⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

{{task}} Functional coverage is a measure of how much a particular function of a system has been verified as correct. It is used heavily in tracking the completeness of the verification of complex System on Chip (SoC) integrated circuits, where it can also be used to track how well the functional ''requirements'' of the system have been verified.

This task uses a sub-set of the calculations sometimes used in tracking functional coverage but uses a more familiar(?) scenario.

;Task Description: The head of the clean-up crews for "The Men in a very dark shade of grey when viewed at night" has been tasked with managing the cleansing of two properties after an incident involving aliens.

She arranges the task hierarchically with a manager for the crews working on each house who return with a breakdown of how they will report on progress in each house.

The overall hierarchy of (sub)tasks is as follows,

```cleaning
house1
bedrooms
bathrooms
bathroom1
bathroom2
outside lavatory
attic
kitchen
living rooms
lounge
dining room
conservatory
playroom
basement
garage
garden
house2
upstairs
bedrooms
suite 1
suite 2
bedroom 3
bedroom 4
bathroom
toilet
attics
groundfloor
kitchen
living rooms
lounge
dining room
conservatory
playroom
wet room & toilet
garage
garden
hot tub suite
basement
cellars
wine cellar
cinema
```

The head of cleanup knows that her managers will report fractional completion of leaf tasks (tasks with no child tasks of their own), and she knows that she will want to modify the weight of values of completion as she sees fit.

Some time into the cleaning, and some coverage reports have come in and she thinks see needs to weight the big house2 60-40 with respect to coverage from house1 She prefers a tabular view of her data where missing weights are assumed to be 1.0 and missing coverage 0.0.

```NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |        |          |
house1                      |40      |          |
bedrooms                |        |0.25      |
bathrooms               |        |          |
bathroom1           |        |0.5       |
bathroom2           |        |          |
outside_lavatory    |        |1         |
attic                   |        |0.75      |
kitchen                 |        |0.1       |
living_rooms            |        |          |
lounge              |        |          |
dining_room         |        |          |
conservatory        |        |          |
playroom            |        |1         |
basement                |        |          |
garage                  |        |          |
garden                  |        |0.8       |
house2                      |60      |          |
upstairs                |        |          |
bedrooms            |        |          |
suite_1         |        |          |
suite_2         |        |          |
bedroom_3       |        |          |
bedroom_4       |        |          |
bathroom            |        |          |
toilet              |        |          |
attics              |        |0.6       |
groundfloor             |        |          |
kitchen             |        |          |
living_rooms        |        |          |
lounge          |        |          |
dining_room     |        |          |
conservatory    |        |          |
playroom        |        |          |
wet_room_&_toilet   |        |          |
garage              |        |          |
garden              |        |0.9       |
hot_tub_suite       |        |1         |
basement                |        |          |
cellars             |        |1         |
wine_cellar         |        |1         |
cinema              |        |0.75      |
```

;Calculation: The coverage of a node in the tree is calculated as the [[wp:Weighted arithmetic mean|weighted average]] of the coverage of its children evaluated bottom-upwards in the tree.

'''The task is to''' calculate the overall coverage of the cleaning task and display the coverage at all levels of the hierarchy on this page, in a manner that visually shows the hierarchy, weights and coverage of all nodes.

;Extra Credit: After calculating the coverage for all nodes, one can also calculate the additional/delta top level coverage that would occur if any (sub)task were to be fully covered from its current fractional coverage. This is done by multiplying the extra coverage that could be gained $1-coverage$ for any node, by the product of the `powers` of its parent nodes from the top down to the node.

The power of a direct child of any parent is given by the power of the parent multiplied by the weight of the child divided by the sum of the weights of all the direct children.

The pseudo code would be:

```method delta_calculation(this, power):
sum_of_weights = sum(node.weight for node in children)
this.delta  = (1 - this.coverage) * power
for node in self.children:
node.delta_calculation(power * node.weight / sum_of_weights)
return this.delta
```

Followed by a call to:

```top.delta_calculation(power=1)
```

'''Note:''' to aid in getting the data into your program you might want to use an alternative, more functional description of the starting data given on the discussion page.

## Go

{{trans|Kotlin}}

```package main

import "fmt"

type FCNode struct {
name     string
weight   int
coverage float64
children []*FCNode
parent   *FCNode
}

func newFCN(name string, weight int, coverage float64) *FCNode {
return &FCNode{name, weight, coverage, nil, nil}
}

func (n *FCNode) addChildren(nodes []*FCNode) {
for _, node := range nodes {
node.parent = n
n.children = append(n.children, node)
}
n.updateCoverage()
}

func (n *FCNode) setCoverage(value float64) {
if n.coverage != value {
n.coverage = value
// update any parent's coverage
if n.parent != nil {
n.parent.updateCoverage()
}
}
}

func (n *FCNode) updateCoverage() {
v1 := 0.0
v2 := 0
for _, node := range n.children {
v1 += float64(node.weight) * node.coverage
v2 += node.weight
}
n.setCoverage(v1 / float64(v2))
}

func (n *FCNode) show(level int) {
indent := level * 4
nl := len(n.name) + indent
fmt.Printf("%*s%*s  %3d   | %8.6f |\n", nl, n.name, 32-nl, "|", n.weight, n.coverage)
if len(n.children) == 0 {
return
}
for _, child := range n.children {
child.show(level + 1)
}
}

var houses = []*FCNode{
newFCN("house1", 40, 0),
newFCN("house2", 60, 0),
}

var house1 = []*FCNode{
newFCN("bedrooms", 1, 0.25),
newFCN("bathrooms", 1, 0),
newFCN("attic", 1, 0.75),
newFCN("kitchen", 1, 0.1),
newFCN("living_rooms", 1, 0),
newFCN("basement", 1, 0),
newFCN("garage", 1, 0),
newFCN("garden", 1, 0.8),
}

var house2 = []*FCNode{
newFCN("upstairs", 1, 0),
newFCN("groundfloor", 1, 0),
newFCN("basement", 1, 0),
}

var h1Bathrooms = []*FCNode{
newFCN("bathroom1", 1, 0.5),
newFCN("bathroom2", 1, 0),
newFCN("outside_lavatory", 1, 1),
}

var h1LivingRooms = []*FCNode{
newFCN("lounge", 1, 0),
newFCN("dining_room", 1, 0),
newFCN("conservatory", 1, 0),
newFCN("playroom", 1, 1),
}

var h2Upstairs = []*FCNode{
newFCN("bedrooms", 1, 0),
newFCN("bathroom", 1, 0),
newFCN("toilet", 1, 0),
newFCN("attics", 1, 0.6),
}

var h2Groundfloor = []*FCNode{
newFCN("kitchen", 1, 0),
newFCN("living_rooms", 1, 0),
newFCN("wet_room_&_toilet", 1, 0),
newFCN("garage", 1, 0),
newFCN("garden", 1, 0.9),
newFCN("hot_tub_suite", 1, 1),
}

var h2Basement = []*FCNode{
newFCN("cellars", 1, 1),
newFCN("wine_cellar", 1, 1),
newFCN("cinema", 1, 0.75),
}

var h2UpstairsBedrooms = []*FCNode{
newFCN("suite_1", 1, 0),
newFCN("suite_2", 1, 0),
newFCN("bedroom_3", 1, 0),
newFCN("bedroom_4", 1, 0),
}

var h2GroundfloorLivingRooms = []*FCNode{
newFCN("lounge", 1, 0),
newFCN("dining_room", 1, 0),
newFCN("conservatory", 1, 0),
newFCN("playroom", 1, 0),
}

func main() {
cleaning := newFCN("cleaning", 1, 0)

topCoverage := cleaning.coverage
fmt.Printf("TOP COVERAGE = %8.6f\n\n", topCoverage)
fmt.Println("NAME HIERARCHY                 | WEIGHT | COVERAGE |")
cleaning.show(0)

h2Basement[2].setCoverage(1) // change Cinema node coverage to 1
diff := cleaning.coverage - topCoverage
fmt.Println("\nIf the coverage of the Cinema node were increased from 0.75 to 1")
fmt.Print("the top level coverage would increase by ")
fmt.Printf("%8.6f to %8.6f\n", diff, topCoverage+diff)
h2Basement[2].setCoverage(0.75) // restore to original value if required
}
```

{{out}}

```
TOP COVERAGE = 0.409167

NAME HIERARCHY                 | WEIGHT | COVERAGE |
cleaning                       |    1   | 0.409167 |
house1                     |   40   | 0.331250 |
bedrooms               |    1   | 0.250000 |
bathrooms              |    1   | 0.500000 |
bathroom1          |    1   | 0.500000 |
bathroom2          |    1   | 0.000000 |
outside_lavatory   |    1   | 1.000000 |
attic                  |    1   | 0.750000 |
kitchen                |    1   | 0.100000 |
living_rooms           |    1   | 0.250000 |
lounge             |    1   | 0.000000 |
dining_room        |    1   | 0.000000 |
conservatory       |    1   | 0.000000 |
playroom           |    1   | 1.000000 |
basement               |    1   | 0.000000 |
garage                 |    1   | 0.000000 |
garden                 |    1   | 0.800000 |
house2                     |   60   | 0.461111 |
upstairs               |    1   | 0.150000 |
bedrooms           |    1   | 0.000000 |
suite_1        |    1   | 0.000000 |
suite_2        |    1   | 0.000000 |
bedroom_3      |    1   | 0.000000 |
bedroom_4      |    1   | 0.000000 |
bathroom           |    1   | 0.000000 |
toilet             |    1   | 0.000000 |
attics             |    1   | 0.600000 |
groundfloor            |    1   | 0.316667 |
kitchen            |    1   | 0.000000 |
living_rooms       |    1   | 0.000000 |
lounge         |    1   | 0.000000 |
dining_room    |    1   | 0.000000 |
conservatory   |    1   | 0.000000 |
playroom       |    1   | 0.000000 |
wet_room_&_toilet  |    1   | 0.000000 |
garage             |    1   | 0.000000 |
garden             |    1   | 0.900000 |
hot_tub_suite      |    1   | 1.000000 |
basement               |    1   | 0.916667 |
cellars            |    1   | 1.000000 |
wine_cellar        |    1   | 1.000000 |
cinema             |    1   | 0.750000 |

If the coverage of the Cinema node were increased from 0.75 to 1
the top level coverage would increase by 0.016667 to 0.425833

```

Using a function from a text outline to an updated text outline.

The raw table (supplied in the task description) is read in from a text file, parsed to a tree structure, and updated by two traversals (one bottom-up and one top down) before being serialised back to a completed outline text, with an additional 'Share of Residue' column: {{Trans|Python}}

```{-# LANGUAGE OverloadedStrings #-}

import System.Directory (doesFileExist)
import qualified Data.Text.Read as T
import qualified Data.Text.IO as T
import qualified Data.Text as T
import Control.Arrow ((&&&), first)
import Numeric (showFFloat)
import Data.Char (isSpace)
import Data.Bool (bool)
import Data.Tree

data Coverage = Coverage
{ name :: T.Text
, weight :: Float
, coverage :: Float
, share :: Float
} deriving (Show)

-- TEST ---------------------------------------------------
fp = "./coverageOutline.txt"

main :: IO ()
main =
doesFileExist fp >>=
bool
(print \$ "File not found: " ++ fp)
(T.readFile fp >>= T.putStrLn . updatedCoverageOutline)

-- UPDATED COVERAGE OUTLINE -------------------------------
updatedCoverageOutline :: T.Text -> T.Text
updatedCoverageOutline s =
let delimiter = "|"
indentedLines = T.lines s
columnNames = init \$ tokenizeWith delimiter (head indentedLines)
in T.unlines
[ tabulation delimiter (columnNames ++ ["SHARE OF RESIDUE"])
, indentedLinesFromTree "    " (showCoverage delimiter) \$
withResidueShares 1.0 \$
foldTree
weightedCoverage
(parseTreeFromOutline delimiter indentedLines)
]

-- WEIGHTED COVERAGE AND SHARES OF REMAINING WORK ---------
weightedCoverage :: Coverage -> Forest Coverage -> Tree Coverage
weightedCoverage x xs =
let cws = ((coverage &&& weight) . rootLabel) <\$> xs
totalWeight = foldr ((+) . snd) 0 cws
in Node
(x
{ coverage =
foldr (\(c, w) a -> (c * w) + a) (coverage x) cws /
bool 1 totalWeight (0 < totalWeight)
})
xs

withResidueShares :: Float -> Tree Coverage -> Tree Coverage
withResidueShares shareOfTotal tree =
let go fraction node =
let forest = subForest node
weights = (weight . rootLabel) <\$> forest
weightTotal = sum weights
nodeRoot = rootLabel node
in Node
(nodeRoot
{ share = fraction * (1 - coverage nodeRoot)
})
(zipWith go (((fraction *) . (/ weightTotal)) <\$> weights) forest)
in go shareOfTotal tree

-- OUTLINE PARSE ------------------------------------------
parseTreeFromOutline :: T.Text -> [T.Text] -> Tree Coverage
parseTreeFromOutline delimiter indentedLines =
(partialRecord . tokenizeWith delimiter) <\$>
head (forestFromLineIndents \$ indentLevelsFromLines \$ tail indentedLines)

forestFromLineIndents :: [(Int, T.Text)] -> [Tree T.Text]
forestFromLineIndents pairs =
let go [] = []
go ((n, s):xs) =
let (firstTreeLines, rest) = span ((n <) . fst) xs
in Node s (go firstTreeLines) : go rest
in go pairs

indentLevelsFromLines :: [T.Text] -> [(Int, T.Text)]
indentLevelsFromLines xs =
let pairs = T.span isSpace <\$> xs
indentUnit =
foldr
(\x a ->
let w = (T.length . fst) x
in bool a w (w < a && 0 < w))
(maxBound :: Int)
pairs
in first (flip div indentUnit . T.length) <\$> pairs

partialRecord :: [T.Text] -> Coverage
partialRecord xs =
let [name, weightText, coverageText] = take 3 (xs ++ repeat "")
in Coverage
{ name = name
, weight = defaultOrRead 1.0 weightText
, coverage = defaultOrRead 0.0 coverageText
, share = 0.0
}

defaultOrRead :: Float -> T.Text -> Float
defaultOrRead n txt = either (const n) fst \$ T.rational txt

tokenizeWith :: T.Text -> T.Text -> [T.Text]
tokenizeWith delimiter = fmap T.strip . T.splitOn delimiter

-- SERIALISATION OF TREE TO TABULATED OUTLINE -------------
indentedLinesFromTree :: T.Text -> (T.Text -> a -> T.Text) -> Tree a -> T.Text
indentedLinesFromTree tab showRoot tree =
let go indent node =
showRoot indent (rootLabel node) :
(subForest node >>= go (T.append tab indent))
in T.unlines \$ go "" tree

showCoverage :: T.Text -> T.Text -> Coverage -> T.Text
showCoverage delimiter indent x =
tabulation
delimiter
([T.append indent (name x), T.pack (showN 0 (weight x))] ++
((T.pack . showN 4) <\$> ([coverage, share] <*> [x])))

tabulation :: T.Text -> [T.Text] -> T.Text
tabulation delimiter =
T.intercalate (T.append delimiter " ") .
zipWith (`T.justifyLeft` ' ') [31, 9, 9, 9]

justifyRight :: Int -> a -> [a] -> [a]
justifyRight n c = (drop . length) <*> (replicate n c ++)

showN :: Int -> Float -> String
showN p n = justifyRight 7 ' ' (showFFloat (Just p) n "")

-- GENERIC ------------------------------------------------
foldTree :: (a -> [b] -> b) -> Tree a -> b
foldTree f = go
where
go (Node x ts) = f x (map go ts)
```

{{Out}}

```NAME_HIERARCHY                 | WEIGHT   | COVERAGE | SHARE OF RESIDUE
cleaning                       |       1  |  0.4092  |  0.5908
house1                     |      40  |  0.3312  |  0.2675
bedrooms               |       1  |  0.2500  |  0.0375
bathrooms              |       1  |  0.5000  |  0.0250
bathroom1          |       1  |  0.5000  |  0.0083
bathroom2          |       1  |  0.0000  |  0.0167
outside_lavatory   |       1  |  1.0000  |  0.0000
attic                  |       1  |  0.7500  |  0.0125
kitchen                |       1  |  0.1000  |  0.0450
living_rooms           |       1  |  0.2500  |  0.0375
lounge             |       1  |  0.0000  |  0.0125
dining_room        |       1  |  0.0000  |  0.0125
conservatory       |       1  |  0.0000  |  0.0125
playroom           |       1  |  1.0000  |  0.0000
basement               |       1  |  0.0000  |  0.0500
garage                 |       1  |  0.0000  |  0.0500
garden                 |       1  |  0.8000  |  0.0100
house2                     |      60  |  0.4611  |  0.3233
upstairs               |       1  |  0.1500  |  0.1700
bedrooms           |       1  |  0.0000  |  0.0500
suite_1        |       1  |  0.0000  |  0.0125
suite_2        |       1  |  0.0000  |  0.0125
bedroom_3      |       1  |  0.0000  |  0.0125
bedroom_4      |       1  |  0.0000  |  0.0125
bathroom           |       1  |  0.0000  |  0.0500
toilet             |       1  |  0.0000  |  0.0500
attics             |       1  |  0.6000  |  0.0200
groundfloor            |       1  |  0.3167  |  0.1367
kitchen            |       1  |  0.0000  |  0.0333
living_rooms       |       1  |  0.0000  |  0.0333
lounge         |       1  |  0.0000  |  0.0083
dining_room    |       1  |  0.0000  |  0.0083
conservatory   |       1  |  0.0000  |  0.0083
playroom       |       1  |  0.0000  |  0.0083
wet_room_&_toilet  |       1  |  0.0000  |  0.0333
garage             |       1  |  0.0000  |  0.0333
garden             |       1  |  0.9000  |  0.0033
hot_tub_suite      |       1  |  1.0000  |  0.0000
basement               |       1  |  0.9167  |  0.0167
cellars            |       1  |  1.0000  |  0.0000
wine_cellar        |       1  |  1.0000  |  0.0000
cinema             |       1  |  0.7500  |  0.0167
```

## J

Implementation (raw data):

```raw=: 0 :0
NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |        |          |
house1                      |40      |          |
bedrooms                |        |0.25      |
bathrooms               |        |          |
bathroom1           |        |0.5       |
bathroom2           |        |          |
outside_lavatory    |        |1         |
attic                   |        |0.75      |
kitchen                 |        |0.1       |
living_rooms            |        |          |
lounge              |        |          |
dining_room         |        |          |
conservatory        |        |          |
playroom            |        |1         |
basement                |        |          |
garage                  |        |          |
garden                  |        |0.8       |
house2                      |60      |          |
upstairs                |        |          |
bedrooms            |        |          |
suite_1         |        |          |
suite_2         |        |          |
bedroom_3       |        |          |
bedroom_4       |        |          |
bathroom            |        |          |
toilet              |        |          |
attics              |        |0.6       |
groundfloor             |        |          |
kitchen             |        |          |
living_rooms        |        |          |
lounge          |        |          |
dining_room     |        |          |
conservatory    |        |          |
playroom        |        |          |
wet_room_&_toilet   |        |          |
garage              |        |          |
garden              |        |0.9       |
hot_tub_suite       |        |1         |
basement                |        |          |
cellars             |        |1         |
wine_cellar         |        |1         |
cinema              |        |0.75      |
)
```

Implementation (unpacking raw data):

```labels=: {.<;._2;._2 raw
'hier wspec cspec'=:|:}.<;._2;._2 raw
level=: (%+./) (0 i.~' '&=)"1 hier
weight=: (+ 0=]) ,".wspec
coverage=:  ,".cspec
```

To understand this implementation, it's best to run it and inspect the data.

That said:

each of the above names is a column variable (with one value for each row in the dataset).

level has values 0, 1, 2, 3 or 4 (depending on depth of indent), and the calculation relies on each indent level using the same number of spaces. It might be smarter to use `level=: (i.~ ~.) (0 i.~' '&=)"1 hier` which only relies on consistent indentation at each level, but ultimately a general case implementation would have to enforce an indentation standard and that sort of mechanism is out of scope for this task.

weight fills in the blanks for weights (1 if not otherwise specified). This calculation is simplified because we do not have to worry about any explicitly 0 weights.

coverage fills in the blanks for coverage (0 if not otherwise specified).

Implementation (translation of leaf coverage to functional coverage):

```merge=: ;@(({.@[,(+}.)~)&.> [: +/\1,_1}.#@>)
unrooted=: ([: merge <@(_1,\$:@}.);.1)^:(0<#)
parent=:  unrooted level
parent_cover=: (] (1}.~.parent)}~ 1}. * %&(parent +//. ]) [)^:_
```

`unrooted` translates indentation information to a [[Tree_traversal#J:_Alternate_implementation|parent tree structure]]. However, the limitations of recursion require we distinguish the parent node from its children, so we use _1 to denote the parent node of the recursive intermediate result unrooted trees. (This works well with using arithmetic to adjust sub-tree indices based on the lengths of preceding sub-trees.) `merge` combines a boxed sequence of these subtrees to form a single tree - we also rely on the first node of each tree being both _1 and the root node.

Thus, `parent_cover` propagates coverage to parent nodes based on the weighted average of coverage at the children.

Task example (format and show result):

```   1 1 }._1 }.":labels,each ":each hier;(,.weight);,.weight parent_cover coverage
NAME_HIERARCHY                  │WEIGHT  │COVERAGE  │
cleaning                        │ 1      │0.409167  │
house1                      │40      │ 0.33125  │
bedrooms                │ 1      │    0.25  │
bathrooms               │ 1      │     0.5  │
bathroom1           │ 1      │     0.5  │
bathroom2           │ 1      │       0  │
outside_lavatory    │ 1      │       1  │
attic                   │ 1      │    0.75  │
kitchen                 │ 1      │     0.1  │
living_rooms            │ 1      │    0.25  │
lounge              │ 1      │       0  │
dining_room         │ 1      │       0  │
conservatory        │ 1      │       0  │
playroom            │ 1      │       1  │
basement                │ 1      │       0  │
garage                  │ 1      │       0  │
garden                  │ 1      │     0.8  │
house2                      │60      │0.461111  │
upstairs                │ 1      │    0.15  │
bedrooms            │ 1      │       0  │
suite_1         │ 1      │       0  │
suite_2         │ 1      │       0  │
bedroom_3       │ 1      │       0  │
bedroom_4       │ 1      │       0  │
bathroom            │ 1      │       0  │
toilet              │ 1      │       0  │
attics              │ 1      │     0.6  │
groundfloor             │ 1      │0.316667  │
kitchen             │ 1      │       0  │
living_rooms        │ 1      │       0  │
lounge          │ 1      │       0  │
dining_room     │ 1      │       0  │
conservatory    │ 1      │       0  │
playroom        │ 1      │       0  │
wet_room_&_toilet   │ 1      │       0  │
garage              │ 1      │       0  │
garden              │ 1      │     0.9  │
hot_tub_suite       │ 1      │       1  │
basement                │ 1      │0.916667  │
cellars             │ 1      │       1  │
wine_cellar         │ 1      │       1  │
cinema              │ 1      │    0.75  │
```

Extra credit:

```trace=: (~.@,each  (0 >. parent)&{)^:_  i.#parent
power=: */@:{&(parent (] % (i.~ ~.)@[ { +//.) weight)@> trace

power*1-weight parent_cover coverage
0.590833 0.2675 0.0375 0.025 0.00833333 0.0166667 0 0.0125 0.045 0.0375 0.0125 0.0125 0.0125 0 0.05 0.05 0.01 0.323333 0.17 0.05 0.0125 0.0125 0.0125 0.0125 0.05 0.05 0.02 0.136667 0.0333333 0.0333333 0.00833333 0.00833333 0.00833333 0.00833333 0.0333333 0.0333333 0.00333333 0 0.0166667 0 0 0.0166667
```

Explanation:

`trace` is, for each node, the set of nodes (or indices of nodes - since we use indices to identify nodes) leading from that node to its root.

`parent (] % (i.~ ~.)@[ { +//.) weight` is the weight of each node divided by the total weight for all nodes with the same parent.

`power` is the product of these relative weights for each member of the trace.

And, `weight parent_cover coverage` was the functional coverage for each node.

## JavaScript

Parsing the outline text to a tree structure, and traversing this with two computations (one bottom-up, and one top-down), before serialising the updated tree to a new outline text.

```(() => {
'use strict';

// updatedCoverageOutline :: String -> String
const updatedCoverageOutline = outlineText => {
const
delimiter = '|',
indentedLines = indentLevelsFromLines(lines(outlineText)),
columns = init(tokenizeWith(delimiter)(snd(indentedLines[0])));

// SERIALISATION OF UPDATED PARSE TREE (TO NEW OUTLINE TEXT)
return tabulation(delimiter)(
columns.concat('SHARE OF RESIDUE\n')
) + unlines(
indentedLinesFromTree(
showCoverage(delimiter))('    ')(

// TWO TRAVERSAL COMPUTATIONS

withResidueShares(1.0)(
foldTree(weightedCoverage)(

// PARSE TREE (FROM OUTLINE TEXT)
fmapTree(compose(
partialRecord, tokenizeWith(delimiter)
))(fst(
forestFromLineIndents(tail(indentedLines))
))
)
))
);
};

// TEST -----------------------------------------------
// main :: IO ()
const main = () =>
console.log(
// strOutline is included as literal text
// at the foot of this code listing.
updatedCoverageOutline(strOutline)
);

// COVERAGE AND SHARES OF RESIDUE ---------------------

// weightedCoverage :: Dict -> Forest Dict -> Tree Dict
const weightedCoverage = x => xs => {
const
cws = map(compose(
fanArrow(x => x.coverage)(x => x.weight),
root
))(xs),
totalWeight = cws.reduce((a, tpl) => a + snd(tpl), 0);
return Node(
insertDict('coverage')(
cws.reduce((a, tpl) => {
const [c, w] = Array.from(tpl);
return a + (c * w);
}, x.coverage) / (
0 < totalWeight ? totalWeight : 1
)
)(x)
)(xs);
};

// withResidueShares :: Float -> Tree Dict -> Tree Dict
const withResidueShares = shareOfTotal => tree => {
const go = fraction => node => {
const
nodeRoot = node.root,
forest = node.nest,
weights = forest.map(x => x.root.weight),
weightTotal = sum(weights);
return Node(
insertDict('share')(
fraction * (1 - nodeRoot.coverage)
)(nodeRoot)
)(
zipWith(go)(
weights.map(w => fraction * (w / weightTotal))
)(forest)
);
};
return go(shareOfTotal)(tree);
};

// OUTLINE PARSED TO TREE -----------------------------

// forestFromLineIndents :: [(Int, String)] -> [Tree String]
const forestFromLineIndents = tuples => {
const go = xs =>
0 < xs.length ? (() => {
const [n, s] = Array.from(xs[0]);
// Lines indented under this line,
// tupled with all the rest.
const [firstTreeLines, rest] = Array.from(
span(x => n < x[0])(xs.slice(1))
);
// This first tree, and then the rest.
return [Node(s)(go(firstTreeLines))]
.concat(go(rest));
})() : [];
return go(tuples);
};

// indentLevelsFromLines :: [String] -> [(Int, String)]
const indentLevelsFromLines = xs => {
const
indentTextPairs = xs.map(compose(
firstArrow(length), span(isSpace)
)),
indentUnit = minimum(indentTextPairs.flatMap(pair => {
const w = fst(pair);
return 0 < w ? [w] : [];
}));
return indentTextPairs.map(
firstArrow(flip(div)(indentUnit))
);
};

// partialRecord :: [String] -> Dict
const partialRecord = xs => {
const [name, weightText, coverageText] = take(3)(
xs.concat(['', '', ''])
);
return {
name: name || '?',
weight: parseFloat(weightText) || 1.0,
coverage: parseFloat(coverageText) || 0.0,
share: 0.0
};
};

// tokenizeWith :: String -> String -> [String]
const tokenizeWith = delimiter =>
// A sequence of trimmed tokens obtained by
// splitting s on the supplied delimiter.
s => s.split(delimiter).map(x => x.trim());

// TREE SERIALIZED TO OUTLINE -------------------------

// indentedLinesFromTree :: (String -> a -> String) ->
// String -> Tree a -> [String]
const indentedLinesFromTree = showRoot =>
strTab => tree => {
const go = indent =>
node => [showRoot(indent)(node.root)]
.concat(node.nest.flatMap(go(strTab + indent)));
return go('')(tree);
};

// showN :: Int -> Float -> String
const showN = p =>
n => justifyRight(7)(' ')(n.toFixed(p));

// showCoverage :: String -> String -> Dict -> String
const showCoverage = delimiter =>
indent => x => tabulation(delimiter)(
[indent + x.name, showN(0)(x.weight)]
.concat([x.coverage, x.share].map(showN(4)))
);

// tabulation :: String -> [String] -> String
const tabulation = delimiter =>
// Up to 4 tokens drawn from the argument list,
// as a single string with fixed left-justified
// white-space widths, between delimiters.
compose(
intercalate(delimiter + ' '),
zipWith(flip(justifyLeft)(' '))([31, 9, 9, 9])
);

// GENERIC AND REUSABLE FUNCTIONS ---------------------

// Node :: a -> [Tree a] -> Tree a
const Node = v => xs => ({
type: 'Node',
root: v, // any type of value (consistent across tree)
nest: xs || []
});

// Tuple (,) :: a -> b -> (a, b)
const Tuple = a => b => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});

// compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
const compose = (...fs) =>
x => fs.reduceRight((a, f) => f(a), x);

// concat :: [[a]] -> [a]
// concat :: [String] -> String
const concat = xs =>
0 < xs.length ? (() => {
const unit = 'string' !== typeof xs[0] ? (
[]
) : '';
return unit.concat.apply(unit, xs);
})() : [];

// div :: Int -> Int -> Int
const div = x => y => Math.floor(x / y);

// either :: (a -> c) -> (b -> c) -> Either a b -> c
const either = fl => fr => e =>
'Either' === e.type ? (
undefined !== e.Left ? (
fl(e.Left)
) : fr(e.Right)
) : undefined;

// Compose a function from a simple value to a tuple of
// the separate outputs of two different functions

// fanArrow (&&&) :: (a -> b) -> (a -> c) -> (a -> (b, c))
const fanArrow = f => g => x => Tuple(f(x))(
g(x)
);

// Lift a simple function to one which applies to a tuple,
// transforming only the first item of the tuple

// firstArrow :: (a -> b) -> ((a, c) -> (b, c))
const firstArrow = f => xy => Tuple(f(xy[0]))(
xy[1]
);

// flip :: (a -> b -> c) -> b -> a -> c
const flip = f =>
1 < f.length ? (
(a, b) => f(b, a)
) : (x => y => f(y)(x));

// fmapTree :: (a -> b) -> Tree a -> Tree b
const fmapTree = f => tree => {
const go = node => Node(f(node.root))(
node.nest.map(go)
);
return go(tree);
};

// foldTree :: (a -> [b] -> b) -> Tree a -> b
const foldTree = f => tree => {
const go = node => f(node.root)(
node.nest.map(go)
);
return go(tree);
};

// foldl1 :: (a -> a -> a) -> [a] -> a
const foldl1 = f => xs =>
1 < xs.length ? xs.slice(1)
.reduce(uncurry(f), xs[0]) : xs[0];

// fst :: (a, b) -> a
const fst = tpl => tpl[0];

// init :: [a] -> [a]
const init = xs =>
0 < xs.length ? (
xs.slice(0, -1)
) : undefined;

// insertDict :: String -> a -> Dict -> Dict
const insertDict = k => v => dct =>
Object.assign({}, dct, {
[k]: v
});

// intercalate :: [a] -> [[a]] -> [a]
// intercalate :: String -> [String] -> String
const intercalate = sep =>
xs => xs.join(sep);

// isSpace :: Char -> Bool
const isSpace = c => /\s/.test(c);

// justifyLeft :: Int -> Char -> String -> String
const justifyLeft = n => cFiller => s =>
n > s.length ? (
) : s;

// justifyRight :: Int -> Char -> String -> String
const justifyRight = n => cFiller => s =>
n > s.length ? (
) : s;

// length :: [a] -> Int
const length = xs =>
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;

// lines :: String -> [String]
const lines = s => s.split(/[\r\n]/);

// map :: (a -> b) -> [a] -> [b]
const map = f => xs =>
(Array.isArray(xs) ? (
xs
) : xs.split('')).map(f);

// minimum :: Ord a => [a] -> a
const minimum = xs =>
0 < xs.length ? (
foldl1(a => x => x < a ? x : a)(xs)
) : undefined;

// root :: Tree a -> a
const root = tree => tree.root;

// showLog :: a -> IO ()
const showLog = (...args) =>
console.log(
args
.map(JSON.stringify)
.join(' -> ')
);

// snd :: (a, b) -> b
const snd = tpl => tpl[1];

// span :: (a -> Bool) -> [a] -> ([a], [a])
const span = p => xs => {
const iLast = xs.length - 1;
return splitAt(
until(i => iLast < i || !p(xs[i]))(
succ
)(0)
)(xs);
};

// splitAt :: Int -> [a] -> ([a], [a])
const splitAt = n => xs =>
Tuple(xs.slice(0, n))(
xs.slice(n)
);

// succ :: Enum a => a -> a
const succ = x =>
1 + x;

// sum :: [Num] -> Num
const sum = xs =>
xs.reduce((a, x) => a + x, 0);

// tail :: [a] -> [a]
const tail = xs =>
0 < xs.length ? xs.slice(1) : [];

// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = n => xs =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));

// uncurry :: (a -> b -> c) -> ((a, b) -> c)
const uncurry = f =>
(x, y) => f(x)(y);

// unlines :: [String] -> String
const unlines = xs => xs.join('\n');

// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p => f => x => {
let v = x;
while (!p(v)) v = f(v);
return v;
};

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = f => xs => ys =>
xs.slice(
0, Math.min(xs.length, ys.length)
).map((x, i) => f(x)(ys[i]));

// SOURCE OUTLINE -----------------------------------------

const strOutline = `NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |        |          |
house1                      |40      |          |
bedrooms                |        |0.25      |
bathrooms               |        |          |
bathroom1           |        |0.5       |
bathroom2           |        |          |
outside_lavatory    |        |1         |
attic                   |        |0.75      |
kitchen                 |        |0.1       |
living_rooms            |        |          |
lounge              |        |          |
dining_room         |        |          |
conservatory        |        |          |
playroom            |        |1         |
basement                |        |          |
garage                  |        |          |
garden                  |        |0.8       |
house2                      |60      |          |
upstairs                |        |          |
bedrooms            |        |          |
suite_1         |        |          |
suite_2         |        |          |
bedroom_3       |        |          |
bedroom_4       |        |          |
bathroom            |        |          |
toilet              |        |          |
attics              |        |0.6       |
groundfloor             |        |          |
kitchen             |        |          |
living_rooms        |        |          |
lounge          |        |          |
dining_room     |        |          |
conservatory    |        |          |
playroom        |        |          |
wet_room_&_toilet   |        |          |
garage              |        |          |
garden              |        |0.9       |
hot_tub_suite       |        |1         |
basement                |        |          |
cellars             |        |1         |
wine_cellar         |        |1         |
cinema              |        |0.75      |`;

// MAIN ---
return main();
})();
```

{{Out}}

```NAME_HIERARCHY                 | WEIGHT   | COVERAGE | SHARE OF RESIDUE
cleaning                       |       1  |  0.4092  |  0.5908
house1                     |      40  |  0.3313  |  0.2675
bedrooms               |       1  |  0.2500  |  0.0375
bathrooms              |       1  |  0.5000  |  0.0250
bathroom1          |       1  |  0.5000  |  0.0083
bathroom2          |       1  |  0.0000  |  0.0167
outside_lavatory   |       1  |  1.0000  |  0.0000
attic                  |       1  |  0.7500  |  0.0125
kitchen                |       1  |  0.1000  |  0.0450
living_rooms           |       1  |  0.2500  |  0.0375
lounge             |       1  |  0.0000  |  0.0125
dining_room        |       1  |  0.0000  |  0.0125
conservatory       |       1  |  0.0000  |  0.0125
playroom           |       1  |  1.0000  |  0.0000
basement               |       1  |  0.0000  |  0.0500
garage                 |       1  |  0.0000  |  0.0500
garden                 |       1  |  0.8000  |  0.0100
house2                     |      60  |  0.4611  |  0.3233
upstairs               |       1  |  0.1500  |  0.1700
bedrooms           |       1  |  0.0000  |  0.0500
suite_1        |       1  |  0.0000  |  0.0125
suite_2        |       1  |  0.0000  |  0.0125
bedroom_3      |       1  |  0.0000  |  0.0125
bedroom_4      |       1  |  0.0000  |  0.0125
bathroom           |       1  |  0.0000  |  0.0500
toilet             |       1  |  0.0000  |  0.0500
attics             |       1  |  0.6000  |  0.0200
groundfloor            |       1  |  0.3167  |  0.1367
kitchen            |       1  |  0.0000  |  0.0333
living_rooms       |       1  |  0.0000  |  0.0333
lounge         |       1  |  0.0000  |  0.0083
dining_room    |       1  |  0.0000  |  0.0083
conservatory   |       1  |  0.0000  |  0.0083
playroom       |       1  |  0.0000  |  0.0083
wet_room_&_toilet  |       1  |  0.0000  |  0.0333
garage             |       1  |  0.0000  |  0.0333
garden             |       1  |  0.9000  |  0.0033
hot_tub_suite      |       1  |  1.0000  |  0.0000
basement               |       1  |  0.9167  |  0.0167
cellars            |       1  |  1.0000  |  0.0000
wine_cellar        |       1  |  1.0000  |  0.0000
cinema             |       1  |  0.7500  |  0.0167
```

## Julia

Most implementations of functional coverage are going to store values in a database. The implementation stores the tree in a CSV file with an index to the parent of each entry to allow reconstitution of the tree.

```using CSV, DataFrames, Formatting

function updatecoverage(dfname, outputname)
dchild = Dict{Int, Vector{Int}}([i => Int[] for i in 0:maximum(df[!, 1])])

for row in eachrow(df)
push!(dchild[row[3]], row[1])
end

function coverage(t)
return dchild[t] == [] ? df[t, :COVERAGE] * df[t, :WEIGHT] :
sum(coverage, dchild[t]) / sum(x -> df[x, :WEIGHT], dchild[t]) * df[t, :WEIGHT]
end

df[!, :COVERAGE] .= coverage.(df.NUMBER)

function possibleincrease(t)
if !isempty(dchild[t])
return 0.0
else
newcoverage = deepcopy(df.COVERAGE)
newcoverage[t] = 1.0
oldcoverage = newcoverage[1]
function potentialcoverage(t)
return dchild[t] == [] ? newcoverage[t] * df[t, :WEIGHT] :
sum(potentialcoverage, dchild[t]) / sum(x -> df[x, :WEIGHT],
dchild[t]) * df[t, :WEIGHT]
end

newcoverage .= potentialcoverage.(df[!, 1])
return newcoverage[1] - oldcoverage
end
end

df.POTENTIAL = possibleincrease.(df[!, 1])

CSV.write(outputname, df)
end

function displaycoveragedb(dfname)
indentlevel(t) = (i = 0; while (j = df[t, 3]) != 0 i += 1; t = j end; i)
indent1 = [indentlevel(i) for i in df.NUMBER]
maxindent = maximum(indent1)
indent2 = maxindent .- indent1
showpot = size(df)[2] == 6
println("INDEX       NAME_HIERARCHY                         WEIGHT      COVERAGE    (POTENTIAL INCREASE)")
for (i, row) in enumerate(eachrow(df))
println(rpad(row[1], 7), "       "^indent1[i], rpad(row[2], 20), "       "^indent2[i],
rpad(row[4], 8), rpad(format(row[5]), 12), showpot && row[6] != 0 ? format(row[6]) : "")
end
end

const dbname = "coverage.csv"
const newdbname = "coverageupdated.csv"

println("Input data:")
displaycoveragedb(dbname)
updatecoverage(dbname, newdbname)
println("\nUpdated data:")
displaycoveragedb(newdbname)

```

{{out}}

```
Input data:
INDEX       NAME_HIERARCHY                         WEIGHT      COVERAGE    (POTENTIAL INCREASE)
1      cleaning                                        1       0
2             house1                                   40      0
3                    bedrooms                          1       0.25
4                    bathrooms                         1       0
5                           bathroom1                  1       0.5
6                           bathroom2                  1       0
7                           outside_lavatory           1       1
8                    attic                             1       0.75
9                    kitchen                           1       0.1
10                   living_rooms                      1       0
11                          lounge                     1       0
12                          dining_room                1       0
13                          conservatory               1       0
14                          playroom                   1       1
15                   basement                          1       0
16                   garage                            1       0
17                   garden                            1       0.8
18            house2                                   60      0
19                   upstairs                          1       0
20                          bedrooms                   1       0
21                                 suite_1             1       0
22                                 suite_2             1       0
23                                 bedroom_3           1       0
24                                 bedroom_4           1       0
25                          bathroom                   1       0
26                          toilet                     1       0
27                          attics                     1       0.6
28                   groundfloor                       1       0
29                          kitchen                    1       0
30                          living_rooms               1       0
31                                 lounge              1       0
32                                 dining_room         1       0
33                                 conservatory        1       0
34                                 playroom            1       0
35                          wet_room_&_toilet          1       0
36                          garage                     1       0
37                          garden                     1       0.9
38                          hot_tub_suite              1       1
39                   basement                          1       0
40                          cellars                    1       1
41                          wine_cellar                1       1
42                          cinema                     1       0.75

Updated data:
INDEX       NAME_HIERARCHY                         WEIGHT      COVERAGE    (POTENTIAL INCREASE)
1      cleaning                                        1       0.409167
2             house1                                   40      13.25
3                    bedrooms                          1       0.25        0.0375
4                    bathrooms                         1       0.5
5                           bathroom1                  1       0.5         0.008333
6                           bathroom2                  1       0           0.016667
7                           outside_lavatory           1       1
8                    attic                             1       0.75        0.0125
9                    kitchen                           1       0.1         0.045
10                   living_rooms                      1       0.25
11                          lounge                     1       0           0.0125
12                          dining_room                1       0           0.0125
13                          conservatory               1       0           0.0125
14                          playroom                   1       1
15                   basement                          1       0           0.05
16                   garage                            1       0           0.05
17                   garden                            1       0.8         0.01
18            house2                                   60      27.666667
19                   upstairs                          1       0.15
20                          bedrooms                   1       0
21                                 suite_1             1       0           0.0125
22                                 suite_2             1       0           0.0125
23                                 bedroom_3           1       0           0.0125
24                                 bedroom_4           1       0           0.0125
25                          bathroom                   1       0           0.05
26                          toilet                     1       0           0.05
27                          attics                     1       0.6         0.02
28                   groundfloor                       1       0.316667
29                          kitchen                    1       0           0.033333
30                          living_rooms               1       0
31                                 lounge              1       0           0.008333
32                                 dining_room         1       0           0.008333
33                                 conservatory        1       0           0.008333
34                                 playroom            1       0           0.008333
35                          wet_room_&_toilet          1       0           0.033333
36                          garage                     1       0           0.033333
37                          garden                     1       0.9         0.003333
38                          hot_tub_suite              1       1
39                   basement                          1       0.916667
40                          cellars                    1       1
41                          wine_cellar                1       1
42                          cinema                     1       0.75        0.016667

```

The input CSV file used:

```
NUMBER,NAME_HIERARCHY,PARENT_NUMBER,WEIGHT,COVERAGE
1,cleaning,0,1,0
2,house1,1,40,0
3,bedrooms,2,1,0.25
4,bathrooms,2,1,0
5,bathroom1,4,1,0.5
6,bathroom2,4,1,0
7,outside_lavatory,4,1,1
8,attic,2,1,0.75
9,kitchen,2,1,0.1
10,living_rooms,2,1,0
11,lounge,10,1,0
12,dining_room,10,1,0
13,conservatory,10,1,0
14,playroom,10,1,1
15,basement,2,1,0
16,garage,2,1,0
17,garden,2,1,0.8
18,house2,1,60,0
19,upstairs,18,1,0
20,bedrooms,19,1,0
21,suite_1,20,1,0
22,suite_2,20,1,0
23,bedroom_3,20,1,0
24,bedroom_4,20,1,0
25,bathroom,19,1,0
26,toilet,19,1,0
27,attics,19,1,0.6
28,groundfloor,18,1,0
29,kitchen,28,1,0
30,living_rooms,28,1,0
31,lounge,30,1,0
32,dining_room,30,1,0
33,conservatory,30,1,0
34,playroom,30,1,0
35,wet_room_&_toilet,28,1,0
36,garage,28,1,0
37,garden,28,1,0.9
38,hot_tub_suite,28,1,1
39,basement,18,1,0
40,cellars,39,1,1
41,wine_cellar,39,1,1
42,cinema,39,1,0.75

```

## Kotlin

```// version 1.2.10

class FCNode(val name: String, val weight: Int = 1, coverage: Double = 0.0) {

var coverage = coverage
set(value) {
if (field != value) {
field = value
// update any parent's coverage
if (parent != null) parent!!.updateCoverage()
}
}

val children = mutableListOf<FCNode>()
var parent: FCNode? = null

fun addChildren(nodes: List<FCNode>) {
nodes.forEach { it.parent = this }
updateCoverage()
}

private fun updateCoverage() {
val v1 = children.sumByDouble { it.weight * it.coverage }
val v2 = children.sumBy { it.weight }
coverage = v1 / v2
}

fun show(level: Int = 0) {
val indent = level * 4
val nl = name.length + indent
print("  %3d   |".format(weight))
println(" %8.6f |".format(coverage))
if (children.size == 0) return
for (child in children) child.show(level + 1)
}
}

val houses = listOf(
FCNode("house1", 40),
FCNode("house2", 60)
)

val house1 = listOf(
FCNode("bedrooms", 1, 0.25),
FCNode("bathrooms"),
FCNode("attic", 1, 0.75),
FCNode("kitchen", 1, 0.1),
FCNode("living_rooms"),
FCNode("basement"),
FCNode("garage"),
FCNode("garden", 1, 0.8)
)

val house2 = listOf(
FCNode("upstairs"),
FCNode("groundfloor"),
FCNode("basement")
)

val h1Bathrooms = listOf(
FCNode("bathroom1", 1, 0.5),
FCNode("bathroom2"),
FCNode("outside_lavatory", 1, 1.0)
)

val h1LivingRooms = listOf(
FCNode("lounge"),
FCNode("dining_room"),
FCNode("conservatory"),
FCNode("playroom", 1, 1.0)
)

val h2Upstairs = listOf(
FCNode("bedrooms"),
FCNode("bathroom"),
FCNode("toilet"),
FCNode("attics", 1, 0.6)
)

val h2Groundfloor = listOf(
FCNode("kitchen"),
FCNode("living_rooms"),
FCNode("wet_room_&_toilet"),
FCNode("garage"),
FCNode("garden", 1, 0.9),
FCNode("hot_tub_suite", 1, 1.0)
)

val h2Basement = listOf(
FCNode("cellars", 1, 1.0),
FCNode("wine_cellar", 1, 1.0),
FCNode("cinema", 1, 0.75)
)

val h2UpstairsBedrooms = listOf(
FCNode("suite_1"),
FCNode("suite_2"),
FCNode("bedroom_3"),
FCNode("bedroom_4")
)

val h2GroundfloorLivingRooms = listOf(
FCNode("lounge"),
FCNode("dining_room"),
FCNode("conservatory"),
FCNode("playroom")
)

fun main(args: Array<String>) {
val cleaning = FCNode("cleaning")

val topCoverage = cleaning.coverage
println("TOP COVERAGE = \${"%8.6f".format(topCoverage)}\n")
println("NAME HIERARCHY                 | WEIGHT | COVERAGE |")
cleaning.show()

h2Basement[2].coverage = 1.0  // change Cinema node coverage to 1.0
val diff = cleaning.coverage - topCoverage
println("\nIf the coverage of the Cinema node were increased from 0.75 to 1.0")
print("the top level coverage would increase by ")
println("\${"%8.6f".format(diff)} to \${"%8.6f".format(topCoverage + diff)}")
h2Basement[2].coverage = 0.75  // restore to original value if required
}
```

{{out}}

```
TOP COVERAGE = 0.409167

NAME HIERARCHY                 | WEIGHT | COVERAGE |
cleaning                       |    1   | 0.409167 |
house1                     |   40   | 0.331250 |
bedrooms               |    1   | 0.250000 |
bathrooms              |    1   | 0.500000 |
bathroom1          |    1   | 0.500000 |
bathroom2          |    1   | 0.000000 |
outside_lavatory   |    1   | 1.000000 |
attic                  |    1   | 0.750000 |
kitchen                |    1   | 0.100000 |
living_rooms           |    1   | 0.250000 |
lounge             |    1   | 0.000000 |
dining_room        |    1   | 0.000000 |
conservatory       |    1   | 0.000000 |
playroom           |    1   | 1.000000 |
basement               |    1   | 0.000000 |
garage                 |    1   | 0.000000 |
garden                 |    1   | 0.800000 |
house2                     |   60   | 0.461111 |
upstairs               |    1   | 0.150000 |
bedrooms           |    1   | 0.000000 |
suite_1        |    1   | 0.000000 |
suite_2        |    1   | 0.000000 |
bedroom_3      |    1   | 0.000000 |
bedroom_4      |    1   | 0.000000 |
bathroom           |    1   | 0.000000 |
toilet             |    1   | 0.000000 |
attics             |    1   | 0.600000 |
groundfloor            |    1   | 0.316667 |
kitchen            |    1   | 0.000000 |
living_rooms       |    1   | 0.000000 |
lounge         |    1   | 0.000000 |
dining_room    |    1   | 0.000000 |
conservatory   |    1   | 0.000000 |
playroom       |    1   | 0.000000 |
wet_room_&_toilet  |    1   | 0.000000 |
garage             |    1   | 0.000000 |
garden             |    1   | 0.900000 |
hot_tub_suite      |    1   | 1.000000 |
basement               |    1   | 0.916667 |
cellars            |    1   | 1.000000 |
wine_cellar        |    1   | 1.000000 |
cinema             |    1   | 0.750000 |

If the coverage of the Cinema node were increased from 0.75 to 1.0
the top level coverage would increase by 0.016667 to 0.425833

```

## Perl

```#!/usr/bin/perl

use strict;
use warnings;

print \$_->[0] for walktree( do { local \$/; <DATA> } );

sub walktree
{
my @parts;
while( \$_[0] =~ /(( *)\S.*\n)((?:\2 .*\n)*)/g )
{
my (\$head, \$body, \$w, \$wsum) = (\$1, \$3, 0, 0);
\$head =~ /^.*?\|(\S*) *\|(\S*) *\|/;
my \$weight = sprintf '%-8s', \$1 || 1;
my \$coverage = sprintf '%-10s', \$2 || 0;
\$w += \$_->[1], \$wsum += \$_->[1] * \$_->[2], \$head .= \$_->[0]
for walktree( \$body );
\$w and \$coverage = sprintf '%-10.8g', \$wsum / \$w;
push @parts, [ \$head =~ s/\|.*/|\$weight|\$coverage|/r, \$weight, \$coverage ];
}
return @parts;
}

__DATA__
NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |        |          |
house1                      |40      |          |
bedrooms                |        |0.25      |
bathrooms               |        |          |
bathroom1           |        |0.5       |
bathroom2           |        |          |
outside_lavatory    |        |1         |
attic                   |        |0.75      |
kitchen                 |        |0.1       |
living_rooms            |        |          |
lounge              |        |          |
dining_room         |        |          |
conservatory        |        |          |
playroom            |        |1         |
basement                |        |          |
garage                  |        |          |
garden                  |        |0.8       |
house2                      |60      |          |
upstairs                |        |          |
bedrooms            |        |          |
suite_1         |        |          |
suite_2         |        |          |
bedroom_3       |        |          |
bedroom_4       |        |          |
bathroom            |        |          |
toilet              |        |          |
attics              |        |0.6       |
groundfloor             |        |          |
kitchen             |        |          |
living_rooms        |        |          |
lounge          |        |          |
dining_room     |        |          |
conservatory    |        |          |
playroom        |        |          |
wet_room_&_toilet   |        |          |
garage              |        |          |
garden              |        |0.9       |
hot_tub_suite       |        |1         |
basement                |        |          |
cellars             |        |1         |
wine_cellar         |        |1         |
cinema              |        |0.75      |

```

{{out}}

```
NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |1       |0.40916667|
house1                      |40      |0.33125   |
bedrooms                |1       |0.25      |
bathrooms               |1       |0.5       |
bathroom1           |1       |0.5       |
bathroom2           |1       |0         |
outside_lavatory    |1       |1         |
attic                   |1       |0.75      |
kitchen                 |1       |0.1       |
living_rooms            |1       |0.25      |
lounge              |1       |0         |
dining_room         |1       |0         |
conservatory        |1       |0         |
playroom            |1       |1         |
basement                |1       |0         |
garage                  |1       |0         |
garden                  |1       |0.8       |
house2                      |60      |0.46111111|
upstairs                |1       |0.15      |
bedrooms            |1       |0         |
suite_1         |1       |0         |
suite_2         |1       |0         |
bedroom_3       |1       |0         |
bedroom_4       |1       |0         |
bathroom            |1       |0         |
toilet              |1       |0         |
attics              |1       |0.6       |
groundfloor             |1       |0.31666667|
kitchen             |1       |0         |
living_rooms        |1       |0         |
lounge          |1       |0         |
dining_room     |1       |0         |
conservatory    |1       |0         |
playroom        |1       |0         |
wet_room_&_toilet   |1       |0         |
garage              |1       |0         |
garden              |1       |0.9       |
hot_tub_suite       |1       |1         |
basement                |1       |0.91666667|
cellars             |1       |1         |
wine_cellar         |1       |1         |
cinema              |1       |0.75      |

```

## Python

### Python: Using lists and tuples

It's actually some of the raw code used when researching this task.

```from itertools import zip_longest

fc2 = '''\
cleaning,,
house1,40,
bedrooms,,.25
bathrooms,,
bathroom1,,.5
bathroom2,,
outside_lavatory,,1
attic,,.75
kitchen,,.1
living_rooms,,
lounge,,
dining_room,,
conservatory,,
playroom,,1
basement,,
garage,,
garden,,.8
house2,60,
upstairs,,
bedrooms,,
suite_1,,
suite_2,,
bedroom_3,,
bedroom_4,,
bathroom,,
toilet,,
attics,,.6
groundfloor,,
kitchen,,
living_rooms,,
lounge,,
dining_room,,
conservatory,,
playroom,,
wet_room_&_toilet,,
garage,,
garden,,.9
hot_tub_suite,,1
basement,,
cellars,,1
wine_cellar,,1
cinema,,.75

'''

NAME, WT, COV = 0, 1, 2

def right_type(txt):
try:
return float(txt)
except ValueError:
return txt

def commas_to_list(the_list, lines, start_indent=0):
'''
Output format is a nest of lists and tuples
lists are for coverage leaves without children items in the list are name, weight, coverage
tuples are 2-tuples for nodes with children. The first element is a list representing the
name, weight, coverage of the node (some to be calculated); the second element is a list of
child elements which may be 2-tuples or lists as above.

the_list is modified in-place
lines must be a generator of successive lines of input like fc2
'''
for n, line in lines:
indent = 0
while line.startswith(' ' * (4 * indent)):
indent += 1
indent -= 1
fields = [right_type(f) for f in line.strip().split(',')]
if indent == start_indent:
the_list.append(fields)
elif indent > start_indent:
lst = [fields]
sub = commas_to_list(lst, lines, indent)
the_list[-1] = (the_list[-1], lst)
if sub not in (None, ['']) :
the_list.append(sub)
else:
return fields if fields else None
return None

def pptreefields(lst, indent=0, widths=['%-32s', '%-8g', '%-10g']):
'''
Pretty prints the format described from function commas_to_list as a table with
names in the first column suitably indented and all columns having a fixed
minimum column width.
'''
lhs = ' ' * (4 * indent)
for item in lst:
if type(item) != tuple:
name, *rest = item
print(widths[0] % (lhs + name), end='|')
for width, item in zip_longest(widths[1:len(rest)], rest, fillvalue=widths[-1]):
if type(item) == str:
width = width[:-1] + 's'
print(width % item, end='|')
print()
else:
item, children = item
name, *rest = item
print(widths[0] % (lhs + name), end='|')
for width, item in zip_longest(widths[1:len(rest)], rest, fillvalue=widths[-1]):
if type(item) == str:
width = width[:-1] + 's'
print(width % item, end='|')
print()
pptreefields(children, indent+1)

def default_field(node_list):
node_list[WT] = node_list[WT] if node_list[WT] else 1.0
node_list[COV] = node_list[COV] if node_list[COV] else 0.0

def depth_first(tree, visitor=default_field):
for item in tree:
if type(item) == tuple:
item, children = item
depth_first(children, visitor)
visitor(item)

def covercalc(tree):
'''
Depth first weighted average of coverage
'''
sum_covwt, sum_wt = 0, 0
for item in tree:
if type(item) == tuple:
item, children = item
item[COV] = covercalc(children)
sum_wt  += item[WT]
sum_covwt += item[COV] * item[WT]
cov = sum_covwt / sum_wt
return cov

if __name__ == '__main__':
lstc = []
commas_to_list(lstc, ((n, ln) for n, ln in enumerate(fc2.split('\n'))))
#pp(lstc, width=1, indent=4, compact=1)

#print('\n\nEXPANDED DEFAULTS\n')
depth_first(lstc)
#pptreefields(['NAME_HIERARCHY WEIGHT COVERAGE'.split()] + lstc)

print('\n\nTOP COVERAGE = %f\n' % covercalc(lstc))
depth_first(lstc)
pptreefields(['NAME_HIERARCHY WEIGHT COVERAGE'.split()] + lstc)
```

{{out}}

```TOP COVERAGE = 0.409167

NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |1       |0.409167  |
house1                      |40      |0.33125   |
bedrooms                |1       |0.25      |
bathrooms               |1       |0.5       |
bathroom1           |1       |0.5       |
bathroom2           |1       |0         |
outside_lavatory    |1       |1         |
attic                   |1       |0.75      |
kitchen                 |1       |0.1       |
living_rooms            |1       |0.25      |
lounge              |1       |0         |
dining_room         |1       |0         |
conservatory        |1       |0         |
playroom            |1       |1         |
basement                |1       |0         |
garage                  |1       |0         |
garden                  |1       |0.8       |
house2                      |60      |0.461111  |
upstairs                |1       |0.15      |
bedrooms            |1       |0         |
suite_1         |1       |0         |
suite_2         |1       |0         |
bedroom_3       |1       |0         |
bedroom_4       |1       |0         |
bathroom            |1       |0         |
toilet              |1       |0         |
attics              |1       |0.6       |
groundfloor             |1       |0.316667  |
kitchen             |1       |0         |
living_rooms        |1       |0         |
lounge          |1       |0         |
dining_room     |1       |0         |
conservatory    |1       |0         |
playroom        |1       |0         |
wet_room_&_toilet   |1       |0         |
garage              |1       |0         |
garden              |1       |0.9       |
hot_tub_suite       |1       |1         |
basement                |1       |0.916667  |
cellars             |1       |1         |
wine_cellar         |1       |1         |
cinema              |1       |0.75      |
```

### Python: Class based and extra credit

A cleaner implementation that uses the class static variable path2node as in the previous example so you don't have to traverse the tree to work out the position to add new nodes. This relies on parent nodes appearing before their children which is the case in the order of the add_node calls.

```# -*- coding: utf-8 -*-

SPACES = 4
class Node:
path2node = {}

def add_node(self, pathname, wt, cov):
path2node = self.path2node
path, name = pathname.strip().rsplit('/', 1)
node = Node(name, wt, cov)
path2node[pathname] = node
path2node[path].child.append(node) # Link the tree

def __init__(self, name="", wt=1, cov=0.0, child=None):
if child is None:
child = []
self.name, self.wt, self.cov, self.child = name, wt, cov, child
self.delta = None
self.sum_wt = wt
if name == "":
# designate the top of the tree
self.path2node[name] = self

def __repr__(self, indent=0):
name, wt, cov, delta, child = (self.name, self.wt, self.cov,
self.delta, self.child)
lhs = ' ' * (SPACES * indent) + "Node(%r," % name
txt = '%-40s wt=%2g, cov=%-8.5g, delta=%-10s, child=[' \
% (lhs, wt, cov, ('n/a' if delta is None else '%-10.7f' % delta))
if not child:
txt += (']),\n')
else:
txt += ('\n')
for c in child:
txt += c.__repr__(indent + 1)
txt += (' ' * (SPACES * indent) + "]),\n")
return txt

def covercalc(self):
'''
Depth first weighted average of coverage
'''
child = self.child
if not child:
return self.cov
sum_covwt, sum_wt = 0, 0
for node in child:
nwt = node.wt
ncov = node.covercalc()
sum_wt += nwt
sum_covwt += ncov * nwt
cov = sum_covwt / sum_wt
self.sum_wt = sum_wt
self.cov = cov
return cov

def deltacalc(self, power=1.0):
'''
Top down distribution of weighted residuals
'''
sum_wt = self.sum_wt
self.delta = delta = (1 - self.cov) * power
for node in self.child:
node.deltacalc(power * node.wt / sum_wt)
return delta

def isclose(a, b, rel_tol=1e-9, abs_tol=1e-9):
return abs(a-b) <= max( rel_tol * max(abs(a), abs(b)), abs_tol )

if __name__ == '__main__':
top = Node()    # Add placeholder for top of tree

top = top.child[0]  # Remove artificial top
cover = top.covercalc()
delta = top.deltacalc()
print('TOP COVERAGE = %g\n' % cover)
print(top)
assert isclose((delta + cover), 1.0), "Top level delta + coverage should " \
"equal 1 instead of (%f + %f)" % (delta, cover)

```

{{out}}

The deltas where checked by, for example, changing the coverage of the cinema in house2 to be 1.0 instead of 0.75 and observing an additional 0.0166667 increase in the top level coverage at node 'cleaning'.

```TOP COVERAGE = 0.409167

Node('cleaning',                         wt= 1, cov=0.40917 , delta=0.5908333 , child=[
Node('house1',                       wt=40, cov=0.33125 , delta=0.2675000 , child=[
Node('bedrooms',                 wt= 1, cov=0.25    , delta=0.0375000 , child=[]),
Node('bathrooms',                wt= 1, cov=0.5     , delta=0.0250000 , child=[
Node('bathroom1',            wt= 1, cov=0.5     , delta=0.0083333 , child=[]),
Node('bathroom2',            wt= 1, cov=0       , delta=0.0166667 , child=[]),
Node('outside_lavatory',     wt= 1, cov=1       , delta=0.0000000 , child=[]),
]),
Node('attic',                    wt= 1, cov=0.75    , delta=0.0125000 , child=[]),
Node('kitchen',                  wt= 1, cov=0.1     , delta=0.0450000 , child=[]),
Node('living_rooms',             wt= 1, cov=0.25    , delta=0.0375000 , child=[
Node('lounge',               wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('dining_room',          wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('conservatory',         wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('playroom',             wt= 1, cov=1       , delta=0.0000000 , child=[]),
]),
Node('basement',                 wt= 1, cov=0       , delta=0.0500000 , child=[]),
Node('garage',                   wt= 1, cov=0       , delta=0.0500000 , child=[]),
Node('garden',                   wt= 1, cov=0.8     , delta=0.0100000 , child=[]),
]),
Node('house2',                       wt=60, cov=0.46111 , delta=0.3233333 , child=[
Node('upstairs',                 wt= 1, cov=0.15    , delta=0.1700000 , child=[
Node('bedrooms',             wt= 1, cov=0       , delta=0.0500000 , child=[
Node('suite_1',          wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('suite_2',          wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('bedroom_3',        wt= 1, cov=0       , delta=0.0125000 , child=[]),
Node('bedroom_4',        wt= 1, cov=0       , delta=0.0125000 , child=[]),
]),
Node('bathroom',             wt= 1, cov=0       , delta=0.0500000 , child=[]),
Node('toilet',               wt= 1, cov=0       , delta=0.0500000 , child=[]),
Node('attics',               wt= 1, cov=0.6     , delta=0.0200000 , child=[]),
]),
Node('groundfloor',              wt= 1, cov=0.31667 , delta=0.1366667 , child=[
Node('kitchen',              wt= 1, cov=0       , delta=0.0333333 , child=[]),
Node('living_rooms',         wt= 1, cov=0       , delta=0.0333333 , child=[
Node('lounge',           wt= 1, cov=0       , delta=0.0083333 , child=[]),
Node('dining_room',      wt= 1, cov=0       , delta=0.0083333 , child=[]),
Node('conservatory',     wt= 1, cov=0       , delta=0.0083333 , child=[]),
Node('playroom',         wt= 1, cov=0       , delta=0.0083333 , child=[]),
]),
Node('wet_room_&_toilet',    wt= 1, cov=0       , delta=0.0333333 , child=[]),
Node('garage',               wt= 1, cov=0       , delta=0.0333333 , child=[]),
Node('garden',               wt= 1, cov=0.9     , delta=0.0033333 , child=[]),
Node('hot_tub_suite',        wt= 1, cov=1       , delta=0.0000000 , child=[]),
]),
Node('basement',                 wt= 1, cov=0.91667 , delta=0.0166667 , child=[
Node('cellars',              wt= 1, cov=1       , delta=0.0000000 , child=[]),
Node('wine_cellar',          wt= 1, cov=1       , delta=0.0000000 , child=[]),
Node('cinema',               wt= 1, cov=0.75    , delta=0.0166667 , child=[]),
]),
]),
]),
```

### Python: Composition of pure functions

Parsing the task statement text directly to a tree of dictionaries, folding a '''weightedTreeAverage''' function over that tree, and further decorating it with a top-down residue-share traversal.

Mainly uses pre-existing generic functions, including '''forestFromLineIndents''', '''foldTree''' and '''fmapTree''': {{Works with|Python|3.7}}

```'''Functional coverage tree'''

from itertools import chain, product
from functools import reduce

# main :: IO ()
def main():
'''Tabular outline serialisation of a parse tree
decorated with computations of:
1. Weighted coverage of each tree node.
2. Each node's share of the total project's
remaining work.
'''
columnWidths = [31, 9, 9, 9]
delimiter = '|'

reportLines = lines(REPORT)
columnTitles = init(columnNames(delimiter)(reportLines[0]))

# SERIALISATION OF DECORATED PARSE TREE
print(titleLine(delimiter)(columnWidths)(
columnTitles + ['share of residue']
))
print(indentedLinesFromTree('    ', tabulation(columnWidths))(

# TWO COMPUTATIONS BY TRAVERSAL
withResidueShares(1.0)(
foldTree(weightedCoverage)(

# TREE FROM PARSE OF OUTLINE TEXT
fmapTree(
recordFromKeysDefaultsDelimiterAndLine(columnTitles)(
[str, float, float])(['?', 1.0, 0.0])(delimiter)
)(
forestFromLineIndents(indentLevelsFromLines(
reportLines[1:]
))[0]
)
)
)
))

# WEIGHTED COVERAGE, AND SHARE OF TOTAL RESIDUE -----------

# weightedCoverage :: Tree Dict ->
# [Tree Dict] -> Tree Dict
def weightedCoverage(x):
'''The weighted coverage of a tree node,
as a function of the weighted averages
of its children.
'''
def go(xs):
cws = [(r['coverage'], r['weight']) for r in [root(x) for x in xs]]
totalWeight = reduce(lambda a, x: a + x[1], cws, 0)
return Node(dict(
x, **{
'coverage': round(reduce(
lambda a, cw: a + (cw[0] * cw[1]),
cws, x['coverage']
) / (totalWeight if 0 < totalWeight else 1), 5)
}
))(xs)
return lambda xs: go(xs)

# withResidueShares :: Float -> Tree Dict -> Tree Dict
def withResidueShares(shareOfTotal):
'''A Tree of dictionaries additionally decorated with each
node's proportion of the total project's outstanding work.
'''
def go(fraction, node):
[nodeRoot, nodeNest] = apList([root, nest])([node])
weights = [root(x)['weight'] for x in nodeNest]
siblingsTotal = sum(weights)
return Node(
insertDict('residual_share')(
round(fraction * (1 - nodeRoot['coverage']), 5)
)(nodeRoot)
)(
map(
go,
[fraction * (w / siblingsTotal) for w in weights],
nodeNest
)
)
return lambda tree: go(shareOfTotal, tree)

# OUTLINE TABULATION --------------------------------------

# tabulation :: [Int] -> String -> Dict -> String
def tabulation(columnWidths):
'''Indented string representation of a node
in a functional coverage tree.
'''
return lambda indent, dct: '| '.join(map(
lambda k, w: (
(indent if 10 < w else '') + str(dct.get(k, ''))
).ljust(w, ' '),
dct.keys(),
columnWidths
))

# titleLine :: String -> [Int] -> [String] -> String
def titleLine(delimiter):
'''A string consisting of a spaced and delimited
series of upper-case column titles.
'''
return lambda columnWidths: lambda ks: (
delimiter + ' '
).join(map(
lambda k, w: k.ljust(w, ' '),
[k.upper() for k in ks],
columnWidths
))

# GENERIC AND REUSABLE FUNCTIONS --------------------------

# Node :: a -> [Tree a] -> Tree a
def Node(v):
'''Constructor for a Tree node which connects a
value of some kind to a list of zero or
more child trees.
'''
return lambda xs: {'type': 'Tree', 'root': v, 'nest': xs}

# Tuple (,) :: a -> b -> (a, b)
def Tuple(x):
'''Constructor for a pair of values,
possibly of two different types.
'''
return lambda y: (
x + (y,)
) if isinstance(x, tuple) else (x, y)

# apList (<*>) :: [(a -> b)] -> [a] -> [b]
def apList(fs):
'''The application of each of a list of functions,
to each of a list of values.
'''
return liftA2List(identity)(fs)

# columnNames :: String -> String -> [String]
def columnNames(delimiter):
'''A list of lower-case keys derived from
a header line and a delimiter character.
'''
return compose(
fmapList(compose(toLower, strip)),
splitOn(delimiter)
)

# compose :: ((a -> a), ...) -> (a -> a)
def compose(*fs):
'''Composition, from right to left,
of a series of functions.
'''
return lambda x: reduce(
lambda a, f: f(a),
fs[::-1], x
)

# concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
'''A concatenated list or string over which a function f
has been mapped.
The list monad can be derived by using an (a -> [b])
function which wraps its output in a list (using an
empty list to represent computational failure).
'''
return lambda xs: (''.join if isinstance(xs, str) else list)(
chain.from_iterable(map(f, xs))
)

# div :: Int -> Int -> Int
def div(x):
'''Integer division.'''
return lambda y: x // y

def firstArrow(f):
'''A simple function lifted to one which applies
to a tuple, transforming only its first item.
'''
return lambda xy: Tuple(f(xy[0]))(
xy[1]
)

# flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
'''The (curried or uncurried) function f with its
arguments reversed.
'''
return lambda a: lambda b: f(b)(a)

# fmapList :: (a -> b) -> [a] -> [b]
def fmapList(f):
'''fmap over a list.
f lifted to a function over a list.
'''
return lambda xs: [f(x) for x in xs]

# fmapTree :: (a -> b) -> Tree a -> Tree b
def fmapTree(f):
'''A new tree holding the results of
applying f to each root in
the existing tree.
'''
def go(x):
return Node(f(x['root']))(
[go(v) for v in x['nest']]
)
return lambda tree: go(tree)

# foldTree :: (a -> [b] -> b) -> Tree a -> b
def foldTree(f):
'''The catamorphism on trees. A summary
value obtained by a depth-first fold.
'''
def go(node):
return f(node['root'])([
go(x) for x in node['nest']
])
return lambda tree: go(tree)

# forestFromLineIndents :: [(Int, String)] -> [Tree String]
def forestFromLineIndents(tuples):
'''A list of trees derived from a list of lines paired
with integers giving their levels of indentation.
'''
def go(xs):
if xs:
(intIndent, txt) = xs[0]
(firstTreeLines, rest) = span(
compose(lt(intIndent), fst)
)(xs[1:])
return [Node(txt)(go(firstTreeLines))] + go(rest)
else:
return []
return go(tuples)

# fst :: (a, b) -> a
def fst(tpl):
'''First member of a pair.'''
return tpl[0]

# identity :: a -> a
def identity(x):
'''The identity function.'''
return x

# indentLevelsFromLines :: [String] -> [(Int, String)]
def indentLevelsFromLines(xs):
'''Each input line stripped of leading
white space, and tupled with a preceding integer
giving its level of indentation from 0 upwards.
'''
indentTextPairs = list(map(
compose(firstArrow(len), span(isSpace)),
xs
))
indentUnit = min(concatMap(
lambda x: [x[0]] if x[0] else []
)(indentTextPairs))
return list(map(
firstArrow(flip(div)(indentUnit)),
indentTextPairs
))

# indentedLinesFromTree :: String -> (String -> a -> String) ->
# [Tree a] -> String
def indentedLinesFromTree(strTab, f):
'''An indented line rendering of a tree, in which
the function f stringifies a root value.
'''
def go(indent):
return lambda node: [f(indent, node['root'])] + concatMap(
go(strTab + indent)
)(node['nest'])
return lambda tree: unlines(go('')(tree))

# init :: [a] -> [a]
def init(xs):
'''A list containing all the elements
of xs except the last.
'''
return xs[:-1]

# insertDict :: String -> a -> Dict -> Dict
def insertDict(k):
'''A new dictionary updated with a (k, v) pair.'''
def go(v, dct):
return dict(dct, **{k: v})
return lambda v: lambda dct: go(v, dct)

# isSpace :: Char -> Bool
# isSpace :: String -> Bool
def isSpace(s):
'''True if s is not empty, and
contains only white space.
'''
return s.isspace()

# liftA2List :: (a -> b -> c) -> [a] -> [b] -> [c]
def liftA2List(f):
'''The binary operator f lifted to a function over two
lists. f applied to each pair of arguments in the
cartesian product of xs and ys.
'''
return lambda xs: lambda ys: [
f(x)(y) for x, y in product(xs, ys)
]

# lines :: String -> [String]
def lines(s):
'''A list of strings,
(containing no newline characters)
derived from a single new-line delimited string.
'''
return s.splitlines()

# lt (<) :: Ord a => a -> a -> Bool
def lt(x):
'''True if x < y.'''
return lambda y: (x < y)

# nest :: Tree a -> [Tree a]
def nest(t):
'''Accessor function for children of tree node.'''
return t['nest'] if 'nest' in t else None

# recordFromKeysDefaultsAndLine :: String ->
# { name :: String, weight :: Float, completion :: Float }
def recordFromKeysDefaultsDelimiterAndLine(columnTitles):
'''A dictionary of key-value pairs, derived from a
delimited string, together with ordered lists of
key-names, types, default values, and a delimiter.
'''
return lambda ts: lambda vs: lambda delim: lambda s: dict(
map(
lambda k, t, v, x: (k, t(x) if x else v),
columnTitles, ts, vs,
map(strip, splitOn(delim)(s))
)
)

# root :: Tree a -> a
def root(t):
'''Accessor function for data of tree node.'''
return t['root'] if 'root' in t else None

# strip :: String -> String
def strip(s):
'''A copy of s without any leading or trailling
white space.
'''
return s.strip()

# span :: (a -> Bool) -> [a] -> ([a], [a])
def span(p):
'''The longest (possibly empty) prefix of xs
that contains only elements satisfying p,
tupled with the remainder of xs.
span p xs is equivalent to (takeWhile p xs, dropWhile p xs).
'''
def go(xs):
lng = len(xs)
return splitAt(
until(lambda i: (lng == i) or not p(xs[i]))(succ)(0)
)(xs)
return lambda xs: go(xs)

# Unimplemented <- splitOn for lists (Eq a => [a] -> [a] -> [[a]])
# splitOn :: String -> String -> [String]
def splitOn(pat):
'''A list of the strings delimited by
instances of a given pattern in s.
'''
return lambda xs: (
xs.split(pat) if isinstance(xs, str) else None
)

# splitAt :: Int -> [a] -> ([a], [a])
def splitAt(n):
'''A tuple pairing the prefix of length n
with the rest of xs.
'''
return lambda xs: (xs[0:n], xs[n:])

# succ :: Enum a => a -> a
def succ(x):
'''The successor of a value.
For numeric types, (1 +).
'''
return 1 + x if isinstance(x, int) else (
chr(1 + ord(x))
)

# toLower :: String -> String
def toLower(s):
'''String in lower case.'''
return s.lower()

# unlines :: [String] -> String
def unlines(xs):
'''A single string formed by the intercalation
of a list of strings with the newline character.
'''
return '\n'.join(xs)

# until :: (a -> Bool) -> (a -> a) -> a -> a
def until(p):
'''The result of repeatedly applying f until p holds.
The initial seed value is x.
'''
def go(f, x):
v = x
while not p(v):
v = f(v)
return v
return lambda f: lambda x: go(f, x)

# MAIN ----------------------------------------------------
if __name__ == '__main__':
REPORT = '''NAME_HIERARCHY                  |WEIGHT  |COVERAGE  |
cleaning                        |        |          |
house1                      |40      |          |
bedrooms                |        |0.25      |
bathrooms               |        |          |
bathroom1           |        |0.5       |
bathroom2           |        |          |
outside_lavatory    |        |1         |
attic                   |        |0.75      |
kitchen                 |        |0.1       |
living_rooms            |        |          |
lounge              |        |          |
dining_room         |        |          |
conservatory        |        |          |
playroom            |        |1         |
basement                |        |          |
garage                  |        |          |
garden                  |        |0.8       |
house2                      |60      |          |
upstairs                |        |          |
bedrooms            |        |          |
suite_1         |        |          |
suite_2         |        |          |
bedroom_3       |        |          |
bedroom_4       |        |          |
bathroom            |        |          |
toilet              |        |          |
attics              |        |0.6       |
groundfloor             |        |          |
kitchen             |        |          |
living_rooms        |        |          |
lounge          |        |          |
dining_room     |        |          |
conservatory    |        |          |
playroom        |        |          |
wet_room_&_toilet   |        |          |
garage              |        |          |
garden              |        |0.9       |
hot_tub_suite       |        |1         |
basement                |        |          |
cellars             |        |1         |
wine_cellar         |        |1         |
cinema              |        |0.75      |'''
main()
```

{{Out}}

```NAME_HIERARCHY                 | WEIGHT   | COVERAGE | SHARE OF RESIDUE
cleaning                       | 1.0      | 0.40917  | 0.59083
house1                     | 40.0     | 0.33125  | 0.2675
bedrooms               | 1.0      | 0.25     | 0.0375
bathrooms              | 1.0      | 0.5      | 0.025
bathroom1          | 1.0      | 0.5      | 0.00833
bathroom2          | 1.0      | 0.0      | 0.01667
outside_lavatory   | 1.0      | 1.0      | 0.0
attic                  | 1.0      | 0.75     | 0.0125
kitchen                | 1.0      | 0.1      | 0.045
living_rooms           | 1.0      | 0.25     | 0.0375
lounge             | 1.0      | 0.0      | 0.0125
dining_room        | 1.0      | 0.0      | 0.0125
conservatory       | 1.0      | 0.0      | 0.0125
playroom           | 1.0      | 1.0      | 0.0
basement               | 1.0      | 0.0      | 0.05
garage                 | 1.0      | 0.0      | 0.05
garden                 | 1.0      | 0.8      | 0.01
house2                     | 60.0     | 0.46111  | 0.32333
upstairs               | 1.0      | 0.15     | 0.17
bedrooms           | 1.0      | 0.0      | 0.05
suite_1        | 1.0      | 0.0      | 0.0125
suite_2        | 1.0      | 0.0      | 0.0125
bedroom_3      | 1.0      | 0.0      | 0.0125
bedroom_4      | 1.0      | 0.0      | 0.0125
bathroom           | 1.0      | 0.0      | 0.05
toilet             | 1.0      | 0.0      | 0.05
attics             | 1.0      | 0.6      | 0.02
groundfloor            | 1.0      | 0.31667  | 0.13667
kitchen            | 1.0      | 0.0      | 0.03333
living_rooms       | 1.0      | 0.0      | 0.03333
lounge         | 1.0      | 0.0      | 0.00833
dining_room    | 1.0      | 0.0      | 0.00833
conservatory   | 1.0      | 0.0      | 0.00833
playroom       | 1.0      | 0.0      | 0.00833
wet_room_&_toilet  | 1.0      | 0.0      | 0.03333
garage             | 1.0      | 0.0      | 0.03333
garden             | 1.0      | 0.9      | 0.00333
hot_tub_suite      | 1.0      | 1.0      | 0.0
basement               | 1.0      | 0.91667  | 0.01667
cellars            | 1.0      | 1.0      | 0.0
wine_cellar        | 1.0      | 1.0      | 0.0
cinema             | 1.0      | 0.75     | 0.01667
```

## Racket

To save on paper, the coverage table needs to be saved to a file (in this case `data/functional-coverage.txt`).

```#lang racket/base
(require racket/list racket/string racket/match racket/format racket/file)

(struct Coverage (name weight coverage weighted-coverage children) #:transparent #:mutable)

;; -| read/parse |------------------------------------------------------------------------------------
(define (build-hierarchies parsed-lines)
(define inr
(match-lambda
['() (values null null)]
[`((,head-indent . ,C) ,tail-lines ...)
(define child? (match-lambda [(cons i _) #:when (> i head-indent) #t] [_ #f]))
(define-values (chlds rels) (splitf-at tail-lines child?))
(define-values (rels-tree rels-rem) (inr rels))
(values (cons (struct-copy Coverage C (children (build-hierarchies chlds))) rels-tree)
rels-rem)]))
(define-values (hierarchies remaining-lines) (inr parsed-lines))
hierarchies)

(define report-line->indent.c/e-line
(match-lambda
[(regexp #px"^( *)([^ ]*) *\\| *([^ ]*) *\\| *([^ ]*) *\\|\$"
(list _
(app string-length indent-length)
name
(or (and (not "") (app string->number wght)) (app (λ (x) 1) wght))
(or (and (not "") (app string->number cvrg)) (app (λ (x) 0) cvrg))))
(cons indent-length (Coverage name wght cvrg 0 #f))]))

(define (report->indent.c/e-list rprt)
(map report-line->indent.c/e-line (drop (string-split rprt "\n") 1)))

;; -| evaluate |--------------------------------------------------------------------------------------
(define find-wght-cvrg
(match-lambda
[(and e (Coverage _ w c _ '())) (struct-copy Coverage e (weighted-coverage (* w c)))]
[(and e (Coverage _ _ _ _ `(,(app find-wght-cvrg (and cdn+ (Coverage _ c-ws _ c-w/cs _))) ...)))
(define chld-wghtd-avg (for/sum ((w (in-list c-ws)) (w/c (in-list c-w/cs))) (* w w/c)))
(struct-copy Coverage e (weighted-coverage (/ chld-wghtd-avg (apply + c-ws))) (children cdn+))]))

;; -| printing |--------------------------------------------------------------------------------------
(define max-description-length
(match-lambda
[(Coverage (app string-length name-length) _ _ _
(list (app max-description-length children-lengths) ...))
(apply max name-length (map add1 children-lengths))]))

(define (~a/right w x)
(~a x #:width w #:align 'right))

(define (~a/decimal n dec-dgts)
(~a/right (+ dec-dgts 3) (if (zero? n) "" (real->decimal-string n dec-dgts))))

(define (print-coverage-tree tree)
(define mdl (max-description-length tree))
(printf "| ~a |WEIGT| COVER |WGHTD CVRG|~%" (~a "NAME" #:width mdl #:align 'center))
(let inr ((depth 0) (tree tree))
(unless (null? tree)
(match tree
[(Coverage name w c w/c chlds)
(printf "| ~a | ~a | ~a | ~a |~%"
(~a (string-append (make-string depth #\space) name) #:width mdl)
(~a/right 3 w) (~a/decimal c 2) (~a/decimal w/c 5))
(for ((c chlds)) (inr (add1 depth) c))]))))

;; ---------------------------------------------------------------------------------------------------
(module+ main
;; data/functional-coverage.txt contains a verbatim copy of
;; the table in the task's description
(for-each
(compose print-coverage-tree find-wght-cvrg)
(build-hierarchies (report->indent.c/e-list (file->string "data/functional-coverage.txt")))))
```

{{out}}

```|         NAME         |WEIGT| COVER |WGHTD CVRG|
| cleaning             |   1 |       |  0.40917 |
|  house1              |  40 |       |  0.33125 |
|   bedrooms           |   1 |  0.25 |  0.25000 |
|   bathrooms          |   1 |       |  0.50000 |
|    bathroom1         |   1 |  0.50 |  0.50000 |
|    bathroom2         |   1 |       |          |
|    outside_lavatory  |   1 |  1.00 |  1.00000 |
|   attic              |   1 |  0.75 |  0.75000 |
|   kitchen            |   1 |  0.10 |  0.10000 |
|   living_rooms       |   1 |       |  0.25000 |
|    lounge            |   1 |       |          |
|    dining_room       |   1 |       |          |
|    conservatory      |   1 |       |          |
|    playroom          |   1 |  1.00 |  1.00000 |
|   basement           |   1 |       |          |
|   garage             |   1 |       |          |
|   garden             |   1 |  0.80 |  0.80000 |
|  house2              |  60 |       |  0.46111 |
|   upstairs           |   1 |       |  0.15000 |
|    bedrooms          |   1 |       |          |
|     suite_1          |   1 |       |          |
|     suite_2          |   1 |       |          |
|     bedroom_3        |   1 |       |          |
|     bedroom_4        |   1 |       |          |
|    bathroom          |   1 |       |          |
|    toilet            |   1 |       |          |
|    attics            |   1 |  0.60 |  0.60000 |
|   groundfloor        |   1 |       |  0.31667 |
|    kitchen           |   1 |       |          |
|    living_rooms      |   1 |       |          |
|     lounge           |   1 |       |          |
|     dining_room      |   1 |       |          |
|     conservatory     |   1 |       |          |
|     playroom         |   1 |       |          |
|    wet_room_&_toilet |   1 |       |          |
|    garage            |   1 |       |          |
|    garden            |   1 |  0.90 |  0.90000 |
|    hot_tub_suite     |   1 |  1.00 |  1.00000 |
|   basement           |   1 |       |  0.91667 |
|    cellars           |   1 |  1.00 |  1.00000 |
|    wine_cellar       |   1 |  1.00 |  1.00000 |
|    cinema            |   1 |  0.75 |  0.75000 |
```