluster

    (

     -- * Types

      Placement

    , Solution(..)

    , Table(..)

    , Removal

    , Score

    , IMove(..)

    -- * Generic functions

    , totalResources

    -- * First phase functions

    , computeBadItems

    -- * Second phase functions

    , computeSolution

    , applySolution

    , printSolution

    , printSolutionLine

    , formatCmds

    , printNodes

    -- * Balacing functions

    , applyMove

    , checkMove

    , compCV

    , printStats

    -- * IAllocator functions

    , allocateOnSingle

    , allocateOnPair

    ) where

import Data.List

import Data.Maybe (isNothing, fromJust)

import Text.Printf (printf)

import Data.Function

import Control.Monad

import qualified Ganeti.HTools.Container as Container

import qualified Ganeti.HTools.Instance as Instance

import qualified Ganeti.HTools.Node as Node

import Ganeti.HTools.Types

import Ganeti.HTools.Utils

-- * Types

-- | A separate name for the cluster score type.

type Score = Double

-- | The description of an instance placement.

type Placement = (Idx, Ndx, Ndx, Score)

-- | A cluster solution described as the solution delta and the list

-- of placements.

data Solution = Solution Int [Placement]

                deriving (Eq, Ord, Show)

-- | A removal set.

data Removal = Removal Node.List [Instance.Instance]

-- | An instance move definition

data IMove = Failover                -- ^ Failover the instance (f)

           | ReplacePrimary Ndx      -- ^ Replace primary (f, r:np, f)

           | ReplaceSecondary Ndx    -- ^ Replace secondary (r:ns)

           | ReplaceAndFailover Ndx  -- ^ Replace secondary, failover (r:np, f)

           | FailoverAndReplace Ndx  -- ^ Failover, replace secondary (f, r:ns)

             deriving (Show)

-- | The complete state for the balancing solution

data Table = Table Node.List Instance.List Score [Placement]

             deriving (Show)

-- * Utility functions

-- | Returns the delta of a solution or -1 for Nothing.

solutionDelta :: Maybe Solution -> Int

solutionDelta sol = case sol of

                      Just (Solution d _) -> d

                      _ -> -1

-- | Cap the removal list if needed.

capRemovals :: [a] -> Int -> [a]

capRemovals removals max_removals =

    if max_removals > 0 then

        take max_removals removals

    else

        removals

-- | Check if the given node list fails the N+1 check.

verifyN1Check :: [Node.Node] -> Bool

verifyN1Check nl = any Node.failN1 nl

-- | Verifies the N+1 status and return the affected nodes.

verifyN1 :: [Node.Node] -> [Node.Node]

verifyN1 nl = filter Node.failN1 nl

{-| Computes the pair of bad nodes and instances.

The bad node list is computed via a simple 'verifyN1' check, and the

bad instance list is the list of primary and secondary instances of

those nodes.

-}

computeBadItems :: Node.List -> Instance.List ->

                   ([Node.Node], [Instance.Instance])

computeBadItems nl il =

  let bad_nodes = verifyN1 $ filter (not . Node.offline) $ Container.elems nl

      bad_instances = map (\idx -> Container.find idx il) $

                      sort $ nub $ concat $

                      map (\ n -> (Node.slist n) ++ (Node.plist n)) bad_nodes

  in

    (bad_nodes, bad_instances)

-- | Compute the total free disk and memory in the cluster.

totalResources :: Node.List -> (Int, Int)

totalResources nl =

    foldl'

    (\ (mem, dsk) node -> (mem + (Node.f_mem node),

                           dsk + (Node.f_dsk node)))

    (0, 0) (Container.elems nl)

-- | Compute the mem and disk covariance.

compDetailedCV :: Node.List -> (Double, Double, Double, Double, Double)

compDetailedCV nl =

    let

        all_nodes = Container.elems nl

        (offline, nodes) = partition Node.offline all_nodes

        mem_l = map Node.p_mem nodes

        dsk_l = map Node.p_dsk nodes

        mem_cv = varianceCoeff mem_l

        dsk_cv = varianceCoeff dsk_l

        n1_l = length $ filter Node.failN1 nodes

        n1_score = (fromIntegral n1_l) / (fromIntegral $ length nodes)

        res_l = map Node.p_rem nodes

        res_cv = varianceCoeff res_l

        offline_inst = sum . map (\n -> (length . Node.plist $ n) +

                                        (length . Node.slist $ n)) $ offline

        online_inst = sum . map (\n -> (length . Node.plist $ n) +

                                       (length . Node.slist $ n)) $ nodes

        off_score = (fromIntegral offline_inst) /

                    (fromIntegral $ online_inst + offline_inst)

    in (mem_cv, dsk_cv, n1_score, res_cv, off_score)

-- | Compute the /total/ variance.

compCV :: Node.List -> Double

compCV nl =

    let (mem_cv, dsk_cv, n1_score, res_cv, off_score) = compDetailedCV nl

    in mem_cv + dsk_cv + n1_score + res_cv + off_score

-- * hn1 functions

-- | Add an instance and return the new node and instance maps.

addInstance :: Node.List -> Instance.Instance ->

               Node.Node -> Node.Node -> Maybe Node.List

addInstance nl idata pri sec =

  let pdx = Node.idx pri

      sdx = Node.idx sec

  in do

      pnode <- Node.addPri pri idata

      snode <- Node.addSec sec idata pdx

      new_nl <- return $ Container.addTwo sdx snode

                         pdx pnode nl

      return new_nl

-- | Remove an instance and return the new node and instance maps.

removeInstance :: Node.List -> Instance.Instance -> Node.List

removeInstance nl idata =

  let pnode = Instance.pnode idata

      snode = Instance.snode idata

      pn = Container.find pnode nl

      sn = Container.find snode nl

      new_nl = Container.addTwo

               pnode (Node.removePri pn idata)

               snode (Node.removeSec sn idata) nl in

  new_nl

-- | Remove an instance and return the new node map.

removeInstances :: Node.List -> [Instance.Instance] -> Node.List

removeInstances = foldl' removeInstance

{-| Compute a new version of a cluster given a solution.

This is not used for computing the solutions, but for applying a

(known-good) solution to the original cluster for final display.

It first removes the relocated instances after which it places them on

their new nodes.

 -}

applySolution :: Node.List -> Instance.List -> [Placement] -> Node.List

applySolution nl il sol =

    let odxes = map (\ (a, b, c, _) -> (Container.find a il,

                                        Node.idx (Container.find b nl),

                                        Node.idx (Container.find c nl))

                    ) sol

        idxes = (\ (x, _, _) -> x) (unzip3 odxes)

        nc = removeInstances nl idxes

    in

      foldl' (\ nz (a, b, c) ->

                 let new_p = Container.find b nz

                     new_s = Container.find c nz in

                 fromJust (addInstance nz a new_p new_s)

           ) nc odxes

-- ** First phase functions

{-| Given a list 1,2,3..n build a list of pairs [(1, [2..n]), (2,

    [3..n]), ...]

-}

genParts :: [a] -> Int -> [(a, [a])]

genParts l count =

    case l of

      [] -> []

      x:xs ->

          if length l < count then

              []

          else

              (x, xs) : (genParts xs count)

-- | Generates combinations of count items from the names list.

genNames :: Int -> [b] -> [[b]]

genNames count1 names1 =

  let aux_fn count names current =

          case count of

            0 -> [current]

            _ ->

                concatMap

                (\ (x, xs) -> aux_fn (count - 1) xs (x:current))

                (genParts names count)

  in

    aux_fn count1 names1 []

{-| Checks if removal of instances results in N+1 pass.

Note: the check removal cannot optimize by scanning only the affected

nodes, since the cluster is known to be not healthy; only the check

placement can make this shortcut.

-}

checkRemoval :: Node.List -> [Instance.Instance] -> Maybe Removal

checkRemoval nl victims =

  let nx = removeInstances nl victims

      failN1 = verifyN1Check (Container.elems nx)

  in

    if failN1 then

      Nothing

    else

      Just $ Removal nx victims

-- | Computes the removals list for a given depth.

computeRemovals :: Node.List

                 -> [Instance.Instance]

                 -> Int

                 -> [Maybe Removal]

computeRemovals nl bad_instances depth =

    map (checkRemoval nl) $ genNames depth bad_instances

-- ** Second phase functions

-- | Single-node relocation cost.

nodeDelta :: Ndx -> Ndx -> Ndx -> Int

nodeDelta i p s =

    if i == p || i == s then

        0

    else

        1

-- | Compute best solution.

--

-- This function compares two solutions, choosing the minimum valid

-- solution.

compareSolutions :: Maybe Solution -> Maybe Solution -> Maybe Solution

compareSolutions a b = case (a, b) of

  (Nothing, x) -> x

  (x, Nothing) -> x

  (x, y) -> min x y

-- | Check if a given delta is worse then an existing solution.

tooHighDelta :: Maybe Solution -> Int -> Int -> Bool

tooHighDelta sol new_delta max_delta =

    if new_delta > max_delta && max_delta >=0 then

        True

    else

        case sol of

          Nothing -> False

          Just (Solution old_delta _) -> old_delta <= new_delta

{-| Check if placement of instances still keeps the cluster N+1 compliant.

    This is the workhorse of the allocation algorithm: given the

    current node and instance maps, the list of instances to be

    placed, and the current solution, this will return all possible

    solution by recursing until all target instances are placed.

-}

checkPlacement :: Node.List            -- ^ The current node list

               -> [Instance.Instance] -- ^ List of instances still to place

               -> [Placement]         -- ^ Partial solution until now

               -> Int                 -- ^ The delta of the partial solution

               -> Maybe Solution      -- ^ The previous solution

               -> Int                 -- ^ Abort if the we go above this delta

               -> Maybe Solution      -- ^ The new solution

checkPlacement nl victims current current_delta prev_sol max_delta =

  let target = head victims

      opdx = Instance.pnode target

      osdx = Instance.snode target

      vtail = tail victims

      have_tail = (length vtail) > 0

      nodes = Container.elems nl

      iidx = Instance.idx target

  in

    foldl'

    (\ accu_p pri ->

         let

             pri_idx = Node.idx pri

             upri_delta = current_delta + nodeDelta pri_idx opdx osdx

             new_pri = Node.addPri pri target

             fail_delta1 = tooHighDelta accu_p upri_delta max_delta

         in

           if fail_delta1 || isNothing(new_pri) then accu_p

           else let pri_nl = Container.add pri_idx (fromJust new_pri) nl in

                foldl'

                (\ accu sec ->

                     let

                         sec_idx = Node.idx sec

                         upd_delta = upri_delta +

                                     nodeDelta sec_idx opdx osdx

                         fail_delta2 = tooHighDelta accu upd_delta max_delta

                         new_sec = Node.addSec sec target pri_idx

                     in

                       if sec_idx == pri_idx || fail_delta2 ||

                          isNothing new_sec then accu

                       else let

                           nx = Container.add sec_idx (fromJust new_sec) pri_nl

                           upd_cv = compCV nx

                           plc = (iidx, pri_idx, sec_idx, upd_cv)

                           c2 = plc:current

                           result =

                               if have_tail then

                                   checkPlacement nx vtail c2 upd_delta

                                                  accu max_delta

                               else

                                   Just (Solution upd_delta c2)

                      in compareSolutions accu result

                ) accu_p nodes

    ) prev_sol nodes

{-| Auxiliary function for solution computation.

We write this in an explicit recursive fashion in order to control

early-abort in case we have met the min delta. We can't use foldr

instead of explicit recursion since we need the accumulator for the

abort decision.

-}

advanceSolution :: [Maybe Removal] -- ^ The removal to process

                -> Int             -- ^ Minimum delta parameter

                -> Int             -- ^ Maximum delta parameter

                -> Maybe Solution  -- ^ Current best solution

                -> Maybe Solution  -- ^ New best solution

advanceSolution [] _ _ sol = sol

advanceSolution (Nothing:xs) m n sol = advanceSolution xs m n sol

advanceSolution ((Just (Removal nx removed)):xs) min_d max_d prev_sol =

    let new_sol = checkPlacement nx removed [] 0 prev_sol max_d

        new_delta = solutionDelta $! new_sol

    in

      if new_delta >= 0 && new_delta <= min_d then

          new_sol

      else

          advanceSolution xs min_d max_d new_sol

-- | Computes the placement solution.

solutionFromRemovals :: [Maybe Removal] -- ^ The list of (possible) removals

                     -> Int             -- ^ Minimum delta parameter

                     -> Int             -- ^ Maximum delta parameter

                     -> Maybe Solution  -- ^ The best solution found

solutionFromRemovals removals min_delta max_delta =

    advanceSolution removals min_delta max_delta Nothing

{-| Computes the solution at the given depth.

This is a wrapper over both computeRemovals and

solutionFromRemovals. In case we have no solution, we return Nothing.

-}

computeSolution :: Node.List        -- ^ The original node data

                -> [Instance.Instance] -- ^ The list of /bad/ instances

                -> Int             -- ^ The /depth/ of removals

                -> Int             -- ^ Maximum number of removals to process

                -> Int             -- ^ Minimum delta parameter

                -> Int             -- ^ Maximum delta parameter

                -> Maybe Solution  -- ^ The best solution found (or Nothing)

computeSolution nl bad_instances depth max_removals min_delta max_delta =

  let

      removals = computeRemovals nl bad_instances depth

      removals' = capRemovals removals max_removals

  in

    solutionFromRemovals removals' min_delta max_delta

-- * hbal functions

-- | Compute best table. Note that the ordering of the arguments is important.

compareTables :: Table -> Table -> Table

compareTables a@(Table _ _ a_cv _) b@(Table _ _ b_cv _ ) =

    if a_cv > b_cv then b else a

-- | Applies an instance move to a given node list and instance.

applyMove :: Node.List -> Instance.Instance

          -> IMove -> (Maybe Node.List, Instance.Instance, Ndx, Ndx)

-- Failover (f)

applyMove nl inst Failover =

    let old_pdx = Instance.pnode inst

        old_sdx = Instance.snode inst

        old_p = Container.find old_pdx nl

        old_s = Container.find old_sdx nl

        int_p = Node.removePri old_p inst

        int_s = Node.removeSec old_s inst

        new_nl = do -- Maybe monad

          new_p <- Node.addPri int_s inst

          new_s <- Node.addSec int_p inst old_sdx

          return $ Container.addTwo old_pdx new_s old_sdx new_p nl

    in (new_nl, Instance.setBoth inst old_sdx old_pdx, old_sdx, old_pdx)

-- Replace the primary (f:, r:np, f)

applyMove nl inst (ReplacePrimary new_pdx) =

    let old_pdx = Instance.pnode inst

        old_sdx = Instance.snode inst

        old_p = Container.find old_pdx nl

        old_s = Container.find old_sdx nl

        tgt_n = Container.find new_pdx nl

        int_p = Node.removePri old_p inst

        int_s = Node.removeSec old_s inst

        new_nl = do -- Maybe monad

          new_p <- Node.addPri tgt_n inst

          new_s <- Node.addSec int_s inst new_pdx

          return $ Container.add new_pdx new_p $

                 Container.addTwo old_pdx int_p old_sdx new_s nl

    in (new_nl, Instance.setPri inst new_pdx, new_pdx, old_sdx)

-- Replace the secondary (r:ns)

applyMove nl inst (ReplaceSecondary new_sdx) =

    let old_pdx = Instance.pnode inst

        old_sdx = Instance.snode inst

        old_s = Container.find old_sdx nl

        tgt_n = Container.find new_sdx nl

        int_s = Node.removeSec old_s inst

        new_nl = Node.addSec tgt_n inst old_pdx >>=

                 \new_s -> return $ Container.addTwo new_sdx

                           new_s old_sdx int_s nl

    in (new_nl, Instance.setSec inst new_sdx, old_pdx, new_sdx)

-- Replace the secondary and failover (r:np, f)

applyMove nl inst (ReplaceAndFailover new_pdx) =

    let old_pdx = Instance.pnode inst

        old_sdx = Instance.snode inst

        old_p = Container.find old_pdx nl

        old_s = Container.find old_sdx nl

        tgt_n = Container.find new_pdx nl

        int_p = Node.removePri old_p inst

        int_s = Node.removeSec old_s inst

        new_nl = do -- Maybe monad

          new_p <- Node.addPri tgt_n inst

          new_s <- Node.addSec int_p inst new_pdx

          return $ Container.add new_pdx new_p $

                 Container.addTwo old_pdx new_s old_sdx int_s nl

    in (new_nl, Instance.setBoth inst new_pdx old_pdx, new_pdx, old_pdx)

-- Failver and replace the secondary (f, r:ns)

applyMove nl inst (FailoverAndReplace new_sdx) =

    let old_pdx = Instance.pnode inst

        old_sdx = Instance.snode inst

        old_p = Container.find old_pdx nl

        old_s = Container.find old_sdx nl

        tgt_n = Container.find new_sdx nl

        int_p = Node.removePri old_p inst

        int_s = Node.removeSec old_s inst

        new_nl = do -- Maybe monad

          new_p <- Node.addPri int_s inst

          new_s <- Node.addSec tgt_n inst old_sdx

          return $ Container.add new_sdx new_s $

                 Container.addTwo old_sdx new_p old_pdx int_p nl

    in (new_nl, Instance.setBoth inst old_sdx new_sdx, old_sdx, new_sdx)

-- | Tries to allocate an instance on one given node.

allocateOnSingle :: Node.List -> Instance.Instance -> Node.Node

                 -> (Maybe Node.List, Instance.Instance)

allocateOnSingle nl inst p =

    let new_pdx = Node.idx p

        new_nl = Node.addPri p inst >>= \new_p ->

                 return $ Container.add new_pdx new_p nl

    in (new_nl, Instance.setBoth inst new_pdx Node.noSecondary)

-- | Tries to allocate an instance on a given pair of nodes.

allocateOnPair :: Node.List -> Instance.Instance -> Node.Node -> Node.Node

               -> (Maybe Node.List, Instance.Instance)

allocateOnPair nl inst tgt_p tgt_s =

    let new_pdx = Node.idx tgt_p

        new_sdx = Node.idx tgt_s

        new_nl = do -- Maybe monad

          new_p <- Node.addPri tgt_p inst

          new_s <- Node.addSec tgt_s inst new_pdx

          return $ Container.addTwo new_pdx new_p new_sdx new_s nl

    in (new_nl, Instance.setBoth inst new_pdx new_sdx)

-- | Tries to perform an instance move and returns the best table

-- between the original one and the new one.

checkSingleStep :: Table -- ^ The original table

                -> Instance.Instance -- ^ The instance to move

                -> Table -- ^ The current best table

                -> IMove -- ^ The move to apply

                -> Table -- ^ The final best table

checkSingleStep ini_tbl target cur_tbl move =

    let

        Table ini_nl ini_il _ ini_plc = ini_tbl

        (tmp_nl, new_inst, pri_idx, sec_idx) = applyMove ini_nl target move

    in

      if isNothing tmp_nl then cur_tbl

      else

          let tgt_idx = Instance.idx target

              upd_nl = fromJust tmp_nl

              upd_cvar = compCV upd_nl

              upd_il = Container.add tgt_idx new_inst ini_il

              upd_plc = (tgt_idx, pri_idx, sec_idx, upd_cvar):ini_plc

              upd_tbl = Table upd_nl upd_il upd_cvar upd_plc

          in

            compareTables cur_tbl upd_tbl

-- | Given the status of the current secondary as a valid new node

-- and the current candidate target node,

-- generate the possible moves for a instance.

possibleMoves :: Bool -> Ndx -> [IMove]

possibleMoves True tdx =

    [ReplaceSecondary tdx,

     ReplaceAndFailover tdx,

     ReplacePrimary tdx,

     FailoverAndReplace tdx]

possibleMoves False tdx =

    [ReplaceSecondary tdx,

     ReplaceAndFailover tdx]

-- | Compute the best move for a given instance.

checkInstanceMove :: [Ndx]             -- Allowed target node indices

                  -> Table             -- Original table

                  -> Instance.Instance -- Instance to move

                  -> Table             -- Best new table for this instance

checkInstanceMove nodes_idx ini_tbl target =

    let

        opdx = Instance.pnode target

        osdx = Instance.snode target

        nodes = filter (\idx -> idx /= opdx && idx /= osdx) nodes_idx

        use_secondary = elem osdx nodes_idx

        aft_failover = if use_secondary -- if allowed to failover

                       then checkSingleStep ini_tbl target ini_tbl Failover

                       else ini_tbl

        all_moves = concatMap (possibleMoves use_secondary) nodes

    in

      -- iterate over the possible nodes for this instance

      foldl' (checkSingleStep ini_tbl target) aft_failover all_moves

-- | Compute the best next move.

checkMove :: [Ndx]               -- ^ Allowed target node indices

          -> Table               -- ^ The current solution

          -> [Instance.Instance] -- ^ List of instances still to move

          -> Table               -- ^ The new solution

checkMove nodes_idx ini_tbl victims =

    let Table _ _ _ ini_plc = ini_tbl

        -- iterate over all instances, computing the best move

        best_tbl =

            foldl'

            (\ step_tbl elem ->

                 if Instance.snode elem == Node.noSecondary then step_tbl

                    else compareTables step_tbl $

                         checkInstanceMove nodes_idx ini_tbl elem)

            ini_tbl victims

        Table _ _ _ best_plc = best_tbl

    in

      if length best_plc == length ini_plc then -- no advancement

          ini_tbl

      else

          best_tbl

-- * Formatting functions

-- | Given the original and final nodes, computes the relocation description.

computeMoves :: String -- ^ The instance name

             -> String -- ^ Original primary

             -> String -- ^ Original secondary

             -> String -- ^ New primary

             -> String -- ^ New secondary

             -> (String, [String])

                -- ^ Tuple of moves and commands list; moves is containing

                -- either @/f/@ for failover or @/r:name/@ for replace

                -- secondary, while the command list holds gnt-instance

                -- commands (without that prefix), e.g \"@failover instance1@\"

computeMoves i a b c d =

    if c == a then {- Same primary -}

        if d == b then {- Same sec??! -}

            ("-", [])

        else {- Change of secondary -}

            (printf "r:%s" d,

             [printf "replace-disks -n %s %s" d i])

    else

        if c == b then {- Failover and ... -}

            if d == a then {- that's all -}

                ("f", [printf "migrate -f %s" i])

            else

                (printf "f r:%s" d,

                 [printf "migrate -f %s" i,

                  printf "replace-disks -n %s %s" d i])

        else

            if d == a then {- ... and keep primary as secondary -}

                (printf "r:%s f" c,

                 [printf "replace-disks -n %s %s" c i,

                  printf "migrate -f %s" i])

            else

                if d == b then {- ... keep same secondary -}

                    (printf "f r:%s f" c,

                     [printf "migrate -f %s" i,

                      printf "replace-disks -n %s %s" c i,

                      printf "migrate -f %s" i])

                else {- Nothing in common -}

                    (printf "r:%s f r:%s" c d,

                     [printf "replace-disks -n %s %s" c i,

                      printf "migrate -f %s" i,

                      printf "replace-disks -n %s %s" d i])

-- | Converts a placement to string format.

printSolutionLine :: Node.List     -- ^ The node list

                  -> Instance.List -- ^ The instance list

                  -> Int           -- ^ Maximum node name length

                  -> Int           -- ^ Maximum instance name length

                  -> Placement     -- ^ The current placement

                  -> Int           -- ^ The index of the placement in

                                   -- the solution

                  -> (String, [String])

printSolutionLine nl il nmlen imlen plc pos =

    let

        pmlen = (2*nmlen + 1)

        (i, p, s, c) = plc

        inst = Container.find i il

        inam = Instance.name inst

        npri = Container.nameOf nl p

        nsec = Container.nameOf nl s

        opri = Container.nameOf nl $ Instance.pnode inst

        osec = Container.nameOf nl $ Instance.snode inst

        (moves, cmds) =  computeMoves inam opri osec npri nsec

        ostr = (printf "%s:%s" opri osec)::String

        nstr = (printf "%s:%s" npri nsec)::String

    in

      (printf "  %3d. %-*s %-*s => %-*s %.8f a=%s"

       pos imlen inam pmlen ostr

       pmlen nstr c moves,

       cmds)

-- | Given a list of commands, prefix them with @gnt-instance@ and

-- also beautify the display a little.

formatCmds :: [[String]] -> String

formatCmds cmd_strs =

    unlines $

    concat $ map (\(a, b) ->

        (printf "echo step %d" (a::Int)):

        (printf "check"):

        (map ("gnt-instance " ++) b)) $

        zip [1..] cmd_strs

-- | Converts a solution to string format.

printSolution :: Node.List

              -> Instance.List

              -> [Placement]

              -> ([String], [[String]])

printSolution nl il sol =

    let

        nmlen = Container.maxNameLen nl

        imlen = Container.maxNameLen il

    in

      unzip $ map (uncurry $ printSolutionLine nl il nmlen imlen) $

            zip sol [1..]

-- | Print the node list.

printNodes :: Node.List -> String

printNodes nl =

    let snl = sortBy (compare `on` Node.idx) (Container.elems nl)

        m_name = maximum . map (length . Node.name) $ snl

        helper = Node.list m_name

        header = printf

                 "%2s %-*s %5s %5s %5s %5s %5s %5s %5s %5s %3s %3s %7s %7s"

                 " F" m_name "Name"

                 "t_mem" "n_mem" "i_mem" "x_mem" "f_mem" "r_mem"

                 "t_dsk" "f_dsk"

                 "pri" "sec" "p_fmem" "p_fdsk"

    in unlines $ (header:map helper snl)

-- | Shows statistics for a given node list.

printStats :: Node.List -> String

printStats nl =

    let (mem_cv, dsk_cv, n1_score, res_cv, off_score) = compDetailedCV nl

    in printf "f_mem=%.8f, r_mem=%.8f, f_dsk=%.8f, n1=%.3f, uf=%.3f"

       mem_cv res_cv dsk_cv n1_score off_score