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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





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                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 3 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 3 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 3 hours ago









                                    b3m2a1b3m2a1

                                    28.3k358163




                                    28.3k358163



























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