How to invert MapIndexed on a ragged structure? How to construct a tree from rules? The Next CEO of Stack OverflowFrom a list to a list of rulesHow to partition a list according to a nested table structure?Visualize a tree structure using TreeGraphExplore a nested listDrop selection of columns from a ragged arrayHow to check if two nested lists have the same structure?Rule-based branching construction of listsHow to convert a tree in a list?Replacement Rule for “flattening” list whilst adding attributesRagged Transpose

Skipping indices in a product

How to count occurrences of text in a file?

How to avoid supervisors with prejudiced views?

WOW air has ceased operation, can I get my tickets refunded?

Why does the UK parliament need a vote on the political declaration?

Interfacing a button to MCU (and PC) with 50m long cable

Help understanding this unsettling image of Titan, Epimetheus, and Saturn's rings?

If a black hole is created from light, can this black hole then move at speed of light?

Is it my responsibility to learn a new technology in my own time my employer wants to implement?

Is there a difference between "Fahrstuhl" and "Aufzug"

Unreliable Magic - Is it worth it?

Non-deterministic sum of floats

Would this house-rule that treats advantage as a +1 to the roll instead (and disadvantage as -1) and allows them to stack be balanced?

Is there a way to save my career from absolute disaster?

Why do we use the plural of movies in this phrase "We went to the movies last night."?

Can you replace a racial trait cantrip when leveling up?

Limits on contract work without pre-agreed price/contract (UK)

What does convergence in distribution "in the Gromov–Hausdorff" sense mean?

How did the Bene Gesserit know how to make a Kwisatz Haderach?

Anatomically Correct Strange Women In Ponds Distributing Swords

How to transpose the 1st and -1th levels of arbitrarily nested array?

Is "for causing autism in X" grammatical?

Does it take more energy to get to Venus or to Mars?

Why don't programming languages automatically manage the synchronous/asynchronous problem?



How to invert MapIndexed on a ragged structure? How to construct a tree from rules?



The Next CEO of Stack OverflowFrom a list to a list of rulesHow to partition a list according to a nested table structure?Visualize a tree structure using TreeGraphExplore a nested listDrop selection of columns from a ragged arrayHow to check if two nested lists have the same structure?Rule-based branching construction of listsHow to convert a tree in a list?Replacement Rule for “flattening” list whilst adding attributesRagged Transpose










4












$begingroup$


I have an arbitrary ragged nested list-of-lists (a tree) like



A = a, b, c, d, e, f, g, h, i, j, k, l, m, n;


Its structure is given by the rules



B = Flatten[MapIndexed[#2 -> #1 &, A, -1]]



1, 1 -> a, 1, 2 -> b, 2, 1 -> c, 2, 2 -> d, 3, 1, 1, 1 -> e, 3, 1, 1, 2 -> f, 3, 1, 1, 3 -> g, 3, 1, 1, 4 -> h, 3, 1, 1, 5 -> i, 3, 1, 2, 1 -> j, 3, 1, 2, 2 -> k, 3, 1, 2, 3 -> l, 3, 2 -> m, 4 -> n




How can I invert this operation? How can I construct A solely from the information given in B?










share|improve this question









$endgroup$
















    4












    $begingroup$


    I have an arbitrary ragged nested list-of-lists (a tree) like



    A = a, b, c, d, e, f, g, h, i, j, k, l, m, n;


    Its structure is given by the rules



    B = Flatten[MapIndexed[#2 -> #1 &, A, -1]]



    1, 1 -> a, 1, 2 -> b, 2, 1 -> c, 2, 2 -> d, 3, 1, 1, 1 -> e, 3, 1, 1, 2 -> f, 3, 1, 1, 3 -> g, 3, 1, 1, 4 -> h, 3, 1, 1, 5 -> i, 3, 1, 2, 1 -> j, 3, 1, 2, 2 -> k, 3, 1, 2, 3 -> l, 3, 2 -> m, 4 -> n




    How can I invert this operation? How can I construct A solely from the information given in B?










    share|improve this question









    $endgroup$














      4












      4








      4





      $begingroup$


      I have an arbitrary ragged nested list-of-lists (a tree) like



      A = a, b, c, d, e, f, g, h, i, j, k, l, m, n;


      Its structure is given by the rules



      B = Flatten[MapIndexed[#2 -> #1 &, A, -1]]



      1, 1 -> a, 1, 2 -> b, 2, 1 -> c, 2, 2 -> d, 3, 1, 1, 1 -> e, 3, 1, 1, 2 -> f, 3, 1, 1, 3 -> g, 3, 1, 1, 4 -> h, 3, 1, 1, 5 -> i, 3, 1, 2, 1 -> j, 3, 1, 2, 2 -> k, 3, 1, 2, 3 -> l, 3, 2 -> m, 4 -> n




      How can I invert this operation? How can I construct A solely from the information given in B?










      share|improve this question









      $endgroup$




      I have an arbitrary ragged nested list-of-lists (a tree) like



      A = a, b, c, d, e, f, g, h, i, j, k, l, m, n;


      Its structure is given by the rules



      B = Flatten[MapIndexed[#2 -> #1 &, A, -1]]



      1, 1 -> a, 1, 2 -> b, 2, 1 -> c, 2, 2 -> d, 3, 1, 1, 1 -> e, 3, 1, 1, 2 -> f, 3, 1, 1, 3 -> g, 3, 1, 1, 4 -> h, 3, 1, 1, 5 -> i, 3, 1, 2, 1 -> j, 3, 1, 2, 2 -> k, 3, 1, 2, 3 -> l, 3, 2 -> m, 4 -> n




      How can I invert this operation? How can I construct A solely from the information given in B?







      list-manipulation data-structures trees






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      RomanRoman

      3,9661022




      3,9661022




















          3 Answers
          3






          active

          oldest

          votes


















          2












          $begingroup$

          Here's a procedural way:



          Block[
          Nothing,
          Module[
          m = Max[Length /@ Keys[B]], arr,
          arr = ConstantArray[Nothing, Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]];
          Map[Function[arr[[Sequence @@ #[[1]]]] = #[[2]]], B];
          arr
          ]
          ]

          a, b, c, d, e, f, g, h, i, j, k, l, m, n





          share|improve this answer









          $endgroup$




















            1












            $begingroup$

            Here's an inefficient but reasonably simple way:



            groupMe[rules_] :=
            If[Head[rules[[1]]] === Rule,
            Values@GroupBy[
            rules,
            (#[[1, 1]] &) ->
            (If[Length[#[[1]]] === 1, #[[2]], #[[1, 2 ;;]] -> #[[2]]] &),
            groupMe
            ],
            rules[[1]]
            ]

            groupMe[B]

            a, b, c, d, e, f, g, h, i, j, k, l, m, n





            share|improve this answer









            $endgroup$




















              1












              $begingroup$

              Here's a convoluted way using pattern replacements:



              DeleteCases[
              With[m = Max[Length /@ Keys[B]],
              Array[
              List,
              Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]
              ] /.
              Map[
              Fold[
              Insert[
              #, ___,
              _,
              Append[ConstantArray[1, #2], -1]] &,
              #[[1]],
              Range[m - Length[#[[1]]]]
              ] -> #[[2]] &,
              B
              ]
              ],
              __Integer,
              Infinity
              ]

              a, b, c, d, e, f, g, h, i, j, k, l, m, n





              share|improve this answer









              $endgroup$













                Your Answer





                StackExchange.ifUsing("editor", function ()
                return StackExchange.using("mathjaxEditing", function ()
                StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
                StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
                );
                );
                , "mathjax-editing");

                StackExchange.ready(function()
                var channelOptions =
                tags: "".split(" "),
                id: "387"
                ;
                initTagRenderer("".split(" "), "".split(" "), channelOptions);

                StackExchange.using("externalEditor", function()
                // Have to fire editor after snippets, if snippets enabled
                if (StackExchange.settings.snippets.snippetsEnabled)
                StackExchange.using("snippets", function()
                createEditor();
                );

                else
                createEditor();

                );

                function createEditor()
                StackExchange.prepareEditor(
                heartbeatType: 'answer',
                autoActivateHeartbeat: false,
                convertImagesToLinks: false,
                noModals: true,
                showLowRepImageUploadWarning: true,
                reputationToPostImages: null,
                bindNavPrevention: true,
                postfix: "",
                imageUploader:
                brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
                contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
                allowUrls: true
                ,
                onDemand: true,
                discardSelector: ".discard-answer"
                ,immediatelyShowMarkdownHelp:true
                );



                );













                draft saved

                draft discarded


















                StackExchange.ready(
                function ()
                StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f194217%2fhow-to-invert-mapindexed-on-a-ragged-structure-how-to-construct-a-tree-from-rul%23new-answer', 'question_page');

                );

                Post as a guest















                Required, but never shown

























                3 Answers
                3






                active

                oldest

                votes








                3 Answers
                3






                active

                oldest

                votes









                active

                oldest

                votes






                active

                oldest

                votes









                2












                $begingroup$

                Here's a procedural way:



                Block[
                Nothing,
                Module[
                m = Max[Length /@ Keys[B]], arr,
                arr = ConstantArray[Nothing, Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]];
                Map[Function[arr[[Sequence @@ #[[1]]]] = #[[2]]], B];
                arr
                ]
                ]

                a, b, c, d, e, f, g, h, i, j, k, l, m, n





                share|improve this answer









                $endgroup$

















                  2












                  $begingroup$

                  Here's a procedural way:



                  Block[
                  Nothing,
                  Module[
                  m = Max[Length /@ Keys[B]], arr,
                  arr = ConstantArray[Nothing, Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]];
                  Map[Function[arr[[Sequence @@ #[[1]]]] = #[[2]]], B];
                  arr
                  ]
                  ]

                  a, b, c, d, e, f, g, h, i, j, k, l, m, n





                  share|improve this answer









                  $endgroup$















                    2












                    2








                    2





                    $begingroup$

                    Here's a procedural way:



                    Block[
                    Nothing,
                    Module[
                    m = Max[Length /@ Keys[B]], arr,
                    arr = ConstantArray[Nothing, Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]];
                    Map[Function[arr[[Sequence @@ #[[1]]]] = #[[2]]], B];
                    arr
                    ]
                    ]

                    a, b, c, d, e, f, g, h, i, j, k, l, m, n





                    share|improve this answer









                    $endgroup$



                    Here's a procedural way:



                    Block[
                    Nothing,
                    Module[
                    m = Max[Length /@ Keys[B]], arr,
                    arr = ConstantArray[Nothing, Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]];
                    Map[Function[arr[[Sequence @@ #[[1]]]] = #[[2]]], B];
                    arr
                    ]
                    ]

                    a, b, c, d, e, f, g, h, i, j, k, l, m, n






                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 2 hours ago









                    b3m2a1b3m2a1

                    28.3k358163




                    28.3k358163





















                        1












                        $begingroup$

                        Here's an inefficient but reasonably simple way:



                        groupMe[rules_] :=
                        If[Head[rules[[1]]] === Rule,
                        Values@GroupBy[
                        rules,
                        (#[[1, 1]] &) ->
                        (If[Length[#[[1]]] === 1, #[[2]], #[[1, 2 ;;]] -> #[[2]]] &),
                        groupMe
                        ],
                        rules[[1]]
                        ]

                        groupMe[B]

                        a, b, c, d, e, f, g, h, i, j, k, l, m, n





                        share|improve this answer









                        $endgroup$

















                          1












                          $begingroup$

                          Here's an inefficient but reasonably simple way:



                          groupMe[rules_] :=
                          If[Head[rules[[1]]] === Rule,
                          Values@GroupBy[
                          rules,
                          (#[[1, 1]] &) ->
                          (If[Length[#[[1]]] === 1, #[[2]], #[[1, 2 ;;]] -> #[[2]]] &),
                          groupMe
                          ],
                          rules[[1]]
                          ]

                          groupMe[B]

                          a, b, c, d, e, f, g, h, i, j, k, l, m, n





                          share|improve this answer









                          $endgroup$















                            1












                            1








                            1





                            $begingroup$

                            Here's an inefficient but reasonably simple way:



                            groupMe[rules_] :=
                            If[Head[rules[[1]]] === Rule,
                            Values@GroupBy[
                            rules,
                            (#[[1, 1]] &) ->
                            (If[Length[#[[1]]] === 1, #[[2]], #[[1, 2 ;;]] -> #[[2]]] &),
                            groupMe
                            ],
                            rules[[1]]
                            ]

                            groupMe[B]

                            a, b, c, d, e, f, g, h, i, j, k, l, m, n





                            share|improve this answer









                            $endgroup$



                            Here's an inefficient but reasonably simple way:



                            groupMe[rules_] :=
                            If[Head[rules[[1]]] === Rule,
                            Values@GroupBy[
                            rules,
                            (#[[1, 1]] &) ->
                            (If[Length[#[[1]]] === 1, #[[2]], #[[1, 2 ;;]] -> #[[2]]] &),
                            groupMe
                            ],
                            rules[[1]]
                            ]

                            groupMe[B]

                            a, b, c, d, e, f, g, h, i, j, k, l, m, n






                            share|improve this answer












                            share|improve this answer



                            share|improve this answer










                            answered 2 hours ago









                            b3m2a1b3m2a1

                            28.3k358163




                            28.3k358163





















                                1












                                $begingroup$

                                Here's a convoluted way using pattern replacements:



                                DeleteCases[
                                With[m = Max[Length /@ Keys[B]],
                                Array[
                                List,
                                Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]
                                ] /.
                                Map[
                                Fold[
                                Insert[
                                #, ___,
                                _,
                                Append[ConstantArray[1, #2], -1]] &,
                                #[[1]],
                                Range[m - Length[#[[1]]]]
                                ] -> #[[2]] &,
                                B
                                ]
                                ],
                                __Integer,
                                Infinity
                                ]

                                a, b, c, d, e, f, g, h, i, j, k, l, m, n





                                share|improve this answer









                                $endgroup$

















                                  1












                                  $begingroup$

                                  Here's a convoluted way using pattern replacements:



                                  DeleteCases[
                                  With[m = Max[Length /@ Keys[B]],
                                  Array[
                                  List,
                                  Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]
                                  ] /.
                                  Map[
                                  Fold[
                                  Insert[
                                  #, ___,
                                  _,
                                  Append[ConstantArray[1, #2], -1]] &,
                                  #[[1]],
                                  Range[m - Length[#[[1]]]]
                                  ] -> #[[2]] &,
                                  B
                                  ]
                                  ],
                                  __Integer,
                                  Infinity
                                  ]

                                  a, b, c, d, e, f, g, h, i, j, k, l, m, n





                                  share|improve this answer









                                  $endgroup$















                                    1












                                    1








                                    1





                                    $begingroup$

                                    Here's a convoluted way using pattern replacements:



                                    DeleteCases[
                                    With[m = Max[Length /@ Keys[B]],
                                    Array[
                                    List,
                                    Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]
                                    ] /.
                                    Map[
                                    Fold[
                                    Insert[
                                    #, ___,
                                    _,
                                    Append[ConstantArray[1, #2], -1]] &,
                                    #[[1]],
                                    Range[m - Length[#[[1]]]]
                                    ] -> #[[2]] &,
                                    B
                                    ]
                                    ],
                                    __Integer,
                                    Infinity
                                    ]

                                    a, b, c, d, e, f, g, h, i, j, k, l, m, n





                                    share|improve this answer









                                    $endgroup$



                                    Here's a convoluted way using pattern replacements:



                                    DeleteCases[
                                    With[m = Max[Length /@ Keys[B]],
                                    Array[
                                    List,
                                    Max /@ Transpose[PadRight[#, m] & /@ Keys[B]]
                                    ] /.
                                    Map[
                                    Fold[
                                    Insert[
                                    #, ___,
                                    _,
                                    Append[ConstantArray[1, #2], -1]] &,
                                    #[[1]],
                                    Range[m - Length[#[[1]]]]
                                    ] -> #[[2]] &,
                                    B
                                    ]
                                    ],
                                    __Integer,
                                    Infinity
                                    ]

                                    a, b, c, d, e, f, g, h, i, j, k, l, m, n






                                    share|improve this answer












                                    share|improve this answer



                                    share|improve this answer










                                    answered 2 hours ago









                                    b3m2a1b3m2a1

                                    28.3k358163




                                    28.3k358163



























                                        draft saved

                                        draft discarded
















































                                        Thanks for contributing an answer to Mathematica Stack Exchange!


                                        • Please be sure to answer the question. Provide details and share your research!

                                        But avoid


                                        • Asking for help, clarification, or responding to other answers.

                                        • Making statements based on opinion; back them up with references or personal experience.

                                        Use MathJax to format equations. MathJax reference.


                                        To learn more, see our tips on writing great answers.




                                        draft saved


                                        draft discarded














                                        StackExchange.ready(
                                        function ()
                                        StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f194217%2fhow-to-invert-mapindexed-on-a-ragged-structure-how-to-construct-a-tree-from-rul%23new-answer', 'question_page');

                                        );

                                        Post as a guest















                                        Required, but never shown





















































                                        Required, but never shown














                                        Required, but never shown












                                        Required, but never shown







                                        Required, but never shown

































                                        Required, but never shown














                                        Required, but never shown












                                        Required, but never shown







                                        Required, but never shown







                                        Popular posts from this blog

                                        Invision Community Contents History See also References External links Navigation menuProprietaryinvisioncommunity.comIPS Community ForumsIPS Community Forumsthis blog entry"License Changes, IP.Board 3.4, and the Future""Interview -- Matt Mecham of Ibforums""CEO Invision Power Board, Matt Mecham Is a Liar, Thief!"IPB License Explanation 1.3, 1.3.1, 2.0, and 2.1ArchivedSecurity Fixes, Updates And Enhancements For IPB 1.3.1Archived"New Demo Accounts - Invision Power Services"the original"New Default Skin"the original"Invision Power Board 3.0.0 and Applications Released"the original"Archived copy"the original"Perpetual licenses being done away with""Release Notes - Invision Power Services""Introducing: IPS Community Suite 4!"Invision Community Release Notes

                                        Canceling a color specificationRandomly assigning color to Graphics3D objects?Default color for Filling in Mathematica 9Coloring specific elements of sets with a prime modified order in an array plotHow to pick a color differing significantly from the colors already in a given color list?Detection of the text colorColor numbers based on their valueCan color schemes for use with ColorData include opacity specification?My dynamic color schemes

                                        Ласкавець круглолистий Зміст Опис | Поширення | Галерея | Примітки | Посилання | Навігаційне меню58171138361-22960890446Bupleurum rotundifoliumEuro+Med PlantbasePlants of the World Online — Kew ScienceGermplasm Resources Information Network (GRIN)Ласкавецькн. VI : Літери Ком — Левиправивши або дописавши її