Tree datastructures
The following shows a tree of data with nesting denoted by visual levels of indentation:
RosettaCode rocks code comparison wiki mocks golfing
A common datastructure for trees is to define node structures having a name and a, (possibly empty), list of child nodes. The nesting of nodes captures the indentation of the tree. Lets call this the nest form.
# E.g. if child nodes are surrounded by brackets # and separated by commas then: RosettaCode(rocks(code, ...), ...) # But only an _example_
Another datastructure for trees is to construct from the root an ordered list of the nodes level of indentation and the name of that node. The indentation for the root node is zero; node 'rocks is indented by one level from the left, and so on. Lets call this the indent form.
0 RosettaCode 1 rocks 2 code ...
- Task
- Create/use a nest datastructure format and textual representation for arbitrary trees.
- Create/use an indent datastructure format and textual representation for arbitrary trees.
- Create methods/classes/proceedures/routines etc to:
- Change from a nest tree datastructure to an indent one.
- Change from an indent tree datastructure to a nest one
- Use the above to encode the example at the start into the nest format, and show it.
- transform the initial nest format to indent format and show it.
- transform the indent format to final nest format and show it.
- Compare initial and final nest formats which should be the same.
- Note
- It's all about showing aspects of the contrasting datastructures as they hold the tree.
- The word "golfing" may be substituted by "trolling" in the tree as golfing can be friendly fun! (just not for RC examples).
- Comparing nested datastructures is secondary - saving formatted output as a string then a string compare would suffice for this task, if its easier.
Show all output on this page.
AppleScript
The 'mocking' task example seems a little unpleasant. Perhaps an alternative ? <lang applescript>use AppleScript version "2.4" use framework "Foundation" use scripting additions
on run
set strOutline to ¬ "The Rosetta stone\n" & ¬ " is a granodiorite stele\n" & ¬ " engraved\n" & ¬ " with Greek and Egyptian texts\n" & ¬ " in different scripts.\n" & ¬ " which, in the 19c, shed new light\n" & ¬ " on various homologies." set forestA to ¬ forestFromNestLevels(indentLevelsFromLines(paragraphs of strOutline)) set indentLevels to nestLevelsFromForest(forestA) set forestB to forestFromNestLevels(indentLevels) -- Logged to Messages panel of macOS Script Editor log intercalate(linefeed & linefeed, {¬ "Outline:", ¬ strOutline, ¬ "Forest from outline:", ¬ forestJSON(forestA), ¬ "Nesting levels from forest:", ¬ toJSON(indentLevels), ¬ "Forest rebuilt from nesting levels", ¬ forestJSON(forestB), ¬ "Equality test:", ¬ "(forestA = forestB) -> " & (forestA = forestB)})
end run
-- TREES ⇄ LEVEL TUPLES ----------------------------------
-- forestFromNestLevels :: [(Int, a)] -> [Tree a] on forestFromNestLevels(tuples)
-- A list of trees derived from a list of values paired -- with integers giving their levels of indentation. script go on |λ|(xs) if 0 < length of xs then set lineOne to item 1 of xs set {intIndent, v} to {fst(lineOne), snd(lineOne)} set {firstTreeLines, remainingLines} to ¬ listFromTuple(|λ|(rest of xs) of ¬ span(compose(lt(intIndent), my fst))) {Node(v, |λ|(firstTreeLines) of go)} & |λ|(remainingLines) of go else {} end if end |λ| end script |λ|(tuples) of go
end forestFromNestLevels
-- nestLevelsFromForest :: [Tree a] -> [(Int, a)]
on nestLevelsFromForest(trees)
-- A flat list of (nest level, value) tuples, -- representing a series of trees. script go on |λ|(level) script on |λ|(tree) Template:Level, root of tree & ¬ concatMap(|λ|(1 + level) of go, nest of tree) end |λ| end script end |λ| end script concatMap(|λ|(0) of go, trees)
end nestLevelsFromForest
-- INDENT LEVELS FROM OUTLINE ----------------------------
--indentLevelsFromLines :: [String] -> [(Int, String)] on indentLevelsFromLines(xs)
set tuples to map(compose(firstArrow(my |length|), ¬ span(my isSpace)), xs) script minimumIndent on |λ|(a, tpl) set n to fst(tpl) bool(a, n, n < a and 0 < n) end |λ| end script set indentUnit to foldl(minimumIndent, 100, tuples) map(firstArrow(flipDiv(indentUnit)), tuples)
end indentLevelsFromLines
-- JSON SERIALISATIONS ------------------------------------
-- forestJSON :: [Tree a] -> JSON String on forestJSON(trees)
toJSON(forestAsNestedPairs(trees))
end forestJSON
-- forestAsNestedPairs :: [Tree a] -> NestedPair [(a, [NestedPair])] on forestAsNestedPairs(xs)
--A simple nested pair representation of a tree. script go on |λ|(tree) {root of tree, map(go, nest of tree)} end |λ| end script map(go, xs)
end forestAsNestedPairs
-- toJSON :: Show a => a -> String on toJSON(a)
set blnAtom to {list, record} does not contain class of a if blnAtom then set obj to {a} else set obj to a end if set ca to current application try set {v, e} to ca's NSJSONSerialization's ¬ dataWithJSONObject:obj options:0 |error|:(reference) on error return ("(Not representatable as JSON)") end try set strJSON to ca's NSString's alloc()'s initWithData:v ¬ encoding:(ca's NSUTF8StringEncoding) if blnAtom then text 2 thru -2 of (strJSON as string) else strJSON as string end if
end toJSON
-- GENERIC ------------------------------------------------
-- Node :: a -> [Tree a] -> Tree a on Node(v, xs)
{type:"Node", root:v, nest:xs}
end Node
-- Tuple (,) :: a -> b -> (a, b)
on Tuple(a, b)
-- Constructor for a pair of values, possibly of two different types. {type:"Tuple", |1|:a, |2|:b, length:2}
end Tuple
-- bool :: a -> a -> Bool -> a
on bool(f, t, p)
if p then set v to t else set v to f end if -- Delayed evaluation, if needed. if handler is class of v then |λ|() of mReturn(v) else v end if
end bool
-- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c on compose(f, g)
script property mf : mReturn(f) property mg : mReturn(g) on |λ|(x) mf's |λ|(mg's |λ|(x)) end |λ| end script
end compose
-- concatMap :: (a -> [b]) -> [a] -> [b] on concatMap(f, xs)
set lng to length of xs set acc to {} tell mReturn(f) repeat with i from 1 to lng set acc to acc & (|λ|(item i of xs, i, xs)) end repeat end tell return acc
end concatMap
-- flipDiv:: Int -> Int -> Int
on flipDiv(a)
-- Integer division, with arguments reversed script on |λ|(b) b div a end |λ| end script
end flipDiv
-- 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)) on firstArrow(f)
script on |λ|(xy) Tuple(mReturn(f)'s |λ|(|1| of xy), |2| of xy) end |λ| end script
end firstArrow
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f) set v to startValue set lng to length of xs repeat with i from 1 to lng set v to |λ|(v, item i of xs, i, xs) end repeat return v end tell
end foldl
-- fst :: (a, b) -> a on fst(tpl)
if class of tpl is record then |1| of tpl else item 1 of tpl end if
end fst
-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬ {my text item delimiters, delim} set str to xs as text set my text item delimiters to dlm str
end intercalate
-- isSpace :: Char -> Bool on isSpace(c)
set i to id of c 32 = i or (9 ≤ i and 13 ≥ i)
end isSpace
-- length :: [a] -> Int on |length|(xs)
set c to class of xs if list is c or string is c then length of xs else (2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite) end if
end |length|
-- listFromTuple :: (a, a ...) -> [a] on listFromTuple(tpl)
items 2 thru -2 of (tpl as list)
end listFromTuple
-- lt :: Ord a => a -> a -> Bool on lt(x)
script on |λ|(y) x < y end |λ| end script
end lt
-- map :: (a -> b) -> [a] -> [b] on map(f, xs)
-- The list obtained by applying f -- to each element of xs. tell mReturn(f) set lng to length of xs set lst to {} repeat with i from 1 to lng set end of lst to |λ|(item i of xs, i, xs) end repeat return lst end tell
end map
-- minimum :: Ord a => [a] -> a on minimum(xs)
set lng to length of xs if lng < 1 then return missing value set m to item 1 of xs repeat with x in xs set v to contents of x if v < m then set m to v end repeat return m
end minimum
-- mReturn :: First-class m => (a -> b) -> m (a -> b) on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper. if script is class of f then f else script property |λ| : f end script end if
end mReturn
-- snd :: (a, b) -> b on snd(tpl)
if class of tpl is record then |2| of tpl else item 2 of tpl end if
end snd
-- span :: (a -> Bool) -> [a] -> ([a], [a]) on span(f)
-- The longest (possibly empty) prefix of xs -- that contains only elements satisfying p, -- tupled with the remainder of xs. -- span(p, xs) eq (takeWhile(p, xs), dropWhile(p, xs)) script on |λ|(xs) set lng to length of xs set i to 0 tell mReturn(f) repeat while i < lng and |λ|(item (i + 1) of xs) set i to i + 1 end repeat end tell splitAt(i, xs) end |λ| end script
end span
-- splitAt :: Int -> [a] -> ([a], [a])
on splitAt(n, xs)
if n > 0 and n < length of xs then if class of xs is text then Tuple(items 1 thru n of xs as text, ¬ items (n + 1) thru -1 of xs as text) else Tuple(items 1 thru n of xs, items (n + 1) thru -1 of xs) end if else if n < 1 then Tuple({}, xs) else Tuple(xs, {}) end if end if
end splitAt</lang>
- Output:
Outline: The Rosetta stone is a granodiorite stele engraved with Greek and Egyptian texts in different scripts. which, in the 19c, shed new light on various homologies. Forest from outline: [["The Rosetta stone",[["is a granodiorite stele",[["engraved",[["with Greek and Egyptian texts",[]]]],["in different scripts.",[]]]],["which, in the 19c, shed new light",[["on various homologies.",[]]]]]]] Nesting levels from forest: [[0,"The Rosetta stone"],[1,"is a granodiorite stele"],[2,"engraved"],[3,"with Greek and Egyptian texts"],[2,"in different scripts."],[1,"which, in the 19c, shed new light"],[2,"on various homologies."]] Forest rebuilt from nesting levels [["The Rosetta stone",[["is a granodiorite stele",[["engraved",[["with Greek and Egyptian texts",[]]]],["in different scripts.",[]]]],["which, in the 19c, shed new light",[["on various homologies.",[]]]]]]] Equality test: (forestA = forestB) -> true
Go
<lang go>package main
import (
"fmt" "strings"
)
type nNode struct {
name string children []nNode
}
type iNode struct {
level int name string
}
func printNest(n nNode, level int) {
if level == 0 { fmt.Println("\n==Nest form==\n") } fmt.Printf("%s%s\n", strings.Repeat(" ", level), n.name) for _, c := range n.children { fmt.Printf("%s", strings.Repeat(" ", level+1)) printNest(c, level+1) }
}
func toNest(iNodes []iNode, start, level int, n *nNode) {
if level == 0 { n.name = iNodes[0].name } for i := start + 1; i < len(iNodes); i++ { if iNodes[i].level == level+1 { c := nNode{iNodes[i].name, nil} toNest(iNodes, i, level+1, &c) n.children = append(n.children, c) } else if iNodes[i].level <= level { return } }
}
func printIndent(iNodes []iNode) {
fmt.Println("\n==Indent form==\n") for _, n := range iNodes { fmt.Printf("%d %s\n", n.level, n.name) }
}
func toIndent(n nNode, level int, iNodes *[]iNode) {
*iNodes = append(*iNodes, iNode{level, n.name}) for _, c := range n.children { toIndent(c, level+1, iNodes) }
}
func main() {
n1 := nNode{"RosettaCode", nil} n2 := nNode{"rocks", []nNode{{"code", nil}, {"comparison", nil}, {"wiki", nil}}} n3 := nNode{"mocks", []nNodeTemplate:"golfing", nil} n1.children = append(n1.children, n2, n3) printNest(n1, 0) var iNodes []iNode toIndent(n1, 0, &iNodes) printIndent(iNodes) var n nNode toNest(iNodes, 0, 0, &n) printNest(n, 0)
}</lang>
- Output:
==Nest form== RosettaCode rocks code comparison wiki mocks golfing ==Indent form== 0 RosettaCode 1 rocks 2 code 2 comparison 2 wiki 1 mocks 2 golfing ==Nest form== RosettaCode rocks code comparison wiki mocks golfing
Haskell
Using the rose tree constructor in the standard Data.Tree module.
Parses the initial tree from outline text, and writes out the flat
and nested structures in a JSON format:
<lang haskell>{-# LANGUAGE OverloadedStrings #-}
import qualified Data.Text.Lazy.Encoding as E import qualified Data.Text.Lazy.IO as T import qualified Data.Text.Lazy as T import Control.Arrow (first) import Data.Char (isSpace) import Data.Bool (bool) import Data.Tree import Data.Aeson import Data.Aeson.Text
-- TREES <-> LIST OF LEVELS <-> TREES ----------------------- nestLevelsFromForest :: [Tree a] -> [(Int, a)] nestLevelsFromForest xs =
let go level node = (level, rootLabel node) : (subForest node >>= go (succ level)) in xs >>= go 0
forestFromNestLevels
:: Ord t => [(t, a)] -> Forest a
forestFromNestLevels pairs =
let go [] = [] go ((n, s):xs) = let (firstTreeLines, rest) = span ((n <) . fst) xs in Node s (go firstTreeLines) : go rest in go pairs
-- INITIAL PARSE TREE OF OUTLINE -------------------------- nestLevelsFromLines xs =
let pairs = T.span isSpace <$> xs indentUnit = foldr (\x a -> let w = (T.length . fst) x in bool a w (w < a && 0 < w)) maxBound pairs in first (flip div indentUnit . T.length) <$> pairs
-- DISPLAY OF JSON SERIALISATION -------------------------- showJSON
:: ToJSON a => a -> T.Text
showJSON = E.decodeUtf8 . encode . toJSON
-- TEST --------------------------------------------------- forestA :: Forest T.Text forestA = (forestFromNestLevels . nestLevelsFromLines) (T.lines outline)
nestLevels :: [(Int, T.Text)] nestLevels = nestLevelsFromForest forestA
forestB :: [Tree T.Text] forestB = forestFromNestLevels nestLevels
main :: IO () main = do
mapM_ T.putStrLn [ "Initial parse tree from outline:\n" , showJSON forestA , "\nFlat list of nesting levels from parse tree:\n" , showJSON nestLevels , "\nTree rebuilt from nest levels:\n" , showJSON forestB ] putStrLn $ "\n\n(Reconstructed tree == parsed tree) -> " ++ show (forestA == forestB)
outline :: T.Text outline =
"RosettaCode\n\ \ rocks\n\ \ code\n\ \ comparison\n\ \ wiki\n\ \ knocks\n\ \ golfing"</lang>
- Output:
Initial parse tree from outline: [["RosettaCode",[["rocks",[["code",[]],["comparison",[]],["wiki",[]]]],["knocks",[["golfing",[]]]]]]] Flat list of nesting levels from parse tree: [[0,"RosettaCode"],[1,"rocks"],[2,"code"],[2,"comparison"],[2,"wiki"],[1,"knocks"],[2,"golfing"]] Tree rebuilt from nest levels: [["RosettaCode",[["rocks",[["code",[]],["comparison",[]],["wiki",[]]]],["knocks",[["golfing",[]]]]]]] (Reconstructed tree == parsed tree) -> True
JavaScript
Parses the initial tree from outline text, and writes out the flat and nested structures in a minimal JSON format: <lang javascript>(() => {
'use strict';
// main :: IO () const main = () => {
// (INDENT, STRING) PAIRS FROM OUTLINE ------------ const indentLevelTuplesA = indentLevelsFromLines( lines(strOutlineB) );
// LIST OF TREES FROM LIST OF (INDENT, STRING) PAIRS const forestA = forestFromIndentLevels( indentLevelTuplesA );
// (INDENT, STRING) PAIRS FROM LIST OF TREES ------ const indentLevelTuplesB = indentLevelsFromForest(forestA);
// LIST OF TREES FROM SECONDARY (INDENT, STRING) PAIRS const forestB = forestFromIndentLevels( indentLevelTuplesB );
// JSON OUTPUT OF FORESTS AND INDENT TUPLES -------
console.log('Tree structure from outline:\n') console.log(jsonFromForest(forestA));
console.log('\n\nIndent levels from tree structure:\n') console.log(jsonFromIndentLevels(indentLevelTuplesB));
console.log('\nTree structure from indent levels:\n') console.log(jsonFromForest(forestB));
console.log( '(Reconstructed tree === parsed tree) -> ' + Boolean(eq(forestA)(forestB)) ); };
// CONVERSIONS BETWEEN OUTLINES, TREES, AND (LEVEL, VALUE) PAIRS
// 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)) ); };
// forestFromIndentLevels :: [(Int, String)] -> [Tree String] const forestFromIndentLevels = 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); };
// indentLevelsFromForest :: [Tree a] -> [(Int, a)] const indentLevelsFromForest = trees => { const go = n => node => [ [n, node.root] ] .concat(node.nest.flatMap(go(1 + n))) return trees.flatMap(go(0)); };
// JSON RENDERING OF NESTED LINES AND (LEVEL, VALUE) PAIRS
// jsonFromForest :: [Tree a] -> JSON String const jsonFromForest = trees => JSON.stringify( nestedListsFromForest(trees), null, 2 );
// nestedListsFromForest :: [Tree a] -> NestedList a const nestedListsFromForest = xs => { const go = node => [node.root, node.nest.map(go)]; return xs.map(go); };
// jsonFromIndentLevels :: [(Int, String)] -> JSON String const jsonFromIndentLevels = xs => JSON.stringify( xs.map(x => Array.from(x)), null, 2 );
// GENERIC 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);
// div :: Int -> Int -> Int const div = x => y => Math.floor(x / y);
// eq (==) :: Eq a => a -> a -> Bool const eq = a => b => { const t = typeof a; return t !== typeof b ? ( false ) : 'object' !== t ? ( 'function' !== t ? ( a === b ) : a.toString() === b.toString() ) : (() => { const kvs = Object.entries(a); return kvs.length !== Object.keys(b).length ? ( false ) : kvs.every(([k, v]) => eq(v)(b[k])); })(); };
// 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));
// 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];
// isSpace :: Char -> Bool const isSpace = c => /\s/.test(c);
// Returns Infinity over objects without finite length. // This enables zip and zipWith to choose the shorter // argument when one is non-finite, like cycle, repeat etc
// 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]/);
// minimum :: Ord a => [a] -> a const minimum = xs => 0 < xs.length ? ( foldl1(a => x => x < a ? x : a)(xs) ) : undefined;
// 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;
// uncurry :: (a -> b -> c) -> ((a, b) -> c) const uncurry = f => (x, y) => f(x)(y);
// until :: (a -> Bool) -> (a -> a) -> a -> a const until = p => f => x => { let v = x; while (!p(v)) v = f(v); return v; };
// SAMPLE OUTLINES ------------------------------------
const strOutlineA = `Heilmeier catechism Objectives and benefits What are you trying to do? Articulate your objectives using absolutely no jargon. What are the problems you address ? How is it done today, and what are the limits of current practice? What is your solution ? What is new in your approach and why do you think it will be successful? Who cares? If you are successful, what difference will it make? Costs What are the risks? How much will it cost? How long will it take? Indicators What are the mid-term and final “exams” to check for success?`;
const strOutlineB = `Rosetta stone is a granodiorite stele engraved with Greek and Egyptian texts in different scripts. which shed new light on various homologies.`;
// MAIN --- return main();
})();</lang>
- Output:
Tree structure from outline: [ [ "Rosetta stone", [ [ "is a granodiorite stele", [ [ "engraved", [ [ "with Greek and Egyptian texts", [] ] ] ], [ "in different scripts.", [] ] ] ], [ "which shed new light", [ [ "on various homologies.", [] ] ] ] ] ] ] Indent levels from tree structure: [ [ 0, "Rosetta stone" ], [ 1, "is a granodiorite stele" ], [ 2, "engraved" ], [ 3, "with Greek and Egyptian texts" ], [ 2, "in different scripts." ], [ 1, "which shed new light" ], [ 2, "on various homologies." ] ] Tree structure from indent levels: [ [ "Rosetta stone", [ [ "is a granodiorite stele", [ [ "engraved", [ [ "with Greek and Egyptian texts", [] ] ] ], [ "in different scripts.", [] ] ] ], [ "which shed new light", [ [ "on various homologies.", [] ] ] ] ] ] ] (Reconstructed tree === parsed tree) -> true
Python
Procedural
Just arranges the standard lists and tuples for the datastructures allowing pprint to show the different arrangement of storage.
<lang python>from pprint import pprint as pp from collections import namedtuple
def to_indent(node, depth=0, flat=None):
if flat is None: flat = [] if node: flat.append((depth, node[0])) for child in node[1]: to_indent(child, depth + 1, flat) return flat
def to_nest(lst, depth=0, level=None):
if level is None: level = [] while lst: d, name = lst[0] if d == depth: children = [] level.append((name, children)) lst.pop(0) elif d > depth: # down to_nest(lst, d, children) elif d < depth: # up return return level[0] if level else None
if __name__ == '__main__':
print('Start Nest format:') nest = ('RosettaCode', [('rocks', [('code', []), ('comparison', []), ('wiki', [])]), ('mocks', [('golfing', [])])]) pp(nest, width=25)
print('\n... To Indent format:') as_ind = to_indent(nest) pp(as_ind, width=25)
print('\n... To Nest format:') as_nest = to_nest(as_ind) pp(as_nest, width=25)
if nest != as_nest: print("Whoops round-trip issues")</lang>
- Output:
Start Nest format: ('RosettaCode', [('rocks', [('code', []), ('comparison', []), ('wiki', [])]), ('mocks', [('golfing', [])])]) ... To Indent format: [(0, 'RosettaCode'), (1, 'rocks'), (2, 'code'), (2, 'comparison'), (2, 'wiki'), (1, 'mocks'), (2, 'golfing')] ... To Nest format: ('RosettaCode', [('rocks', [('code', []), ('comparison', []), ('wiki', [])]), ('mocks', [('golfing', [])])])
Functional
Using a Node constructor with root and nest keys for the value and sub-forest of each tree node, and serialising both trees and nesting-level lists to JSON-compatible formats.
Functional composition, as an alternative to .append() and .pop() mutations.
(Initial tree constructed as the parse of an outline text)
<lang python>Tree data structures
from itertools import chain, takewhile import json
- 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}
- forestFromNestLevels :: [(Int, a)] -> [Tree a]
def forestFromNestLevels(tuples):
A list of trees derived from a list of values paired with integers giving their levels of indentation. def go(xs): if xs: (intIndent, v) = xs[0] (firstTreeLines, rest) = span( lambda x: intIndent < x[0] )(xs[1:]) return [Node(v)(go(firstTreeLines))] + go(rest) else: return [] return go(tuples)
- nestLevelsFromForest :: [Tree a] -> [(Int, a)]
def nestLevelsFromForest(xs):
A flat list of (nest level, value) tuples, representing a series of trees. def go(level): return lambda node: [(level, node['root'])] + concatMap( go(1 + level) )(node['nest']) return concatMap(go(0))(xs)
- TEST ----------------------------------------------------
- main :: IO ()
def main():
Conversion from trees to flat lists of nest levels, and back again, with each stage shown as a JSON string. forestA = forestFromNestLevels( indentLevelsFromLines(OUTLINE.splitlines()) ) nestLevels = nestLevelsFromForest(forestA) forestB = forestFromNestLevels(nestLevels)
for x in [ 'Parse tree from outline text:\n', forestJSON(forestA),
'\nNesting level list from tree:\n', json.dumps(nestLevels, indent=2),
'\nTree rebuilt from nesting level list:\n', forestJSON(forestB), ]: print(x) print( '(Reconstructed forest == parsed forest) -> ' + str(forestA == forestB) )
- INITIAL TREE FROM PARSE OF OUTLINE TEXT -----------------
- 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 = [ (n, s[n:]) for (n, s) in ((len(list(takewhile(isSpace, x))), x) for x in xs) ] indentUnit = min(concatMap( lambda x: [x[0]] if x[0] else [] )(indentTextPairs)) return [ (x[0] // indentUnit, x[1]) for x in indentTextPairs ]
- JSON SERIALISATION --------------------------------------
- forestJSON :: [Tree a] -> JSON String
def forestJSON(trees):
A simple JSON serialisation of a list of trees, with each tree node represented as a [value, nodes] pair. return json.dumps( forestAsNestedPairs(trees), indent=2 )
- forestAsNestedPairs :: [Tree a] -> NestedPair [(a, [NestedPair])]
def forestAsNestedPairs(xs):
A simple nested pair representation of a tree. def go(node): return [node['root'], [go(x) for x in node['nest']]] return [go(x) for x in xs]
- GENERIC -------------------------------------------------
- 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)) )
- isSpace :: Char -> Bool
- isSpace :: String -> Bool
def isSpace(s):
True if s is not empty, and contains only white space. return s.isspace()
- 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): prefix = list(takewhile(p, xs)) return (prefix, xs[len(prefix):]) return lambda xs: go(xs)
- MAIN ---
if __name__ == '__main__':
OUTLINE = Rosetta stone is a granodiorite stele engraved with Greek and Egyptian texts in different scripts. which shed new light on various homologies.
main()</lang>
- Output:
Parse tree from outline text: [ [ "Rosetta stone", [ [ "is a granodiorite stele", [ [ "engraved", [ [ "with Greek and Egyptian texts", [] ] ] ], [ "in different scripts.", [] ] ] ], [ "which shed new light", [ [ "on various homologies.", [] ] ] ] ] ] ] Nesting level list from tree: [ [ 0, "Rosetta stone" ], [ 1, "is a granodiorite stele" ], [ 2, "engraved" ], [ 3, "with Greek and Egyptian texts" ], [ 2, "in different scripts." ], [ 1, "which shed new light" ], [ 2, "on various homologies." ] ] Tree rebuilt from nesting level list: [ [ "Rosetta stone", [ [ "is a granodiorite stele", [ [ "engraved", [ [ "with Greek and Egyptian texts", [] ] ] ], [ "in different scripts.", [] ] ] ], [ "which shed new light", [ [ "on various homologies.", [] ] ] ] ] ] ] (Reconstructed forest == parsed forest) -> True