how to draw a tree for nested lists
Tree from nesting levels
You are encouraged to solve this task according to the task description, using any language you may know.
Given a flat list of integers greater than zero, representing object nesting levels, e.g. [1, 2, 4], generate a tree formed from nested lists of those nesting level integers where:
- Every int appears, in order, at its depth of nesting.
- If the next level int is greater than the previous then it appears in a sub-list of the list containing the previous item
The generated tree data structure should ideally be in a languages nested list format that can be used for further calculations rather than something just calculated for printing.
An input of [1, 2, 4] should produce the equivalent of: [1, [2, [[4]]]] where 1 is at depth1, 2 is two deep and 4 is nested 4 deep.
[1, 2, 4, 2, 2, 1] should produce [1, [2, [[4]], 2, 2], 1].
All the nesting integers are in the same order but at the correct nesting levels.
Similarly [3, 1, 3, 1] should generate [[[3]], 1, [[3]], 1]
- Task
Generate and show here the results for the following inputs:
-
-
[] -
[1, 2, 4] -
[3, 1, 3, 1] -
[1, 2, 3, 1] -
[3, 2, 1, 3] -
[3, 3, 3, 1, 1, 3, 3, 3]
-
AppleScript [edit]
Iterative [edit]
on treeFromNestingLevels ( input ) set maxLevel to 0 repeat with thisLevel in input if ( thisLevel > maxLevel ) then set maxLevel to thisLevel end repeat if ( maxLevel < 2 ) then return input set emptyList to {} repeat with testLevel from maxLevel to 2 by - 1 set output to {} set subnest to {} repeat with thisLevel in input set thisLevel to thisLevel's contents if (( thisLevel's class is integer ) and ( thisLevel < testLevel )) then if ( subnest ≠ emptyList ) then set subnest to {} set end of output to thisLevel else if ( subnest = emptyList ) then set end of output to subnest set end of subnest to thisLevel end if end repeat set input to output end repeat return output end treeFromNestingLevels -- Task code: local output , astid , input , part1 , errMsg set output to {} set astid to AppleScript's text item delimiters repeat with input in {{}, { 1 , 2 , 4 }, { 3 , 1 , 3 , 1 }, { 1 , 2 , 3 , 1 }, { 3 , 2 , 1 , 3 }, { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 }} set input to input's contents set AppleScript's text item delimiters to ", " set part1 to "{" & input & "} nests to: {" -- It's a pain having to parse nested lists to text, so throw a deliberate error and parse the error message instead. try || of treeFromNestingLevels ( input ) on error errMsg set AppleScript's text item delimiters to { "{" , "}" } set end of output to part1 & (( text from text item 2 to text item - 2 of errMsg ) & "}" ) end try end repeat set AppleScript's text item delimiters to linefeed set output to output as text set AppleScript's text item delimiters to astid return output "{} nests to: {} {1, 2, 4} nests to: {1, {2, {{4}}}} {3, 1, 3, 1} nests to: {{{3}}, 1, {{3}}, 1} {1, 2, 3, 1} nests to: {1, {2, {3}}, 1} {3, 2, 1, 3} nests to: {{{3}, 2}, 1, {{3}}} {3, 3, 3, 1, 1, 3, 3, 3} nests to: {{{3, 3, 3}}, 1, 1, {{3, 3, 3}}}" Recursive [edit]
Same task code and output as above.
on treeFromNestingLevels ( input ) script recursion property emptyList : {} on recurse ( input , currentLevel ) set output to {} set subnest to {} repeat with thisLevel in input set thisLevel to thisLevel's contents if ( thisLevel > currentLevel ) then set end of subnest to thisLevel else if ( subnest ≠ emptyList ) then set end of output to recurse ( subnest , currentLevel + 1 ) set subnest to {} end if set end of output to thisLevel end if end repeat if ( subnest ≠ emptyList ) then set end of output to recurse ( subnest , currentLevel + 1 ) return output end recurse end script return recursion's recurse ( input , 1 ) end treeFromNestingLevels Functional [edit]
Mapping from the sparse list format to a generic tree structure, and using both:
-
- a generic forestFromNestLevels function to map from a normalised input list to a generic tree, and
- a standard catamorphism over trees (foldTree) to generate both the nested list format, and the round-trip regeneration of a sparse list from the generic tree.
----------------- FOREST FROM NEST LEVELS ---------------- -- forestFromNestLevels :: [(Int, a)] -> [Tree a] on forestFromNestLevels ( pairs ) script go on |λ| ( xs ) if {} ≠ xs then set { n , v } to item 1 of xs script deeper on |λ| ( x ) n < item 1 of x end |λ| end script set { descendants , rs } to ¬ |λ| ( rest of xs ) of span ( deeper ) { Node ( v , |λ| ( descendants ))} & |λ| ( rs ) else {} end if end |λ| end script |λ| ( pairs ) of go end forestFromNestLevels -- nestedList :: Maybe Int -> Nest -> Nest on nestedList ( maybeLevel , xs ) set subTree to concat ( xs ) if maybeLevel ≠ missing value then if {} ≠ subTree then { maybeLevel , subTree } else { maybeLevel } end if else { subTree } end if end nestedList -- treeFromSparseLevelList :: [Int] -> Tree Maybe Int on treeFromSparseLevelList ( xs ) { missing value , ¬ forestFromNestLevels ( rooted ( normalized ( xs )))} end treeFromSparseLevelList -------------------------- TESTS ------------------------- on run set tests to { ¬ {}, ¬ { 1 , 2 , 4 }, ¬ { 3 , 1 , 3 , 1 }, ¬ { 1 , 2 , 3 , 1 }, ¬ { 3 , 2 , 1 , 3 }, ¬ { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 }} script translate on |λ| ( ns ) set tree to treeFromSparseLevelList ( ns ) set bracketNest to root ( foldTree ( my nestedList , tree )) set returnTrip to foldTree ( my levelList , tree ) map ( my showList , { ns , bracketNest , returnTrip }) end |λ| end script set testResults to {{ "INPUT" , "NESTED" , "ROUND-TRIP" }} & map ( translate , tests ) set { firstColWidth , secondColWidth } to map ( widest ( testResults ), { fst , snd }) script display on |λ| ( triple ) intercalate ( " -> " , ¬ { justifyRight ( firstColWidth , space , item 1 of triple )} & ¬ { justifyLeft ( secondColWidth , space , item 2 of triple )} & ¬ { item 3 of triple }) end |λ| end script linefeed & unlines ( map ( display , testResults )) end run -- widest :: ((a, a) -> a) -> [String] -> Int on widest ( xs ) script on |λ| ( f ) maximum ( map ( compose ( my | length | , mReturn ( f )), xs )) end |λ| end script end widest -------------- FROM TREE BACK TO SPARSE LIST ------------- -- levelListFromNestedList :: Maybe a -> NestedList -> [a] on levelList ( maybeLevel , xs ) if maybeLevel ≠ missing value then concat ( maybeLevel & xs ) else concat ( xs ) end if end levelList ----- NORMALIZED TO A STRICTER GENERIC DATA STRUCTURE ---- -- normalized :: [Int] -> [(Int, Maybe Int)] on normalized ( xs ) -- Explicit representation of implicit nodes. if {} ≠ xs then set x to item 1 of xs if 1 > x then normalized ( rest of xs ) else set h to {{ x , x }} if 1 = length of xs then h else if 1 < (( item 2 of xs ) - x ) then set ys to h & {{ 1 + x , missing value }} else set ys to h end if ys & normalized ( rest of xs ) end if end if else {} end if end normalized -- rooted :: [(Int, Maybe Int)] -> [(Int, Maybe Int)] on rooted ( pairs ) -- Path from the virtual root to the first explicit node. if {} ≠ pairs then set { n , _ } to item 1 of pairs if 1 ≠ n then script go on |λ| ( x ) { x , missing value } end |λ| end script map ( go , enumFromTo ( 1 , n - 1 )) & pairs else pairs end if else {} end if end rooted ------------------ GENERIC TREE FUNCTIONS ---------------- -- Node :: a -> [Tree a] -> Tree a on Node ( v , xs ) -- {type:"Node", root:v, nest:xs} { v , xs } end Node -- foldTree :: (a -> [b] -> b) -> Tree a -> b on foldTree ( f , tree ) script go property g : mReturn ( f ) on |λ| ( tree ) tell g to |λ| ( root ( tree ), map ( go , nest ( tree ))) end |λ| end script |λ| ( tree ) of go end foldTree -- nest :: Tree a -> [a] on nest ( oTree ) item 2 of oTree -- nest of oTree end nest -- root :: Tree a -> a on root ( oTree ) item 1 of oTree -- root of oTree end root ---------------------- OTHER GENERIC --------------------- -- 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 -- concat :: [[a]] -> [a] on concat ( xs ) set lng to length of xs set acc to {} repeat with i from 1 to lng set acc to acc & item i of xs end repeat acc end concat -- enumFromTo :: Int -> Int -> [Int] on enumFromTo ( m , n ) if m ≤ n then set lst to {} repeat with i from m to n set end of lst to i end repeat lst else {} end if end enumFromTo -- 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 s to xs as text set my text item delimiters to dlm s end intercalate -- justifyLeft :: Int -> Char -> String -> String on justifyLeft ( n , cFiller , strText ) if n > length of strText then text 1 thru n of ( strText & replicate ( n , cFiller )) else strText end if end justifyLeft -- justifyRight :: Int -> Char -> String -> String on justifyRight ( n , cFiller , strText ) if n > length of strText then text - n thru - 1 of (( replicate ( n , cFiller ) as text ) & strText ) else strText end if end justifyRight -- 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 | -- 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 -- 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 -- maximum :: Ord a => [a] -> a on maximum ( xs ) script on |λ| ( a , b ) if a is missing value or b > a then b else a end if end |λ| end script foldl ( result , missing value , xs ) end maximum -- Egyptian multiplication - progressively doubling a list, appending -- stages of doubling to an accumulator where needed for binary -- assembly of a target length -- replicate :: Int -> String -> String on replicate ( n , s ) -- Egyptian multiplication - progressively doubling a list, -- appending stages of doubling to an accumulator where needed -- for binary assembly of a target length script p on |λ| ({ n }) n ≤ 1 end |λ| end script script f on |λ| ({ n , dbl , out }) if ( n mod 2 ) > 0 then set d to out & dbl else set d to out end if { n div 2 , dbl & dbl , d } end |λ| end script set xs to | until | ( p , f , { n , s , "" }) item 2 of xs & item 3 of xs end replicate -- 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 -- showList :: [a] -> String on showList ( xs ) "[" & intercalate ( ", " , map ( my show , xs )) & "]" end showList on show ( v ) if list is class of v then showList ( v ) else v as text end if end show -- 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 lng > i and |λ| ( item ( 1 + i ) of xs ) set i to 1 + i 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 { items 1 thru n of xs as text , ¬ items ( n + 1 ) thru - 1 of xs as text } else { items 1 thru n of xs , items ( n + 1 ) thru - 1 of xs } end if else if n < 1 then {{}, xs } else { xs , {}} end if end if end splitAt -- unlines :: [String] -> String on unlines ( xs ) -- A single string formed by the intercalation -- of a list of strings with the newline character. set { dlm , my text item delimiters } to ¬ { my text item delimiters , linefeed } set s to xs as text set my text item delimiters to dlm s end unlines -- until :: (a -> Bool) -> (a -> a) -> a -> a on | until | ( p , f , x ) set v to x set mp to mReturn ( p ) set mf to mReturn ( f ) repeat until mp's |λ| ( v ) set v to mf's |λ| ( v ) end repeat v end | until | INPUT -> NESTED -> ROUND-TRIP [] -> [] -> [] [1, 2, 4] -> [1, [2, [[4]]]] -> [1, 2, 4] [3, 1, 3, 1] -> [[[3]], 1, [[3]], 1] -> [3, 1, 3, 1] [1, 2, 3, 1] -> [1, [2, [3]], 1] -> [1, 2, 3, 1] [3, 2, 1, 3] -> [[[3], 2], 1, [[3]]] -> [3, 2, 1, 3] [3, 3, 3, 1, 1, 3, 3, 3] -> [[[3, 3, 3]], 1, 1, [[3, 3, 3]]] -> [3, 3, 3, 1, 1, 3, 3, 3]
C++ [edit]
Uses C++20
#include <any> #include <iostream> #include <iterator> #include <vector> using namespace std ; // Make a tree that is a vector of either values or other trees vector < any > MakeTree ( input_iterator auto first , input_iterator auto last , int depth = 1 ) { vector < any > tree ; while ( first < last && depth <= * first ) { if ( * first == depth ) { // add a single value tree . push_back ( * first ); ++ first ; } else // (depth < *b) { // add a subtree tree . push_back ( MakeTree ( first , last , depth + 1 )); first = find ( first + 1 , last , depth ); } } return tree ; } // Print an input vector or tree void PrintTree ( input_iterator auto first , input_iterator auto last ) { cout << "[" ; for ( auto it = first ; it != last ; ++ it ) { if ( it != first ) cout << ", " ; if constexpr ( is_integral_v < remove_reference_t < decltype ( * first ) >> ) { // for printing the input vector cout << * it ; } else { // for printing the tree if ( it -> type () == typeid ( unsigned int )) { // a single value cout << any_cast < unsigned int > ( * it ); } else { // a subtree const auto & subTree = any_cast < vector < any >> ( * it ); PrintTree ( subTree . begin (), subTree . end ()); } } } cout << "]" ; } int main ( void ) { auto execises = vector < vector < unsigned int >> { {}, { 1 , 2 , 4 }, { 3 , 1 , 3 , 1 }, { 1 , 2 , 3 , 1 }, { 3 , 2 , 1 , 3 }, { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 } }; for ( const auto & e : execises ) { auto tree = MakeTree ( e . begin (), e . end ()); PrintTree ( e . begin (), e . end ()); cout << " Nests to: \n " ; PrintTree ( tree . begin (), tree . end ()); cout << " \n\n " ; } } [] Nests to: [] [1, 2, 4] Nests to: [1, [2, [[4]]]] [3, 1, 3, 1] Nests to: [[[3]], 1, [[3]], 1] [1, 2, 3, 1] Nests to: [1, [2, [3]], 1] [3, 2, 1, 3] Nests to: [[[3], 2], 1, [[3]]] [3, 3, 3, 1, 1, 3, 3, 3] Nests to: [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
Fōrmulæ [edit]
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
Go [edit]
Iterative [edit]
package main import "fmt" type any = interface {} func toTree ( list [] int ) any { s := [] any {[] any {}} for _ , n := range list { for n != len ( s ) { if n > len ( s ) { inner := [] any {} s [ len ( s ) - 1 ] = append ( s [ len ( s ) - 1 ].([] any ), inner ) s = append ( s , inner ) } else { s = s [ 0 : len ( s ) - 1 ] } } s [ len ( s ) - 1 ] = append ( s [ len ( s ) - 1 ].([] any ), n ) for i := len ( s ) - 2 ; i >= 0 ; i -- { le := len ( s [ i ].([] any )) s [ i ].([] any )[ le - 1 ] = s [ i + 1 ] } } return s [ 0 ] } func main () { tests := [][] int { {}, { 1 , 2 , 4 }, { 3 , 1 , 3 , 1 }, { 1 , 2 , 3 , 1 }, { 3 , 2 , 1 , 3 }, { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 }, } for _ , test := range tests { nest := toTree ( test ) fmt . Printf ( "%17s => %v\n" , fmt . Sprintf ( "%v" , test ), nest ) } } [] => [] [1 2 4] => [1 [2 [[4]]]] [3 1 3 1] => [[[3]] 1 [[3]] 1] [1 2 3 1] => [1 [2 [3]] 1] [3 2 1 3] => [[[3] 2] 1 [[3]]] [3 3 3 1 1 3 3 3] => [[[3 3 3]] 1 1 [[3 3 3]]]
Recursive [edit]
package main import "fmt" type any = interface {} func toTree ( list [] int , index , depth int ) ( int , [] any ) { var soFar [] any for index < len ( list ) { t := list [ index ] if t == depth { soFar = append ( soFar , t ) } else if t > depth { var deeper [] any index , deeper = toTree ( list , index , depth + 1 ) soFar = append ( soFar , deeper ) } else { index = index - 1 break } index = index + 1 } if depth > 1 { return index , soFar } return - 1 , soFar } func main () { tests := [][] int { {}, { 1 , 2 , 4 }, { 3 , 1 , 3 , 1 }, { 1 , 2 , 3 , 1 }, { 3 , 2 , 1 , 3 }, { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 }, } for _ , test := range tests { _ , nest := toTree ( test , 0 , 1 ) fmt . Printf ( "%17s => %v\n" , fmt . Sprintf ( "%v" , test ), nest ) } } Same as iterative version.
Guile [edit]
;; helper function that finds the rest that are less than or equal ( define ( rest-less-eq x ls ) ( cond (( null? ls ) #f ) (( <= ( car ls ) x ) ls ) ( else ( rest-less-eq x ( cdr ls ))))) ;; nest the input as a tree ( define ( make-tree input depth ) ( cond (( null? input ) ' ()) (( eq? input #f ) ' ()) (( = depth ( car input )) ( cons ( car input )( make-tree ( cdr input ) depth ))) (( < depth ( car input )) ( cons ( make-tree input ( + depth 1 )) ( make-tree ( rest-less-eq depth input ) depth ))) ( #t ' ()) )) ( define examples ' (() ( 1 2 4 ) ( 3 1 3 1 ) ( 1 2 3 1 ) ( 3 2 1 3 ) ( 3 3 3 1 1 3 3 3 ))) ( define ( run-examples x ) ( if ( null? x ) ' () ( begin ( display ( car x ))( display " -> " ) ( display ( make-tree ( car x ) 1 ))( display "\n" ) ( run-examples ( cdr x ))))) ( run-examples examples ) () -> () (1 2 4) -> (1 (2 ((4)))) (3 1 3 1) -> (((3)) 1 ((3)) 1) (1 2 3 1) -> (1 (2 (3)) 1) (3 2 1 3) -> (((3) 2) 1 ((3))) (3 3 3 1 1 3 3 3) -> (((3 3 3)) 1 1 ((3 3 3)))
Haskell [edit]
The output notation shown here would be rejected by Haskell because of the inconsistency of the types in each 'list' – sometime integer, sometimes list of integer, sometimes list of list of integer etc.
For the task description's format that can be used for further calculations we can turn to Haskell's Data.Tree types, which give us a Forest (a consistently-typed list of Trees), where a single Tree combines some node value with a Forest of Trees.
The node value will have to be a sum type like `Maybe Int`, where implicit Tree nodes (that have no explicit Int value) have a `Nothing` value.
For display purposes, we can either show the list of Tree records directly, or use the drawForest and drawTree functions defined in the standard Data.Tree module.
We can reverse the translation, from tree back to sparse list, without loss of information, by using a standard fold. See sparseLevelsFromTree below:
{-# LANGUAGE TupleSections #-} import Data.Bifunctor ( bimap ) import Data.Tree ( Forest , Tree ( .. ), drawTree , foldTree ) ------------- TREE FROM NEST LEVELS (AND BACK) ----------- treeFromSparseLevels :: [ Int ] -> Tree ( Maybe Int ) treeFromSparseLevels = Node Nothing . forestFromNestLevels . rooted . normalised sparseLevelsFromTree :: Tree ( Maybe Int ) -> [ Int ] sparseLevelsFromTree = foldTree go where go Nothing xs = concat xs go ( Just x ) xs = x : concat xs forestFromNestLevels :: [( Int , a )] -> Forest a forestFromNestLevels = go where go [] = [] go (( n , v ) : xs ) = uncurry ( : ) $ bimap ( Node v . go ) go ( span (( n < ) . fst ) xs ) --------------------- TEST AND DISPLAY ------------------- main :: IO () main = mapM_ ( \ xs -> putStrLn ( "From: " <> show xs ) >> let tree = treeFromSparseLevels xs in putStrLn (( drawTree . fmap show ) tree ) >> putStrLn ( "Back to: " <> show ( sparseLevelsFromTree tree ) <> " \n\n " ) ) [ [] , [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ] ] ----------- MAPPING TO A STRICTER DATA STRUCTURE --------- -- Path from the virtual root to the first explicit node. rooted :: [( Int , Maybe Int )] -> [( Int , Maybe Int )] rooted [] = [] rooted xs = go $ filter (( 1 <= ) . fst ) xs where go xs @ (( 1 , mb ) : _ ) = xs go xs @ (( n , mb ) : _ ) = fmap (, Nothing ) [ 1 .. pred n ] <> xs -- Representation of implicit nodes. normalised [] = [] normalised [ x ] = [( x , Just x )] normalised ( x : y : xs ) | 1 < ( y - x ) = ( x , Just x ) : ( succ x , Nothing ) : normalised ( y : xs ) | otherwise = ( x , Just x ) : normalised ( y : xs ) From: [] Nothing Back to: [] From: [1,2,4] Nothing | `- Just 1 | `- Just 2 | `- Nothing | `- Just 4 Back to: [1,2,4] From: [3,1,3,1] Nothing | +- Nothing | | | `- Nothing | | | `- Just 3 | +- Just 1 | | | `- Nothing | | | `- Just 3 | `- Just 1 Back to: [3,1,3,1] From: [1,2,3,1] Nothing | +- Just 1 | | | `- Just 2 | | | `- Just 3 | `- Just 1 Back to: [1,2,3,1] From: [3,2,1,3] Nothing | +- Nothing | | | +- Nothing | | | | | `- Just 3 | | | `- Just 2 | `- Just 1 | `- Nothing | `- Just 3 Back to: [3,2,1,3] From: [3,3,3,1,1,3,3,3] Nothing | +- Nothing | | | `- Nothing | | | +- Just 3 | | | +- Just 3 | | | `- Just 3 | +- Just 1 | `- Just 1 | `- Nothing | +- Just 3 | +- Just 3 | `- Just 3 Back to: [3,3,3,1,1,3,3,3]
J [edit]
Without any use cases for these trees, it's difficult to know if any implementation is correct.
As a side note here, the notation used to describe these trees has some interesting consequences in the context of J:
[[[ 3 ]], 1 , [[ 3 ]], 1 1 1 [[[ 3 ]], 1 , [[ 3 ]], 1 ] | syntax error But, on a related note, there are type issues to consider -- in J's type system, a box (which is what we would use here to represent a tree node) cannot exist in a tuple with an integer. A box can, however, contain an integer. This makes a literal interpretation of the task somewhat... difficult. We might, hypothetically, say that we are working with boxes containing integers and that it's these boxes which must achieve a specific nesting level. (If we fail to make this distinction then we wind up with a constraint which forces some tree nodes to be structured different from what appears to be the task specification. Whether or not this is an important issue is difficult to determine without use cases. So, for now, let's assume that this is an important distinction.)
Anyways, here's an interpretation which might be close enough to the task description:
NB. first we nest each integer to the required depth, independently NB. then we recursively merge deep boxes NB. for consistency, if there are no integers, we box that empty list dtree =: {{ <^: ( 0 = L . ) merge <^:] each y }} merge =: {{ if. ( 0 =#$ y ) +. 2 > L . y do. y return.end. NB. done if no deep boxes left shallow =. 2 > L ." 0 y NB. locate shallow boxes group =. shallow } ( +/\ shallow ) ,:-#\ y NB. find groups of adjacent deep boxes merge each group , each //. y NB. combine them and recursively merge their contents }} Task example:
dtree '' ┌┐ ││ └┘ dtree 1 2 4 ┌─────────────┐ │┌─┬─────────┐│ ││ 1 │┌─┬─────┐││ ││ ││ 2 │┌───┐│││ ││ ││ ││┌─┐││││ ││ ││ │││ 4 │││││ ││ ││ ││└─┘││││ ││ ││ │└───┘│││ ││ │└─┴─────┘││ │└─┴─────────┘│ └─────────────┘ dtree 3 1 3 1 ┌─────────────────┐ │┌─────┬─┬─────┬─┐│ ││┌───┐│ 1 │┌───┐│ 1 ││ │││┌─┐││ ││┌─┐││ ││ ││││ 3 │││ │││ 3 │││ ││ │││└─┘││ ││└─┘││ ││ ││└───┘│ │└───┘│ ││ │└─────┴─┴─────┴─┘│ └─────────────────┘ dtree 1 2 3 1 ┌─────────────┐ │┌─┬───────┬─┐│ ││ 1 │┌─┬───┐│ 1 ││ ││ ││ 2 │┌─┐││ ││ ││ ││ ││ 3 │││ ││ ││ ││ │└─┘││ ││ ││ │└─┴───┘│ ││ │└─┴───────┴─┘│ └─────────────┘ dtree 3 2 1 3 ┌─────────────────┐ │┌───────┬─┬─────┐│ ││┌───┬─┐│ 1 │┌───┐││ │││┌─┐│ 2 ││ ││┌─┐│││ ││││ 3 ││ ││ │││ 3 ││││ │││└─┘│ ││ ││└─┘│││ ││└───┴─┘│ │└───┘││ │└───────┴─┴─────┘│ └─────────────────┘ dtree 3 3 3 1 1 3 3 3 ┌─────────────────────────┐ │┌─────────┬─┬─┬─────────┐│ ││┌───────┐│ 1 │ 1 │┌───────┐││ │││┌─┬─┬─┐││ │ ││┌─┬─┬─┐│││ ││││ 3 │ 3 │ 3 │││ │ │││ 3 │ 3 │ 3 ││││ │││└─┴─┴─┘││ │ ││└─┴─┴─┘│││ ││└───────┘│ │ │└───────┘││ │└─────────┴─┴─┴─────────┘│ └─────────────────────────┘ Note that merge does not concern itself with the contents of boxes, only their nesting depth. This means that we could replace the implementation of dtree with some similar mechanism if we wished to use this approach with something else. For example:
t =: ;: '(a b c) d (e f g)' p =: ;: '()' d =: +/\-/ p =/ t k =: =/ p =/ t merge d <@]^:[&.>& ( k &# ) t ┌───────┬─┬───────┐ │┌─┬─┬─┐│ d │┌─┬─┬─┐│ ││ a │ b │ c ││ ││ e │ f │ g ││ │└─┴─┴─┘│ │└─┴─┴─┘│ └───────┴─┴───────┘ Or, generalizing:
pnest =: {{ t =. ;: y NB. tokens p =. ( ;: '()' ) =/ t NB. paren token matches d =: +/\-/ p NB. paren token depths k =: =/ p NB. keep non-paren tokens merge d <@]^:[&.>& ( k &# ) t NB. exercise task }} Example use:
pnest '((a b) c (d e) f) g (h i)' ┌─────────────────┬─┬─────┐ │┌─────┬─┬─────┬─┐│ g │┌─┬─┐│ ││┌─┬─┐│ c │┌─┬─┐│ f ││ ││ h │ i ││ │││ a │ b ││ ││ d │ e ││ ││ │└─┴─┘│ ││└─┴─┘│ │└─┴─┘│ ││ │ │ │└─────┴─┴─────┴─┘│ │ │ └─────────────────┴─┴─────┘ Julia [edit]
function makenested ( list ) nesting = 0 str = isempty ( list ) ? "[]" : "" for n in list if n > nesting str *= "[" ^ ( n - nesting ) nesting = n elseif n < nesting str *= "]" ^ ( nesting - n ) * ", " nesting = n end str *= " $n , " end str *= "]" ^ nesting return eval ( Meta . parse ( str )) end for test in [[], [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ]] result = " $test => $ ( makenested ( test )) " println ( replace ( result , "Any" => "" )) end [] => [] [1, 2, 4] => [1, [2, [[4]]]] [3, 1, 3, 1] => [[[3]], 1, [[3]], 1] [1, 2, 3, 1] => [1, [2, [3]], 1] [3, 2, 1, 3] => [[[3], 2], 1, [[3]]] [3, 3, 3, 1, 1, 3, 3, 3] => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
Nim [edit]
In a strongly and statically typed language as Nim, there is no way to mix integer values and lists. So, we have defined a variant type Node able to contain either an integer value or a list of Node objects, depending on the value of a discriminator. The procedure newTree converts a list of levels into a list of nodes with the appropriate nesting.
import sequtils , strutils type Kind = enum kValue , kList Node = ref object case kind : Kind of kValue : value : int of kList : list : seq [ Node ] proc newTree ( s : varargs [ int ] ): Node = ## Build a tree from a list of level values. var level = 1 result = Node ( kind : kList ) var stack = @[ result ] for n in s : if n <= 0 : raise newException ( ValueError , "expected a positive integer, got " & $ n ) let node = Node ( kind : kValue , value : n ) if n < level : # Unstack lists. stack . setLen ( n ) level = n else : while n > level : # Create intermediate lists. let newList = Node ( kind : kList ) stack [ ^ 1 ] . list . add newList stack . add newList inc level # Add value. stack [ ^ 1 ] . list . add node proc `$` ( node : Node ): string = ## Display a tree using a nested lists representation. if node . kind == kValue : $ node . value else : '[' & node . list . mapIt ( $ it ). join ( ", " ) & ']' for list in [ newSeq [ int ] (), # Empty list (== @[]). @[ 1 , 2 , 4 ] , @[ 3 , 1 , 3 , 1 ] , @[ 1 , 2 , 3 , 1 ] , @[ 3 , 2 , 1 , 3 ] , @[ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ]] : echo ( $ list ). align ( 25 ), " → " , newTree ( list ) @[] → [] @[1, 2, 4] → [1, [2, [[4]]]] @[3, 1, 3, 1] → [[[3]], 1, [[3]], 1] @[1, 2, 3, 1] → [1, [2, [3]], 1] @[3, 2, 1, 3] → [[[3], 2], 1, [[3]]] @[3, 3, 3, 1, 1, 3, 3, 3] → [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
OxygenBasic [edit]
uses console declare DemoTree(string src) DemoTree "[]" DemoTree "[1, 2, 4]" DemoTree "[3, 1, 3, 1]" DemoTree "[1, 2, 3, 1]" DemoTree "[3, 2, 1, 3]" DemoTree "[3, 3, 3, 1, 1, 3, 3, 3]" pause end /* RESULTS: ======== [] [] [1, 2, 4] [ 1,[ 2,[[ 4]]]] [3, 1, 3, 1] [[[ 3]], 1,[[ 3]], 1] [1, 2, 3, 1] [ 1,[ 2,[ 3]], 1] [3, 2, 1, 3] [[[ 3], 2], 1,[[ 3]]] [3, 3, 3, 1, 1, 3, 3, 3] [[[ 3, 3, 3]], 1, 1,[[ 3, 3, 3]]] */ sub DemoTree(string src) ======================== string tree=nuls 1000 'TREE OUTPUT int i=1 'src char iterator int j=1 'tree char iterator byte bs at strptr src 'src bytes byte bt at strptr tree 'tree bytes int bl=len src 'end of src int lvl 'current tree level int olv 'prior tree level int v 'number value string vs 'number in string form do exit if i>bl select bs[i] case 91 '[' i++ case 93 ']' if i=bl gosub writex endif i++ case 44 ',' i++ gosub writex case 0 to 32 'white space i++ 'bt[j]=" " : j++ case 48 to 57 '0..9' gosub ReadDigits case else i++ end select loop tree=left(tree,j-1) output src cr output tree cr cr exit sub 'SUBROUTINES OF DEMOTREE: ========================= writex: ======= olv=lvl if i>=bl if v=0 and olv=0 tree="[]" : j=3 ret endif endif if v<olv gosub WriteRbr endif if olv gosub WriteComma endif if v>olv gosub WriteLbr endif gosub WriteDigits '3]]' if i>=bl v=0 gosub WriteRbr endif ret ReadDigits: =========== v=0 while i<=bl select bs[i] case 48 to 57 '1..9 v*=10 : v+=bs[i]-48 'digit case else exit while end select i++ wend ret ' WriteDigits: ============ vs=" "+str(v) : mid(tree,j,vs) : j+=len vs ret WriteLbr: ========= while v>lvl bt[j]=91 : j++ : lvl++ wend ret WriteRbr: ========= while v<lvl bt[j]=93 : j++ : lvl-- wend ret WriteComma: =========== bt[j]=44 : j++ ',' ret end sub Perl [edit]
String Eval [edit]
#!/usr/bin/perl use strict ; use warnings ; use Data::Dump qw(dd pp) ; my @tests = ( [] ,[ 1 , 2 , 4 ] ,[ 3 , 1 , 3 , 1 ] ,[ 1 , 2 , 3 , 1 ] ,[ 3 , 2 , 1 , 3 ] ,[ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ] ); for my $before ( @tests ) { dd { before => $before }; local $_ = ( pp $before ) =~ s/\d+/ '['x($&-1) . $& . ']'x($&-1) /ge r ; 1 while s/\](,\s*)\[/$1/ ; my $after = eval ; dd { after => $after }; } { before => [] } { after => [] } { before => [1, 2, 4] } { after => [1, [2, [[4]]]] } { before => [3, 1, 3, 1] } { after => [[[3]], 1, [[3]], 1] } { before => [1, 2, 3, 1] } { after => [1, [2, [3]], 1] } { before => [3, 2, 1, 3] } { after => [[[3], 2], 1, [[3]]] } { before => [3, 3, 3, 1, 1, 3, 3, 3] } { after => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]] } Iterative [edit]
use 5.020_000 ; # Also turns on `strict` use warnings ; use experimental qw<signatures> ; use Data::Dump qw<pp> ; sub new_level ( $stack ) { my $e = [] ; push @ { $stack -> [ - 1 ] }, $e ; push @ { $stack }, $e ; } sub to_tree_iterative ( @xs ) { my $nested = [] ; my $stack = [ $nested ]; for my $x ( @xs ) { new_level ( $stack ) while $x > @ { $stack }; pop @ { $stack } while $x < @ { $stack }; push @ { $stack -> [ - 1 ]}, $x ; } return $nested ; } my @tests = ( [] ,[ 1 , 2 , 4 ],[ 3 , 1 , 3 , 1 ],[ 1 , 2 , 3 , 1 ],[ 3 , 2 , 1 , 3 ],[ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ]); say sprintf ( '%15s => ' , join ( ' ' , @ { $_ })), pp ( to_tree_iterative ( @ { $_ })) for @tests ; => [] 1 2 4 => [1, [2, [[4]]]] 3 1 3 1 => [[[3]], 1, [[3]], 1] 1 2 3 1 => [1, [2, [3]], 1] 3 2 1 3 => [[[3], 2], 1, [[3]]] 3 3 3 1 1 3 3 3 => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
Phix [edit]
I was thinking along the same lines but admit I had a little peek at the (recursive) python solution..
function test ( sequence s , integer level = 1 , idx = 1 ) sequence res = {}, part while idx <= length ( s ) do switch compare ( s [ idx ], level ) do case + 1 : { idx , part } = test ( s , level + 1 , idx ) res = append ( res , part ) case 0 : res &= s [ idx ] case - 1 : idx -= 1 exit end switch idx += 1 end while return iff ( level = 1 ? res :{ idx , res }) end function constant tests = {{}, { 1 , 2 , 4 }, -- {1, 2, 4, 2, 2, 1}, -- (fine too) { 3 , 1 , 3 , 1 }, { 1 , 2 , 3 , 1 }, { 3 , 2 , 1 , 3 }, { 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 }} for i = 1 to length ( tests ) do sequence ti = tests [ i ], res = test ( ti ), rpp = ppf ( res ,{ pp_Nest , 3 , pp_Indent , 4 }) printf ( 1 , "%v nests to %v\n or %s\n" ,{ ti , res , rpp }) end for
{} nests to {} or {} {1,2,4} nests to {1,{2,{{4}}}} or {1, {2, {{4}}}} {3,1,3,1} nests to {{{3}},1,{{3}},1} or {{{3}}, 1, {{3}}, 1} {1,2,3,1} nests to {1,{2,{3}},1} or {1, {2, {3}}, 1} {3,2,1,3} nests to {{{3},2},1,{{3}}} or {{{3}, 2}, 1, {{3}}} {3,3,3,1,1,3,3,3} nests to {{{3,3,3}},1,1,{{3,3,3}}} or {{{3, 3, 3}}, 1, 1, {{3, 3, 3}}} iterative [edit]
function nest ( sequence input ) if length ( input ) then for level = max ( input ) to 2 by - 1 do sequence output = {} bool subnest = false for i = 1 to length ( input ) do object ii = input [ i ] if integer ( ii ) and ii < level then subnest = false output &= ii elsif not subnest then output &= {{ ii }} subnest = true else output [$] &= { ii } end if end for input = output end for end if return input end function
Same output (using nest instead of test)
Python [edit]
Python: Procedural [edit]
Python: Recursive [edit]
def to_tree ( x , index = 0 , depth = 1 ): so_far = [] while index < len ( x ): this = x [ index ] if this == depth : so_far . append ( this ) elif this > depth : index , deeper = to_tree ( x , index , depth + 1 ) so_far . append ( deeper ) else : # this < depth: index -= 1 break index += 1 return ( index , so_far ) if depth > 1 else so_far if __name__ == "__main__" : from pprint import pformat def pnest ( nest : list , width : int = 9 ) -> str : text = pformat ( nest , width = width ) . replace ( ' \n ' , ' \n ' ) print ( f " OR { text } \n " ) exercises = [ [], [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ], ] for flat in exercises : nest = to_tree ( flat ) print ( f " { flat } NESTS TO: { nest } " ) pnest ( nest ) [] NESTS TO: [] OR [] [1, 2, 4] NESTS TO: [1, [2, [[4]]]] OR [1, [2, [[4]]]] [3, 1, 3, 1] NESTS TO: [[[3]], 1, [[3]], 1] OR [[[3]], 1, [[3]], 1] [1, 2, 3, 1] NESTS TO: [1, [2, [3]], 1] OR [1, [2, [3]], 1] [3, 2, 1, 3] NESTS TO: [[[3], 2], 1, [[3]]] OR [[[3], 2], 1, [[3]]] [3, 3, 3, 1, 1, 3, 3, 3] NESTS TO: [[[3, 3, 3]], 1, 1, [[3, 3, 3]]] OR [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
Python: Iterative [edit]
def to_tree ( x : list ) -> list : nested = [] stack = [ nested ] for this in x : while this != len ( stack ): if this > len ( stack ): innermost = [] # new level stack [ - 1 ] . append ( innermost ) # nest it stack . append ( innermost ) # push it else : # this < stack: stack . pop ( - 1 ) stack [ - 1 ] . append ( this ) return nested Using the same main block it produces the same output as the recursive case above.
Python: Functional [edit]
A translation of the sparse level-lists to a stricter generic data structure gives us access to standard tree-walking functions, allowing for simpler top-level functions, and higher levels of code reuse.
Here, for example, we apply:
- a generic tree-drawing (drawTree) function, and
- a generic catamorphism over trees (foldTree) for:
- the generation of a bracket-nest from an underlying tree, and
- a return-trip regeneration of the sparse level list from the same tree.
Each node in the underlying tree structure is a tuple of a value (None or an integer), and list of child nodes:
Node (None|Int) :: ((None|Int), [Node])
'''Tree from nesting levels''' from itertools import chain , repeat from operator import add # treeFromSparseLevels :: [Int] -> Tree Maybe Int def treeFromSparseLevels ( levelList ): '''A Forest (list of Trees) of (Maybe Int) values, in which implicit nodes have the value None. ''' return Node ( None )( forestFromLevels ( rooted ( normalized ( levelList )) ) ) # forestFromLevels :: [(Int, a)] -> [Tree a] def forestFromLevels ( nvs ): '''A list of generic trees derived from a list of values paired with integers representing nesting depths. ''' def go ( xs ): if xs : level , v = xs [ 0 ] children , rest = span ( lambda x : level < x [ 0 ] )( xs [ 1 :]) return [ Node ( v )( go ( children ))] + go ( rest ) else : return [] return go ( nvs ) # bracketNest :: Maybe Int -> Nest -> Nest def bracketNest ( maybeLevel ): '''An arbitrary nest of bracketed lists and sublists. ''' def go ( xs ): subNest = concat ( xs ) return [ subNest ] if None is maybeLevel else ( [ maybeLevel , subNest ] if subNest else ( [ maybeLevel ] ) ) return go # showTree :: Tree Maybe Int -> String def showTree ( tree ): '''A string representation of a Maybe Int tree. ''' return drawTree ( fmapTree ( repr )( tree ) ) # sparseLevelsFromTree :: Tree (Maybe Int) -> [Int] def sparseLevelsFromTree ( tree ): '''Sparse representation of the tree a list of nest level integers. ''' def go ( x ): return lambda xs : concat ( xs ) if ( None is x ) else [ x ] + concat ( xs ) return foldTree ( go )( tree ) # ------------------------- TEST ------------------------- # main :: IO () def main (): '''Test the building and display of normalized forests from level integers. ''' for xs in [ [], [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ] ]: tree = treeFromSparseLevels ( xs ) ( print ( 'From: ' + repr ( xs )), print ( 'Through tuple nest:' ), print ( repr ( tree )), print ( ' \n Tree:' ), print ( showTree ( tree )), print ( ' \n to bracket nest:' ), print ( repr ( root ( foldTree ( bracketNest )( tree )) ) ), print ( 'and back to: ' + ( repr ( sparseLevelsFromTree ( tree )) ) ), print () ) # ------ TRANSLATION TO A CONSISTENT DATA STRUCTURE ------ # normalized :: [Int] -> [(Int, Maybe Int)] def normalized ( xs ): '''Explicit representation of implicit nodes. ''' if xs : x = xs [ 0 ] h = [( x , x )] return h if 1 == len ( xs ) else ( h + [( 1 + x , None )] if ( 1 < ( xs [ 1 ] - x ) ) else h ) + normalized ( xs [ 1 :]) else : return [] # rooted :: [(Int, Maybe Int)] -> [(Int, Maybe Int)] def rooted ( pairs ): '''Path from the virtual root to the first explicit node. ''' def go ( xs ): n = xs [ 0 ][ 0 ] return xs if 1 == n else ( [( x , Nothing ()) for x in range ( 1 , n )] + xs ) return go ([ x for x in pairs if 1 <= x [ 0 ] ]) if pairs else [] # ---------------- GENERIC TREE 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 : ( v , xs ) # draw :: Tree a -> [String] def draw ( node ): '''List of the lines of an ASCII diagram of a tree. ''' def shift_ ( h , other , xs ): return list ( map ( add , chain ( [ h ], ( repeat ( other , len ( xs ) - 1 ) ) ), xs )) def drawSubTrees ( xs ): return ( ( [ '|' ] + shift_ ( '├─ ' , '│ ' , draw ( xs [ 0 ]) ) + drawSubTrees ( xs [ 1 :]) ) if 1 < len ( xs ) else [ '|' ] + shift_ ( '└─ ' , ' ' , draw ( xs [ 0 ]) ) ) if xs else [] return ( root ( node )) . splitlines () + ( drawSubTrees ( nest ( node )) ) # drawForest :: [Tree String] -> String def drawForest ( trees ): '''A simple unicode character representation of a list of trees. ''' return ' \n ' . join ( map ( drawTree , trees )) # drawTree :: Tree a -> String def drawTree ( tree ): '''ASCII diagram of a tree.''' return ' \n ' . join ( draw ( tree )) # fmapTree :: (a -> b) -> Tree a -> Tree b def fmapTree ( f ): '''A new tree holding the results of an application of f to each root in the existing tree. ''' def go ( x ): return Node ( f ( root ( x )) )([ go ( v ) for v in nest ( x )]) return go # foldTree :: (a -> [b] -> b) -> Tree a -> b def foldTree ( f ): '''The catamorphism on trees. A summary value defined by a depth-first fold. ''' def go ( node ): return f ( root ( node ))([ go ( x ) for x in nest ( node ) ]) return go # nest :: Tree a -> [Tree a] def nest ( t ): '''Accessor function for children of tree node.''' return t [ 1 ] # root :: Tree a -> a def root ( t ): '''Accessor function for data of tree node.''' return t [ 0 ] # -------------------- GENERIC OTHER --------------------- # Nothing :: () -> Maybe a def Nothing (): '''Constructor for an empty Maybe (option type) value. Empty wrapper returned where a computation is not possible. ''' return None # concat :: [[a]] -> [a] # concat :: [String] -> String def concat ( xs ): '''The concatenation of all the elements in a list or iterable. ''' def f ( ys ): zs = list ( chain ( * ys )) return '' . join ( zs ) if isinstance ( ys [ 0 ], str ) else zs return ( f ( xs ) if isinstance ( xs , list ) else ( chain . from_iterable ( xs ) ) ) if xs else [] # 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 match ( ab ): b = ab [ 1 ] return not b or not p ( b [ 0 ]) def f ( ab ): a , b = ab return a + [ b [ 0 ]], b [ 1 :] def go ( xs ): return until ( match )( f )(([], xs )) return go # 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 ): def g ( x ): v = x while not p ( v ): v = f ( v ) return v return g return go # MAIN --- if __name__ == '__main__' : main () From: [] Through tuple nest: (None, []) Tree: None to bracket nest: [] and back to: [] From: [1, 2, 4] Through tuple nest: (None, [(1, [(2, [(None, [(4, [])])])])]) Tree: None | └─ 1 | └─ 2 | └─ None | └─ 4 to bracket nest: [1, [2, [[4]]]] and back to: [1, 2, 4] From: [3, 1, 3, 1] Through tuple nest: (None, [(None, [(None, [(3, [])])]), (1, [(None, [(3, [])])]), (1, [])]) Tree: None | ├─ None │ | │ └─ None │ | │ └─ 3 | ├─ 1 │ | │ └─ None │ | │ └─ 3 | └─ 1 to bracket nest: [[[3]], 1, [[3]], 1] and back to: [3, 1, 3, 1] From: [1, 2, 3, 1] Through tuple nest: (None, [(1, [(2, [(3, [])])]), (1, [])]) Tree: None | ├─ 1 │ | │ └─ 2 │ | │ └─ 3 | └─ 1 to bracket nest: [1, [2, [3]], 1] and back to: [1, 2, 3, 1] From: [3, 2, 1, 3] Through tuple nest: (None, [(None, [(None, [(3, [])]), (2, [])]), (1, [(None, [(3, [])])])]) Tree: None | ├─ None │ | │ ├─ None │ │ | │ │ └─ 3 │ | │ └─ 2 | └─ 1 | └─ None | └─ 3 to bracket nest: [[[3], 2], 1, [[3]]] and back to: [3, 2, 1, 3] From: [3, 3, 3, 1, 1, 3, 3, 3] Through tuple nest: (None, [(None, [(None, [(3, []), (3, []), (3, [])])]), (1, []), (1, [(None, [(3, []), (3, []), (3, [])])])]) Tree: None | ├─ None │ | │ └─ None │ | │ ├─ 3 │ | │ ├─ 3 │ | │ └─ 3 | ├─ 1 | └─ 1 | └─ None | ├─ 3 | ├─ 3 | └─ 3 to bracket nest: [[[3, 3, 3]], 1, 1, [[3, 3, 3]]] and back to: [3, 3, 3, 1, 1, 3, 3, 3]
Quackery [edit]
[ stack ] is prev ( --> s ) [ temp take swap join temp put ] is add$ ( x --> ) [ dup [] = if done 0 prev put $ "' " temp put witheach [ dup prev take - over prev put dup 0 > iff [ times [ $ "[ " add$ ] ] else [ abs times [ $ "] " add$ ] ] number$ space join add$ ] prev take times [ $ "] " add$ ] temp take quackery ] is nesttree ( [ --> [ ) ' [ [ ] [ 1 2 4 ] [ 3 1 3 1 ] [ 1 2 3 1 ] [ 3 2 1 3 ] [ 3 3 3 1 1 3 3 3 ] ] witheach [ dup echo say " --> " nesttree echo cr cr ] [ ] --> [ ] [ 1 2 4 ] --> [ 1 [ 2 [ [ 4 ] ] ] ] [ 3 1 3 1 ] --> [ [ [ 3 ] ] 1 [ [ 3 ] ] 1 ] [ 1 2 3 1 ] --> [ 1 [ 2 [ 3 ] ] 1 ] [ 3 2 1 3 ] --> [ [ [ 3 ] 2 ] 1 [ [ 3 ] ] ] [ 3 3 3 1 1 3 3 3 ] --> [ [ [ 3 3 3 ] ] 1 1 [ [ 3 3 3 ] ] ]
Raku [edit]
Iterative [edit]
sub new_level ( @stack --> Nil ) { my $e = []; push @stack.tail, $e; push @stack, $e; } sub to_tree_iterative ( @xs --> List ) { my $nested = []; my @stack = $nested; for @xs -> Int $x { new_level(@stack) while $x > @stack; pop @stack while $x < @stack; push @stack.tail, $x; } return $nested; } my @tests = (), (1, 2, 4), (3, 1, 3, 1), (1, 2, 3, 1), (3, 2, 1, 3), (3, 3, 3, 1, 1, 3, 3, 3); say .Str.fmt( '%15s => ' ), .&to_tree_iterative for @tests; => [] 1 2 4 => [1 [2 [[4]]]] 3 1 3 1 => [[[3]] 1 [[3]] 1] 1 2 3 1 => [1 [2 [3]] 1] 3 2 1 3 => [[[3] 2] 1 [[3]]] 3 3 3 1 1 3 3 3 => [[[3 3 3]] 1 1 [[3 3 3]]]
Recursive [edit]
sub to_tree_recursive ( @list, $index is copy, $depth ) { my @so_far = gather while $index <= @list.end { my $t = @list[$index]; given $t <=> $depth { when Order::Same { take $t; } when Order::More { ( $index, my $n1 ) = to_tree_recursive( @list, $index, $depth + 1 ); take $n1; } when Order::Less { $index--; last; } } $index++; } my $i = ($depth > 1) ?? $index !! -1; return $i, @so_far; } my @tests = (), (1, 2, 4), (3, 1, 3, 1), (1, 2, 3, 1), (3, 2, 1, 3), (3, 3, 3, 1, 1, 3, 3, 3); say .Str.fmt( '%15s => ' ), to_tree_recursive( $_, 0, 1 ).[1] for @tests; => [] 1 2 4 => [1 [2 [[4]]]] 3 1 3 1 => [[[3]] 1 [[3]] 1] 1 2 3 1 => [1 [2 [3]] 1] 3 2 1 3 => [[[3] 2] 1 [[3]]] 3 3 3 1 1 3 3 3 => [[[3 3 3]] 1 1 [[3 3 3]]]
String Eval [edit]
use MONKEY-SEE-NO-EVAL; sub to_tree_string_eval ( @xs --> Array ) { my @gap = [ |@xs, 0 ] Z- [ 0, |@xs ]; my @open = @gap.map( '[' x * ); my @close = @gap.map( ']' x -* ); my @wrapped = [Z~] @open, @xs, @close.skip; return EVAL @wrapped.join(',').subst(:g, ']]', '],]') || '[]'; } my @tests = (), (1, 2, 4), (3, 1, 3, 1), (1, 2, 3, 1), (3, 2, 1, 3), (3, 3, 3, 1, 1, 3, 3, 3); say .Str.fmt( '%15s => ' ), .&to_tree_string_eval for @tests; => [] 1 2 4 => [1 [2 [[4]]]] 3 1 3 1 => [[[3]] 1 [[3]] 1] 1 2 3 1 => [1 [2 [3]] 1] 3 2 1 3 => [[[3] 2] 1 [[3]]] 3 3 3 1 1 3 3 3 => [[[3 3 3]] 1 1 [[3 3 3]]]
Wren [edit]
Iterative [edit]
import "/seq" for Stack import "/fmt" for Fmt var toTree = Fn . new { | list | var nested = [] var s = Stack . new () s . push ( nested ) for ( n in list ) { while ( n != s . count ) { if ( n > s . count ) { var inner = [] s . peek (). add ( inner ) s . push ( inner ) } else { s . pop () } } s . peek (). add ( n ) } return nested } var tests = [ [], [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ] ] for ( test in tests ) { var nest = toTree . call ( test ) Fmt . print ( "$24n => $n" , test , nest ) } [] => [] [1, 2, 4] => [1, [2, [[4]]]] [3, 1, 3, 1] => [[[3]], 1, [[3]], 1] [1, 2, 3, 1] => [1, [2, [3]], 1] [3, 2, 1, 3] => [[[3], 2], 1, [[3]]] [3, 3, 3, 1, 1, 3, 3, 3] => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
Recursive [edit]
import "/fmt" for Fmt var toTree // recursive toTree = Fn . new { | list , index , depth | var soFar = [] while ( index < list . count ) { var t = list [ index ] if ( t == depth ) { soFar . add ( t ) } else if ( t > depth ) { var n = toTree . call ( list , index , depth + 1 ) index = n [ 0 ] soFar . add ( n [ 1 ]) } else { index = index - 1 break } index = index + 1 } if ( depth > 1 ) return [ index , soFar ] return [ - 1 , soFar ] } var tests = [ [], [ 1 , 2 , 4 ], [ 3 , 1 , 3 , 1 ], [ 1 , 2 , 3 , 1 ], [ 3 , 2 , 1 , 3 ], [ 3 , 3 , 3 , 1 , 1 , 3 , 3 , 3 ] ] for ( test in tests ) { var n = toTree . call ( test , 0 , 1 ) Fmt . print ( "$24n => $n" , test , n [ 1 ]) } Same as iterative version.
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Source: https://rosettacode.org/wiki/Tree_from_nesting_levels
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