Tree from nesting levels: Difference between revisions
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{{
Given a flat list of integers greater than zero, representing object nesting
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===Iterative===
<
set maxLevel to 0
repeat with thisLevel in input
Line 80:
set output to output as text
set AppleScript's text item delimiters to astid
return output</
{{output}}
<
{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===
Same task code and output as above.
<
script recursion
property emptyList : {}
Line 119:
return recursion's recurse(input, 1)
end treeFromNestingLevels</
===Functional===
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.
<syntaxhighlight lang="applescript">----------------- 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|</syntaxhighlight>
<pre>
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]</pre>
=={{header|C++}}==
Uses C++20
<syntaxhighlight lang="cpp">#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";
}
}
</syntaxhighlight>
{{out}}
<pre>
[] 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]]]
</pre>
=={{header|C sharp|C#}}==
{{works with|C sharp|12}}
<syntaxhighlight lang="csharp">public static class TreeFromNestingLevels
{
public static void Main()
{
List<int[]> tests = [[], [1,2,4], [3,1,3,1], [1,2,3,1], [3,2,1,3], [3,3,3,1,1,3,3,3]];
Console.WriteLine($"{"Input",24} -> {"Nested",-32} -> Round-trip");
foreach (var test in tests) {
var tree = BuildTree(test);
string input = $"[{string.Join(", ", test)}]";
string roundTrip = $"[{string.Join(", ", tree.ToList())}]";
Console.WriteLine($"{input,24} -> {tree,-32} -> {roundTrip}");
}
}
private static Tree BuildTree(int[] levels)
{
Tree root = new(0);
Tree current = root;
foreach (int level in levels) {
while (current.Level > level) current = current.Parent;
current = current.Parent.Add(level);
}
return root;
}
private class Tree
{
public int Level { get; }
public Tree Parent { get; }
private readonly List<Tree> children = [];
public Tree(int level, Tree? parent = null)
{
Level = level;
Parent = parent ?? this;
}
public Tree Add(int level)
{
if (Level == level) return this;
Tree tree = new(Level + 1, this);
children.Add(tree);
return tree.Add(level);
}
public override string ToString() => children.Count == 0
? (Level == 0 ? "[]" : $"{Level}")
: $"[{string.Join(", ", children.Select(c => c.ToString()))}]";
public List<int> ToList()
{
List<int> list = [];
ToList(this, list);
return list;
}
private static void ToList(Tree tree, List<int> list)
{
if (tree.children.Count == 0) {
if (tree.Level > 0) list.Add(tree.Level);
} else {
foreach (Tree child in tree.children) {
ToList(child, list);
}
}
}
}
}</syntaxhighlight>
{{out}}
<pre>
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]</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
const TreeData1: array [0..0] of integer = (0);
const TreeData2: array [0..2] of integer = (1, 2, 4);
const TreeData3: array [0..3] of integer = (3, 1, 3, 1);
const TreeData4: array [0..3] of integer = (1, 2, 3, 1);
const TreeData5: array [0..3] of integer = (3, 2, 1, 3);
const TreeData6: array [0..7] of integer = (3, 3, 3, 1, 1, 3, 3, 3);
function GetDataString(Data: array of integer): string;
var I: integer;
begin
Result:='[';
for I:=0 to High(Data) do
begin
if I<>0 then Result:=Result+', ';
Result:=Result+IntToStr(Data[I]);
end;
Result:=Result+']';
end;
function GetNestingLevel(Data: array of integer): string;
var Level,Level2: integer;
var I,J,HLen: integer;
begin
Level:=0;
Result:='';
for I:=0 to High(Data) do
begin
Level2:=Data[I];
if Level2>Level then for J:=Level to Level2-1 do Result:=Result+'['
else if Level2<Level then
begin
for J:=Level-1 downto Level2 do Result:=Result+']';
Result:=Result+', ';
end
else if Level2=0 then
begin
Result:='[]';
break;
end
else Result:=Result+', ';
Result:=Result+IntToStr(Level2);
Level:=Level2;
if (I<High(Data)) and (Level<Data[I+1]) then Result:=Result+', ';
end;
for J:=Level downto 1 do Result:=Result+']';
end;
procedure ShowNestData(Memo: TMemo; Data: array of integer);
begin
Memo.Lines.Add(GetDataString(Data)+' Nests to: ');
Memo.Lines.Add(GetNestingLevel(Data));
Memo.Lines.Add('');
end;
procedure ShowNestingLevels(Memo: TMemo);
var S: string;
begin
ShowNestData(Memo,TreeData1);
ShowNestData(Memo,TreeData2);
ShowNestData(Memo,TreeData3);
ShowNestData(Memo,TreeData4);
ShowNestData(Memo,TreeData5);
ShowNestData(Memo,TreeData6);
end;
</syntaxhighlight>
{{out}}
<pre>
[0] 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]]]
Elapsed Time: 21.513 ms.
</pre>
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Tree_from_nesting_levels}}
'''Solution'''
[[File:Fōrmulæ - Tree from nesting levels 01.png]]
'''Test cases'''
[[File:Fōrmulæ - Tree from nesting levels 02.png]]
[[File:Fōrmulæ - Tree from nesting levels 03.png]]
Notice that in Fōrmulæ an array of arrays (of the same cardinality each) is automatically shown as a matrix.
[[File:Fōrmulæ - Tree from nesting levels 04.png]]
[[File:Fōrmulæ - Tree from nesting levels 05.png]]
[[File:Fōrmulæ - Tree from nesting levels 06.png]]
[[File:Fōrmulæ - Tree from nesting levels 07.png]]
[[File:Fōrmulæ - Tree from nesting levels 08.png]]
[[File:Fōrmulæ - Tree from nesting levels 09.png]]
[[File:Fōrmulæ - Tree from nesting levels 10.png]]
[[File:Fōrmulæ - Tree from nesting levels 11.png]]
[[File:Fōrmulæ - Tree from nesting levels 12.png]]
[[File:Fōrmulæ - Tree from nesting levels 13.png]]
'''Other test cases'''
Cases generated with random numbers:
[[File:Fōrmulæ - Tree from nesting levels 14.png]]
[[File:Fōrmulæ - Tree from nesting levels 15.png]]
=={{header|FreeBASIC}}==
<syntaxhighlight lang="vb">Sub ShowTree(List() As Integer)
Dim As Integer I, NestLevel = 0
For I = 0 To Ubound(List)
While List(I) < NestLevel
Print "]";
NestLevel -= 1
Wend
If List(I) = 0 Then
Print
Elseif I <> Lbound(List) Then Print ", ";
End If
While List(I) > NestLevel
Print "[";
NestLevel += 1
Wend
If NestLevel <> 0 Then Print NestLevel;
Next I
End Sub
Dim As Integer list(0 To ...) = {0}
ShowTree(list())
Dim As Integer list0(0 To ...) = {1, 2, 4, 0}
ShowTree(list0())
Dim As Integer list1(0 To ...) = {3, 1, 3, 1, 0}
ShowTree(list1())
Dim As Integer list2(0 To ...) = {1, 2, 3, 1, 0}
ShowTree(list2())
Dim As Integer list3(0 To ...) = {3, 2, 1, 3, 0}
ShowTree(list3())
Dim As Integer list4(0 To ...) = {3, 3, 3, 1, 1, 3, 3, 3, 0}
ShowTree(list4())
Dim As Integer list5(0 To ...) = {1, 2, 4, 2, 2, 1, 0}
ShowTree(list5())
Sleep</syntaxhighlight>
{{out}}
<pre> 'Note that [0] displays nothing.
[ 1, [ 2, [[ 4]]]]
[[[ 3]], 1, [[ 3]], 1]
[ 1, [ 2, [ 3]], 1]
[[[ 3], 2], 1, [[ 3]]]
[[[ 3, 3, 3]], 1, 1, [[ 3, 3, 3]]]
[ 1, [ 2, [[ 4]], 2, 2], 1]</pre>
=={{header|Go}}==
===Iterative===
{{trans|Python}}
<
import "fmt"
Line 164 ⟶ 1,015:
fmt.Printf("%17s => %v\n", fmt.Sprintf("%v", test), nest)
}
}</
{{out}}
Line 178 ⟶ 1,029:
===Recursive===
{{trans|Python}}
<
import "fmt"
Line 219 ⟶ 1,070:
fmt.Printf("%17s => %v\n", fmt.Sprintf("%v", test), nest)
}
}</
{{out}}
<pre>
Same as iterative version.
</pre>
=={{header|Guile}}==
<syntaxhighlight lang="scheme">;; 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)
</syntaxhighlight>
{{out}}
<pre>
() -> ()
(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)))
</pre>
Line 236 ⟶ 1,135:
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:
<syntaxhighlight lang="haskell">{-# LANGUAGE TupleSections #-}
import Data.Bifunctor (bimap)
import Data.Tree (Forest, Tree (..), drawTree, foldTree)
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
Line 261 ⟶ 1,169:
main :: IO ()
main =
mapM_
putStrLn ("From: " <> show xs)
in
>>
( "Back to:
)
----------- MAPPING TO A STRICTER DATA STRUCTURE ---------
Line 298 ⟶ 1,206:
(x, Just x) :
(succ x, Nothing) : normalised (y : xs)
| otherwise = (x, Just x) : normalised (y : xs)</
{{Out}}
<pre>From: []
Nothing
Back to: []
From: [1,2,4]
Nothing
|
Line 315 ⟶ 1,225:
`- Just 4
Back to: [1,2,4]
From: [3,1,3,1]
Nothing
|
Line 333 ⟶ 1,245:
`- Just 1
Back to: [3,1,3,1]
From: [1,2,3,1]
Nothing
|
Line 344 ⟶ 1,258:
|
`- Just 1
Back to: [1,2,3,1]
From: [3,2,1,3]
Nothing
|
Line 363 ⟶ 1,279:
`- Just 3
Back to: [3,2,1,3]
From: [3,3,3,1,1,3,3,3]
Nothing
|
Line 388 ⟶ 1,306:
|
`- Just 3
Back to: [3,3,3,1,1,3,3,3]</pre>
=={{header|J}}==
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:
<syntaxhighlight lang="j"> [[[3]], 1, [[3]], 1
1 1
[[[3]], 1, [[3]], 1]
|syntax error</syntaxhighlight>
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:
<syntaxhighlight lang="j">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
}}</syntaxhighlight>
Task example:
<syntaxhighlight lang="j"> 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││││
│││└─┴─┴─┘││ │ ││└─┴─┴─┘│││
││└───────┘│ │ │└───────┘││
│└─────────┴─┴─┴─────────┘│
└─────────────────────────┘</syntaxhighlight>
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:
<syntaxhighlight lang="j"> 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││
│└─┴─┴─┘│ │└─┴─┴─┘│
└───────┴─┴───────┘</syntaxhighlight>
Or, generalizing:
<syntaxhighlight lang="j">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
}}</syntaxhighlight>
Example use:
<syntaxhighlight lang="j"> pnest '((a b) c (d e) f) g (h i)'
┌─────────────────┬─┬─────┐
│┌─────┬─┬─────┬─┐│g│┌─┬─┐│
││┌─┬─┐│c│┌─┬─┐│f││ ││h│i││
│││a│b││ ││d│e││ ││ │└─┴─┘│
││└─┴─┘│ │└─┴─┘│ ││ │ │
│└─────┴─┴─────┴─┘│ │ │
└─────────────────┴─┴─────┘</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public final class TreeNestingLevels {
public static void main(String[] args) {
List<List<Integer>> lists = List.of(
Arrays.asList(),
Arrays.asList( 1, 2, 4 ),
Arrays.asList( 3, 1, 3, 1 ),
Arrays.asList( 1, 2, 3, 1 ),
Arrays.asList( 3, 2, 1, 3 ),
Arrays.asList( 3, 3, 3, 1, 1, 3, 3, 3 )
);
for ( List<Integer> list : lists ) {
List<Object> tree = createTree(list);
System.out.println(list + " --> " + tree);
}
}
private static List<Object> createTree(List<Integer> list) {
return makeTree(list, 0, 1);
}
private static List<Object> makeTree(List<Integer> list, int index, int depth) {
List<Object> tree = new ArrayList<Object>();
int current;
while ( index < list.size() && depth <= ( current = list.get(index) ) ) {
if ( depth == current ) {
tree.add(current);
index += 1;
} else {
tree.add(makeTree(list, index, depth + 1));
final int position = list.subList(index, list.size()).indexOf(depth);
index += ( position == -1 ) ? list.size() : position;
}
}
return tree;
}
}
</syntaxhighlight>
{{ out }}
<pre>
[] --> []
[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]]]
</pre>
=={{header|Julia}}==
<
nesting = 0
str = isempty(list) ? "[]" : ""
Line 413 ⟶ 1,514:
end
</
<pre>
[] => []
Line 422 ⟶ 1,523:
[3, 3, 3, 1, 1, 3, 3, 3] => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
</pre>
=={{header|Nim}}==
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 <code>Node</code> able to contain either an integer value or a list of Node objects, depending on the value of a discriminator. The procedure <code>newTree</code> converts a list of levels into a list of nodes with the appropriate nesting.
<syntaxhighlight lang="nim">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)</syntaxhighlight>
{{out}}
<pre> @[] → []
@[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]]]</pre>
=={{header|OxygenBasic}}==
<syntaxhighlight lang="text">
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
</syntaxhighlight>
=={{header|Perl}}==
===String Eval===
<syntaxhighlight lang="perl">#!/usr/bin/perl
use strict;
Line 447 ⟶ 1,757:
my $after = eval;
dd { after => $after };
}</
{{out}}
<pre>
Line 463 ⟶ 1,773:
{ after => [[[3, 3, 3]], 1, 1, [[3, 3, 3]]] }
</pre>
===Iterative===
{{trans|Raku}}
<syntaxhighlight lang="perl">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;
}
sub to_tree_iterative ( @xs ) {
my $nested = [];
my $stack = [$nested];
for my $x (@xs) {
new_level($stack) while $x >
push
}
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;</syntaxhighlight>
{{out}}
<pre>
=> []
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]]]
</pre>
=={{header|Phix}}==
I was thinking along the same lines but admit I had a little peek at the (recursive) python solution..
<!--<syntaxhighlight lang="phix">-->
<span style="color: #008080;">function</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">idx</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">part</span>
<span style="color: #008080;">while</span> <span style="color: #000000;">idx</span><span style="color: #0000FF;"><=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">switch</span> <span style="color: #7060A8;">compare</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">],</span><span style="color: #000000;">level</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">case</span> <span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">part</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">part</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">case</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">idx</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> <span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #000000;">idx</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #000000;">res</span><span style="color: #0000FF;">:{</span><span style="color: #000000;">idx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">},</span>
<span style="color: #000080;font-style:italic;">-- {1, 2, 4, 2, 2, 1}, -- (fine too)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">}}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ti</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">rpp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ppf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pp_Indent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%v nests to %v\n or %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">ti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rpp</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 533 ⟶ 1,880:
</pre>
=== iterative ===
<!--<syntaxhighlight lang="phix">-->
<span style="color: #008080;">function</span> <span style="color: #000000;">nest</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">input</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">input</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">input</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">output</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">subnest</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">input</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">ii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">input</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #004080;">integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ii</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #000000;">ii</span><span style="color: #0000FF;"><</span><span style="color: #000000;">level</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">subnest</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #000000;">output</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">ii</span>
<span style="color: #008080;">elsif</span> <span style="color: #008080;">not</span> <span style="color: #000000;">subnest</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">output</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">ii</span><span style="color: #0000FF;">}}</span>
<span style="color: #000000;">subnest</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span
<span style="color: #000000;">output</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">&=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">ii</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">input</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">output</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">input</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<!--</syntaxhighlight>-->
Same output (using nest instead of test)
Line 561 ⟶ 1,910:
===Python: Procedural===
====Python: Recursive====
<
so_far = []
while index < len(x):
Line 595 ⟶ 1,944:
nest = to_tree(flat)
print(f"{flat} NESTS TO: {nest}")
pnest(nest)</
{{out}}
Line 635 ⟶ 1,984:
====Python: Iterative====
<
nested = []
stack = [nested]
Line 649 ⟶ 1,998:
return nested
</syntaxhighlight>
{{out}}
Line 657 ⟶ 2,006:
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:
<pre>Node (None|Int) :: ((None|Int), [Node])</pre>
<syntaxhighlight lang="python">'''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
'''
return
forestFromLevels(
rooted(normalized(levelList))
)
)
Line 694 ⟶ 2,054:
#
def
'''
'''
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(
)
# 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)
Line 721 ⟶ 2,105:
[3, 3, 3, 1, 1, 3, 3, 3]
]:
tree = treeFromSparseLevels(xs)
(
print('From: ' + repr(xs)),
print('Through tuple nest:'),
print(repr(tree)),
print('\nTree:'),
print(showTree(tree)),
print('\nto bracket nest:'),
print(
repr(
root(foldTree(bracketNest)(tree))
)
),
print(
)
),
Line 740 ⟶ 2,135:
if xs:
x = xs[0]
h = [(x,
return h if 1 == len(xs) else (
h + [(1 + x,
1 < (xs[1] - x)
) else h
Line 773 ⟶ 2,168:
more child trees.
'''
return lambda xs:
Line 830 ⟶ 2,225:
def go(x):
return Node(
f(
)([go(v) for v in
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
Line 838 ⟶ 2,245:
def nest(t):
'''Accessor function for children of tree node.'''
return t
Line 844 ⟶ 2,251:
def root(t):
'''Accessor function for data of tree node.'''
return t
# -------------------- GENERIC OTHER ---------------------
# Nothing :: () -> Maybe a
Line 862 ⟶ 2,261:
Empty wrapper returned where a computation is not possible.
'''
return
#
# concat :: [String] -> String
def concat(xs):
'''The concatenation of all the elements
in
'''
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 []
Line 878 ⟶ 2,286:
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):
Line 910 ⟶ 2,319:
# MAIN ---
if __name__ == '__main__':
main()</
{{Out}}
<pre>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
|
└─
|
└─
|
└─
|
└─
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
|
├─
│ |
│ └─
│ |
│ └─
|
├─
│ |
│ └─
│ |
│ └─
|
└─
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
|
├─
│ |
│ └─
│ |
│ └─
|
└─
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
|
├─
│ |
│ ├─
│ │ |
│ │ └─
│ |
│ └─
|
└─
|
└─
|
└─
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
|
├─
│ |
│ └─
│ |
│ ├─
│ |
│ ├─
│ |
│ └─
|
├─
|
└─
|
└─
|
├─
|
├─
|
└─
to bracket nest:
[[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
and back to: [3, 3, 3, 1, 1, 3, 3, 3]</pre>
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> [ 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 ]</syntaxhighlight>
{{out}}
<pre>[ ] --> [ ]
[ 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 ] ] ]
</pre>
=={{header|Raku}}==
===Iterative===
{{trans|Python}}
<syntaxhighlight lang="raku"
my $e = [];
push @stack.tail, $e;
Line 1,017 ⟶ 2,525:
}
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;</
{{out}}
<pre>
Line 1,027 ⟶ 2,535:
3 3 3 1 1 3 3 3 => [[[3 3 3]] 1 1 [[3 3 3]]]
</pre>
===Recursive===
{{trans|Python}}
<syntaxhighlight lang="raku" line>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;</syntaxhighlight>
{{out}}
<pre>
=> []
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]]]
</pre>
===String Eval===
{{trans|Perl}}
<syntaxhighlight lang="raku"
sub to_tree_string_eval ( @xs --> Array ) {
my @gap = [ |@xs, 0 ] Z- [ 0, |@xs ];
Line 1,041 ⟶ 2,586:
}
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;</
{{out}}
<pre>
Line 1,057 ⟶ 2,602:
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<
import "./fmt" for Fmt
var toTree = Fn.new { |list|
Line 1,090 ⟶ 2,635:
var nest = toTree.call(test)
Fmt.print("$24n => $n", test, nest)
}</
{{out}}
Line 1,104 ⟶ 2,649:
===Recursive===
{{trans|Python}}
<
var toTree // recursive
Line 1,138 ⟶ 2,683:
var n = toTree.call(test, 0, 1)
Fmt.print("$24n => $n", test, n[1])
}</
{{out}}
<pre>
Same as iterative version.
</pre>
=={{header|XPL0}}==
A sentinel 0 is used to terminate the input arrays because XPL0 does not have built-in lists.
Note that [0] displays nothing.
<syntaxhighlight lang "XPL0">proc ShowTree(List);
int List, NestLevel, I;
[NestLevel:= 0;
for I:= 0 to -1>>1 do
[while List(I) < NestLevel do
[ChOut(0, ^]); NestLevel:= NestLevel-1];
if List(I) = 0 then [CrLf(0); return];
if I # 0 then Text(0, ", ");
while List(I) > NestLevel do
[ChOut(0, ^[); NestLevel:= NestLevel+1];
IntOut(0, NestLevel);
];
];
[ShowTree([0]);
ShowTree([1, 2, 4, 0]);
ShowTree([3, 1, 3, 1, 0]);
ShowTree([1, 2, 3, 1, 0]);
ShowTree([3, 2, 1, 3, 0]);
ShowTree([3, 3, 3, 1, 1, 3, 3, 3, 0]);
ShowTree([1, 2, 4, 2, 2, 1, 0]);
]</syntaxhighlight>
{{out}}
<pre>
[1, [2, [[4]]]]
[[[3]], 1, [[3]], 1]
[1, [2, [3]], 1]
[[[3], 2], 1, [[3]]]
[[[3, 3, 3]], 1, 1, [[3, 3, 3]]]
[1, [2, [[4]], 2, 2], 1]
</pre>
| |||