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TriesWithFrequencies.m
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TriesWithFrequencies.m
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(*
Tries with frequencies Mathematica package
Copyright (C) 2013 - 2018 Anton Antonov
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Written by Anton Antonov,
ʇǝu˙oǝʇsod@ǝqnɔuouoʇuɐ,
Windermere, Florida, USA.
*)
(*
Mathematica is (C) Copyright 1988-2018 Wolfram Research, Inc.
Protected by copyright law and international treaties.
Unauthorized reproduction or distribution subject to severe civil
and criminal penalties.
Mathematica is a registered trademark of Wolfram Research, Inc.
*)
(* :Title: TriesWithFrequencies *)
(* :Context: TriesWithFrequencies` *)
(* :Author: Anton Antonov *)
(* :Date: 2018-04-16 *)
(* :Package Version: 1.0 *)
(* :Mathematica Version: 11.3 *)
(* :Copyright: (c) 2018 Anton Antonov *)
(* :Keywords: *)
(* :Discussion:
Duplicates the functionalities of TriesWithFrequencies.m:
https://github.com/antononcube/MathematicaForPrediction/blob/master/TriesWithFrequenciesV9.m
using Associations.
# Design
An Association Trie with Frequencies (ATF) has the form:
<| key1 -> <| $TrieValue->_?NumberQ, ___ |> |>
Here is a concrete example:
<|a1 -> <|$TrieValue -> 3, b1 -> <|$TrieValue -> 2, c1 -> <|$TrieValue -> 1|>, c2 -> <|$TrieValue -> 1|>|>, b2 -> <|$TrieValue -> 1|>|>|>
In most cases the top-most key is $TrieRoot. For example, examine the result of
TrieCreate[{{a1, b1, c1}, {a1, b1, c2}, {a1, b2}}]
(* <|$TrieRoot -> <|$TrieValue -> 3, a1 -> <|b1 -> <|c1 -> <|$TrieValue -> 1|>,
c2 -> <|$TrieValue -> 1|>, $TrieValue -> 2|>, b2 -> <|$TrieValue -> 1|>, $TrieValue -> 3|>|>|> *)
*)
BeginPackage["TriesWithFrequencies`"];
$TrieRoot::usage = "Symbol marking the root of a trie.";
$TrieValue::usage = "Symbol used as a key for a trie node value.";
TrieQ::usage = "A predicate is an expression a trie.";
TrieWithTrieRootQ = "A predicate is an expression a trie with a root that is $TrieRoot.";
TrieBodyQ::usage = "A predicate is an expression a trie body.";
TrieRuleQ::usage = "A predicate is an expression a trie rule.";
TrieValueRuleQ::usage = "A predicate is an expression a trie value rule.";
TrieRetrieve::usage = "TrieRetrieve[t_, w_List] gives the node corresponding to the last \"character\" of the \"word\" w in the trie t.";
TrieSubTrie::usage = "TrieSubTrie[t_, w_List] gives the sub-trie corresponding to the last \"character\" of the \"word\" w in the trie t.";
TriePosition::usage = "TriePosition[ tr_, ks_List ] finds a sub-list of the list of keys \
ks that corresponds to a sub-trie in the trie tr.";
ToTrieWithRoot::usage = "ToTrieWithRoot[tr] convert a trie into trie with root.";
TrieBlank::usage = "TrieBlank[] makes a blank trie.";
TrieCreate::usage = "TrieCreate[words:{_List..}] creates a trie from a list of lists.";
TrieCreateBySplit::usage = "TrieCreateBySplit[ ws:{_String..}, patt:\"\"] creates a trie object \
from a list of strings that are split with a given pattern patt.";
TrieInsert::usage = "TrieInsert[t_, w_List] insert a \"word\" to the trie t. \
TrieInsert[t_, w_List, val_] inserts a key and a corresponding value.";
TrieMerge::usage = "TrieMerge[t1_, t2_] merges two tries.";
TrieShrink::usage = "TrieShrink[tr_?TrieQ] shrinks the leaves and internal nodes of the trie tr into prefixes. \
TrieShrink[tr_?TrieQ, sep_String] does the shrinking of string nodes with the string separator sep.";
TrieToRules::usage = "Converts a trie into a list of rules suitable for visualization with GraphPlot and LayeredGraphPlot. \
To each trie node is added a list of its level and its traversal order.";
TrieForm::usage = "Graph plot for a trie.";
TrieValueTotal::usage = "TrieValueTotal[trb_?TrieBodyQ] gives the total sum of the values in a trie body.";
TrieNodeProbabilities::usage = "Converts the frequencies at the nodes of a trie into probabilities. \
The value of the option \"ProbabilityModifier\" is a function that is applied to the computed probabilities.";
TrieNodeFrequencies::usage = "Converts the probabilities at the nodes of a trie into frequencies. \
The value of the option \"FrequencyModifier\" is a function that is applied to the computed frequencies.";
TrieLeafProbabilities::usage = "Gives the probabilities to end up at each of the leaves by paths from the root of the trie.";
TrieLeafProbabilitiesWithPositions::usage = "Gives the probabilities to end up at each of the leaves by paths from the root of the trie. \
For each leaf its position in the trie is given.";
TriePathFromPosition::usage = "TriePathFromPosition[trie,pos] gives a list of nodes from the root of a trie to the node at a specified position.";
TrieRootToLeafPaths::usage = "TrieRootToLeafPaths[trie] gives all paths from the root node to the leaf nodes.";
TrieRootToLeafPathRules::usage = "TrieRootToLeafPathRules[trie] gives rules for all paths from the root node to the leaf node values.";
TrieRootToLeafPathProbabilityRules::usage = "TrieRootToLeafPathProbabilityRules[trie] gives path probability rules \
for all paths from the root node to the leaf nodes.";
TrieGetWords::usage = "TrieGetWords[ tr_, sw_List ] gives a list words in tr that start with sw. \
The second argument can be All.";
TrieRemove::usage = "TrieRemove removes a \"word\" from a trie.";
TrieThresholdRemove::usage = "TrieThresholdRemove[tr_, th_?NumberQ, opts] removes nodes that have values below \
a specified threshold. \
If the value postfixVal of the option \"Postfix\" is different than NULL or None then \
the dropped nodes are replaced with postfixVal -> removedTotal, \
where removedTotal is the total of the values of the dropped nodes. \
If the option \"BelowThreshold\" is to False, the nodes with values above the threshold are removed";
TrieParetoFractionRemove::usage = "TrieParetoFractionRemove[tr_, fr_?NumberQ, opts] removes nodes that have values
below the thresholds derived by the specified Pareto principle fraction. \
If the value postfixVal of the option \"Postfix\" is different than NULL or None then \
the dropped nodes are replaced with postfixVal -> removedTotal, \
where removedTotal is the total of the values of the dropped nodes. \
If the option \"RemoveBottomElements\" is set to False, \
then the nodes with Pareto values below the derived thresholds are removed.";
TrieHasCompleteMatchQ::usage = "TrieHasCompleteMatchQ[ tr_, sw_List ] finds does a fraction \
of the list sw is a complete match in the trie tr.";
TrieContains::usage = "TrieContains[ tr_, sw_List ] finds is the list sw a complete match in the trie tr.";
TrieMemberQ::usage = "Same as TrieContains.";
TrieKeyExistsQ::usage = "TrieKeyExistsQ[tr_, sw_List] finds is the list sw a key in the trie tr.";
TrieKeyQ::usage = "Synonym of TrieKeyExistsQ.";
TriePrune::usage = "TriePrune[t, maxLvl] prunes the trie to a maximum node level. (The root is level 0.)";
TrieKeyValueTraverse::usage = "TrieKeyValueTraverse[t, composeFunc, joinFunc, nodeFunc] traverses a trie.";
TrieKeyTraverse::usage = "TrieKeyTraverse[t, composeFunc, joinFunc] traverses the keys of a trie.";
TrieRandomChoice::usage = "TrieRandomChoice[t, n] gives n random \"words\" from the trie t.";
TrieMap::usage = "TrieMap[t, preFunc, postFunc] traverses the trie t and applies preFunc and postFunc at each node.";
TrieNodeCounts::usage = "TrieNodeCounts[t] gives and association with the total number of nodes, internal nodes only, and leaves only.";
TrieDepth::usage = "TrieDepth[tr] gives the maximum level of the trie tr.";
TrieToJSON::usage = "TrieToJSON[tr] converts a trie to a corresponding JSON expression.";
TrieToListTrie::usage = "TrieToListTrie[tr] converts an Association based trie to a List based trie. (The \"old\" approach.)";
ToTrieFromJSON::usage = "ToTrieFromJSON[jsonTrie:{_Rule...}] converts a JSON import into a Trie object. \
ToTrieFromJSON[jsonTrie:{_Rule...}, elementNames:{key_String, value_String, children_String}] is going to use \
the specified element names for the conversion.";
TrieComparisonGrid::usage = "Makes a grid trie plots for a specified list of trie expressions.";
TrieClassify::usage = "TrieClassify[tr_,record_] classifies a record using a trie. \
The signature TrieClassify[tr_,record_,prop_] can take properties as the ones given to ClassifierFunction. \
TrieClassify[tr_,record_] is the same as TrieClassify[tr_,record_,\"Decision\"].";
Begin["`Private`"];
(************************************************************)
(* Trie predicates *)
(************************************************************)
Clear[TrieBodyQ];
SyntaxInformation[TrieBodyQ] = { "ArgumentsPattern" -> { _ } };
TrieBodyQ[a_Association] := KeyExistsQ[a, $TrieValue];
TrieBodyQ[___] := False;
Clear[TrieQ];
SyntaxInformation[TrieQ] = { "ArgumentsPattern" -> { _ } };
TrieQ[a_Association] := MatchQ[a, Association[x_ -> b_?TrieBodyQ]];
TrieQ[___] := False;
Clear[TrieRuleQ];
SyntaxInformation[TrieRuleQ] = { "ArgumentsPattern" -> { _ } };
TrieRuleQ[a_Rule] := MatchQ[a, Rule[x_, b_?TrieBodyQ]];
TrieRuleQ[___] := False;
Clear[TrieValueRuleQ];
SyntaxInformation[TrieValueRuleQ] = { "ArgumentsPattern" -> { _ } };
TrieValueRuleQ[a_Rule] := MatchQ[a, Rule[$TrieValue, _]];
TrieValueRuleQ[___] := False;
Clear[TrieWithTrieRootQ];
TrieWithTrieRootQ[a_Association] := MatchQ[a, Association[$TrieRoot -> b_?TrieBodyQ]];
TrieWithTrieRootQ[___] := False;
(************************************************************)
(* Trie stats *)
(************************************************************)
Clear[TrieNodeCounts];
SyntaxInformation[TrieNodeCounts] = { "ArgumentsPattern" -> { _ } };
TrieNodeCounts[tr_] :=
Block[{cs},
cs = {Count[tr, <|___, $TrieValue -> _, ___|>, Infinity], Count[tr, <|$TrieValue -> _|>, Infinity]};
<|"total" -> cs[[1]], "internal" -> cs[[1]] - cs[[2]], "leaves" -> cs[[2]]|>
];
Clear[TrieDepth];
SyntaxInformation[TrieDepth] = { "ArgumentsPattern" -> { _ } };
TrieDepth[tr_?TrieQ] := Depth[tr] - 2;
(************************************************************)
(* Trivial trie *)
(************************************************************)
Clear[TrieBlank];
TrieBlank[] := <|$TrieRoot -> <|$TrieValue -> 0|>|>;
(************************************************************)
(* Trie conversion *)
(************************************************************)
Clear[ToTrieWithRoot];
ToTrieWithRoot[ tr_?TrieWithTrieRootQ ] := tr;
ToTrieWithRoot[ tr_?TrieQ ] :=
Block[{},
<| $TrieRoot -> Join[ <| $TrieValue -> tr[[1]][$TrieValue] |>, tr ] |>
] /; !TrieWithTrieRootQ[tr];
(************************************************************)
(* Trie merge related *)
(************************************************************)
Clear[TrieMerge];
SyntaxInformation[TrieMerge] = { "ArgumentsPattern" -> { _, _ } };
TrieMerge[<||>, <||>] := <||>;
TrieMerge[t1_?TrieQ, t2_?TrieQ] :=
Block[{ckey},
Which[
TrueQ[Keys[t1] == Keys[t2]],
ckey = First@Keys[t1];
<|
ckey ->
Join[
Merge[{t1[ckey], t2[ckey]}, TrieMerge],
<|$TrieValue -> (t1[ckey][$TrieValue] + t2[ckey][$TrieValue])|>
]
|>,
True,
Join[t1, t2]
]
];
TrieMerge[{<||>, t2_Association}] := t2;
TrieMerge[{t1_Association, <||>}] := t1;
TrieMerge[{t1_Association}] := t1;
TrieMerge[{t1_Association, t2_Association}] :=
Block[{},
Join[Merge[{KeyDrop[t1, $TrieValue], KeyDrop[t2, $TrieValue]},
TrieMerge], <|$TrieValue -> (t1[$TrieValue] + t2[$TrieValue])|>]
];
Clear[TrieMake];
SyntaxInformation[TrieMake] = { "ArgumentsPattern" -> { _, _. } };
TrieMake[chars_List] := TrieMake[chars, 1];
TrieMake[chars_List, v_Integer] := TrieMake[chars, v, v];
TrieMake[chars_List, v_Integer, v0_Integer] :=
Fold[<|#2 -> <|$TrieValue -> v, #1|>|> &, <|Last[chars] -> <|$TrieValue -> v0|>|>,
Reverse@Most@chars];
Clear[TrieInsert];
SyntaxInformation[TrieInsert] = { "ArgumentsPattern" -> { _, _, _. } };
TrieInsert[tr_?TrieQ, word_List] :=
TrieMerge[tr, <|$TrieRoot -> Join[<|$TrieValue -> 1|>, TrieMake[word, 1]]|>];
TrieInsert[tr_, word_List, value_] :=
Block[{},
TrieMerge[
tr, <|$TrieRoot -> Join[<|$TrieValue -> 1|>, TrieMake[word, 0, value]]|>]
];
(************************************************************)
(* Trie creation functions *)
(************************************************************)
Clear[TrieCreate1];
SyntaxInformation[TrieCreate1] = { "ArgumentsPattern" -> { _ } };
TrieCreate1[{}] := <|$TrieRoot -> <|$TrieValue -> 0|>|>;
TrieCreate1[words : {_List ..}] :=
Fold[TrieInsert, <|
$TrieRoot -> Join[<|$TrieValue -> 1|>, TrieMake[First[words], 1]]|>, Rest@words];
Clear[TrieCreate];
SyntaxInformation[TrieCreate] = { "ArgumentsPattern" -> { _ } };
TrieCreate[{}] := <|$TrieRoot -> <|$TrieValue -> 0|>|>;
TrieCreate[words : {_List ..}] :=
Block[{},
If[Length[words] <= 5, TrieCreate1[words], (*ELSE*)
TrieMerge[TrieCreate[Take[words, Floor[Length[words] / 2]]],
TrieCreate[Take[words, {Floor[Length[words] / 2] + 1, Length[words]}]]]
]
];
Clear[TrieCreateBySplit];
SyntaxInformation[TrieCreateBySplit] = { "ArgumentsPattern" -> { _, _. } };
TrieCreateBySplit[words : {_String ..}, patt_ : ""] :=
TrieCreate[ Map[StringSplit[#, ""]&, words]];
(************************************************************)
(* Trie retrieval functions *)
(************************************************************)
Clear[TrieSubTrie, TrieSubTriePathRec];
SyntaxInformation[TrieSubTrie] = { "ArgumentsPattern" -> { _, _ } };
TrieSubTrie::wargs = "The first argument is expected to be a trie; the second argument is expected to be a list.";
TrieSubTrie[tr_?TrieQ, wordArg_List ] :=
Block[{path, word = wordArg},
If[TrieWithTrieRootQ[tr] && !MatchQ[word, {$TrieRoot, ___}], word = Prepend[word, $TrieRoot] ];
path = TrieSubTriePathRec[tr, word ];
If[Length[path] == 0, {},
<|Last[path] -> tr[ Sequence @@ path ]|>
]
];
TrieSubTrie[___] :=
Block[{},
Message[TrieSubTrie::wargs];
$Failed
];
TrieSubTriePathRec[tr_, {}] := {};
TrieSubTriePathRec[tr_, word_List] :=
If[KeyExistsQ[tr, First[word]],
Join[{First[word]}, TrieSubTriePathRec[tr[First[word]], Rest[word]]],
{}
] /; TrieBodyQ[tr] || TrieQ[tr];
Clear[TriePosition];
SyntaxInformation[TriePosition] = { "ArgumentsPattern" -> { _, _ } };
TriePosition[tr_?TrieQ, word_List] :=
If[TrieWithTrieRootQ[tr] && !MatchQ[word, {$TrieRoot, ___}],
TrieSubTriePathRec[tr, Prepend[word, $TrieRoot] ],
TrieSubTriePathRec[tr, word ]
];
Clear[TrieRetrieve];
SyntaxInformation[TrieRetrieve] = { "ArgumentsPattern" -> { _, _ } };
TrieRetrieve[tr_?TrieQ, wordArg_List] :=
Block[{p, word = wordArg},
If[TrieWithTrieRootQ[tr] && !MatchQ[word, {$TrieRoot, ___}], word = Prepend[word, $TrieRoot] ];
p = tr[ Sequence @@ word ];
If[ FreeQ[p, _Missing], p,
(*ELSE*)
p = TriePosition[tr, wordArg];
Which[
Length[p] == 0, {},
True, tr[ Sequence @@ p ]
]
]
];
(************************************************************)
(* Trie key query functions *)
(************************************************************)
Clear[TrieHasCompleteMatchQ];
SyntaxInformation[TrieHasCompleteMatchQ] = { "ArgumentsPattern" -> { _, _ } };
TrieHasCompleteMatchQ[tr_?TrieQ, word_List ] :=
Block[{pos, b},
pos = TriePosition[tr, word];
If[ Length[pos] == 0, Return[False] ];
b = False;
While[ Length[pos] > 0 && !b,
b = TrieValueTotal[ tr[ Sequence @@ pos ] ] < tr[ Sequence @@ pos, $TrieValue ];
pos = Most[pos];
];
b
];
Clear[TrieContains];
SyntaxInformation[TrieContains] = { "ArgumentsPattern" -> { _, _ } };
TrieContains[tr_?TrieQ, wordArg_List ] :=
Block[{pos, word = wordArg},
If[ TrieWithTrieRootQ[tr] && !MatchQ[word, {$TrieRoot, ___}], word = Prepend[word, $TrieRoot] ];
pos = TriePosition[tr, word];
If[ Length[pos] == Length[word],
TrieValueTotal[ tr[ Sequence @@ pos ] ] < tr[ Sequence @@ pos, $TrieValue ],
(* ELSE *)
False
]
];
TrieMemberQ = TrieContains;
Clear[TrieKeyExistsQ];
SyntaxInformation[TrieKeyExistsQ] = { "ArgumentsPattern" -> { _, _ } };
TrieKeyExistsQ[ tr_?TrieQ, wordArg_List ] :=
Block[{pos, word = wordArg},
If[ TrieWithTrieRootQ[tr] && !MatchQ[word, {$TrieRoot, ___}], word = Prepend[word, $TrieRoot] ];
pos = TriePosition[tr, word];
Length[pos] == Length[word]
];
Clear[TrieKeyQ];
TrieKeyQ = TrieKeyExistsQ;
(************************************************************)
(* TrieNodeProbabilities and related functions *)
(************************************************************)
Clear[TrieNodeProbabilities, TrieNodeProbabilitiesRec];
SyntaxInformation[TrieNodeProbabilities] = { "ArgumentsPattern" -> { _, OptionsPattern[] } };
Options[TrieNodeProbabilities] = {"ProbabilityModifier" -> N};
Options[TrieNodeProbabilitiesRec] = Options[TrieNodeProbabilities];
TrieNodeProbabilities[tr_?TrieQ, opts : OptionsPattern[]] :=
Block[{},
<|First[Keys[tr]] -> Join[TrieNodeProbabilitiesRec[First@Values[tr], opts], <|$TrieValue -> 1|>]|>
];
TrieNodeProbabilitiesRec[trb_?TrieBodyQ, opts : OptionsPattern[]] :=
Block[{sum, res, pm = OptionValue["ProbabilityModifier"]},
Which[
Length[Keys[trb]] == 1, trb,
True,
If[trb[$TrieValue] == 0,
sum = TrieValueTotal[trb],
sum = trb[$TrieValue]
];
res = Map[TrieNodeProbabilitiesRec[#] &, KeyDrop[trb, $TrieValue]];
res = Replace[res, <|a___, $TrieValue -> x_, b___|> :> <|a, $TrieValue -> pm[x / sum], b|>, {1}];
Join[res, KeyTake[trb, $TrieValue]]
]
];
Clear[TrieValueTotal];
TrieValueTotal[trb_?TrieBodyQ] := Total[Map[#[$TrieValue] &, KeyDrop[trb, $TrieValue]]];
Clear[TrieLeafProbabilities, TrieLeafProbabilitiesRec];
SyntaxInformation[TrieLeafProbabilities] = { "ArgumentsPattern" -> { _ } };
TrieLeafProbabilities::ntnode = "Non trie node was encountered: `1`. A trie node has two elements prefix and frequency.";
TrieLeafProbabilities[trieArg_?TrieQ] :=
Block[{res},
res =
Which[
TrueQ[trieArg[First@Keys@trieArg][$TrieValue] == 0],
(* This does not match any signature. *)
TrieLeafProbabilitiesRec[trieArg],
True,
TrieLeafProbabilitiesRec[First@Keys@trieArg, First@Values@trieArg]
];
If[Length[res] == 1, res, Merge[res, Total]]
];
TrieLeafProbabilities[args__] :=
Block[{},
Message[TrieLeafProbabilities::ntnode, {args}];
Return[<||>]
];
TrieLeafProbabilitiesRec[k_, trb_?TrieBodyQ] :=
Block[{res, sum},
Which[
Length[Keys[trb]] == 1,
{k -> trb[$TrieValue]},
True,
sum = TrieValueTotal[trb];
res = KeyValueMap[TrieLeafProbabilitiesRec, KeyDrop[trb, $TrieValue]];
If[sum < 1,
res = Append[res, k -> (1 - sum)]
];
res = Map[#[[1]] -> #[[2]] * trb[$TrieValue] &, Flatten[res, 1]]
]
];
(************************************************************)
(* TrieShrink and related functions *)
(************************************************************)
Clear[NodeJoin];
NodeJoin[n_String] := n;
NodeJoin[n1_String, n2_String] := n1 <> n2;
NodeJoin[n1_List, n2_String] := List[n1, n2];
NodeJoin[n_] := List[n];
NodeJoin[n1_List, n2_List] := Join[n1, n2];
NodeJoin[n1_, n2_List] := Prepend[n2, n1];
NodeJoin[n1_List, n2_] := Append[n1, n2];
NodeJoin[n1_, n2_] := List[n1, n2];
Clear[TrieShrink, TrieShrinkRec];
SyntaxInformation[TrieShrink] = { "ArgumentsPattern" -> { _, _. } };
TrieShrink::wargs = "The first argument is expected to be a trie; the second, optional argument is expected to a string.";
TrieShrink[tr_?TrieQ] := TrieShrinkRec[tr];
TrieShrink[tr_?TrieQ, sep_String] :=
Block[{res},
NodeJoin[n1_String, n2_String] := n1 <> sep <> n2;
res = TrieShrinkRec[tr];
NodeJoin[n1_String, n2_String] := n1 <> n2;
res
];
TrieShrink[___] := Message[TrieShrink::wargs];
TrieShrinkRec[{}] := {};
TrieShrinkRec[tr_?TrieQ] := TrieShrinkRec[First[Normal[tr]]];
TrieShrinkRec[tr_?TrieRuleQ] :=
Block[{vals = tr[[2]], key = tr[[1]], valKeys },
valKeys = Keys @ KeyDrop[vals, $TrieValue];
Which[
Length[ vals ] == 1,
tr,
key =!= $TrieRoot && Length[vals] == 2 && vals[$TrieValue] == vals[First @ valKeys][$TrieValue],
TrieShrinkRec[ <| NodeJoin[ key, First[valKeys] ] -> vals[First @ valKeys] |> ],
True,
<| key -> Join[ <| $TrieValue -> vals[$TrieValue] |>, Association @ Map[ TrieShrinkRec, Normal @ KeyDrop[vals, $TrieValue] ] ] |>
]
];
(************************************************************)
(* Trie root to leaf functions *)
(************************************************************)
(* I am not particularly happy with using FixedPoint. This has to be profiled. *)
Clear[TrieRootToLeafPaths];
SyntaxInformation[TrieRootToLeafPaths] = { "ArgumentsPattern" -> { _ } };
TrieRootToLeafPaths[tr_?TrieQ] :=
Map[List @@@ Most[#[[1]]] &,
FixedPoint[
Flatten[Normal[#] /.
Rule[n_, m_?TrieBodyQ] :>
Which[
Length[m] == 1,
KeyMap[Append[n, #] &, m],
m[$TrieValue] > TrieValueTotal[m] || TrieValueTotal[m] < 1,
Join[ KeyMap[Append[n, # -> m[#][$TrieValue]] &, KeyDrop[m, $TrieValue]], KeyMap[Append[n, #] &, KeyTake[m, $TrieValue]] ],
True,
KeyMap[Append[n, # -> m[#][$TrieValue]] &, KeyDrop[m, $TrieValue]]], 1] &,
KeyMap[{# -> First[Values[tr]][$TrieValue]} &, tr]]
];
(* This is implemented because it looks neat, and it can be used for tensor creation. *)
Clear[TrieRootToLeafPathRules];
TrieRootToLeafPathRules[tr_?TrieQ] :=
Association[
Map[ Most[#[[1]]] -> #[[2]] &,
FixedPoint[
Flatten[Normal[#] /.
Rule[n_, m_?TrieBodyQ] :>
If[Length[m] == 1 || m[$TrieValue] > TrieValueTotal[m] || TrieValueTotal[m] < 1,
KeyMap[Append[n, #] &, m],
KeyMap[Append[n, #] &, KeyDrop[m, $TrieValue]]], 1] &,
KeyMap[{#} &, tr]
]
]
];
Clear[TrieRootToLeafPathProbabilityRules];
TrieRootToLeafPathProbabilityRules[tr_?TrieQ] :=
ReverseSort @ Association @ Map[ #[[All, 1]] -> Apply[Times, #[[All, 2]]] &, TrieRootToLeafPaths[tr] ];
(************************************************************)
(* TrieGetWords *)
(************************************************************)
Clear[TrieGetWords];
SyntaxInformation[TrieGetWords] = { "ArgumentsPattern" -> { _, _. } };
TrieGetWords::args = "The first of argument is expected to be a trie, the second argument is expected to be a list or All.";
TrieGetWords[ tr_?TrieQ, word : ( _List | All ) : All ] :=
Which[
TrueQ[word === All] || ListQ[word] && Length[word] == 0,
Map[ Join, Keys @ TrieRootToLeafPathRules[tr] ],
ListQ[word] || TrieKeyExistsQ[tr, word],
Map[ Join[Most[word], #]&, Keys @ TrieRootToLeafPathRules[TrieSubTrie[tr, word]] ],
True,
{}
];
TrieGetWords[___] :=
Block[{},
Message[TrieGetWords::args];
$Failed
];
(************************************************************)
(* TriePrune *)
(************************************************************)
Clear[TriePrune, TriePruneRec];
SyntaxInformation[TriePrune] = { "ArgumentsPattern" -> { _, _ } };
TriePrune::args = "The first argument is expected to be a trie. \
The second argument is expected to be a positive integer.";
TriePrune[trie_?TrieQ, maxLevel_Integer] :=
Block[{},
Association[TriePruneRec[First @ Normal @ trie, maxLevel, 0]]
] /; maxLevel > 0;
TriePrune[___] :=
Block[{},
Message[TriePrune::args];
$Failed
];
TriePruneRec[tr_?TrieRuleQ, maxLevel_Integer, level_Integer] :=
Block[{key = tr[[1]]},
Which[
Length[tr] == 0, {},
Length[tr[[2]]] == 1, tr,
maxLevel <= level, key -> KeyTake[tr[[2]], $TrieValue],
True,
key ->
Join[
Association @ KeyValueMap[ TriePruneRec[#1 -> #2, maxLevel, level + 1] &, KeyDrop[tr[[2]], $TrieValue] ],
KeyTake[tr[[2]], $TrieValue]
]
]
];
(************************************************************)
(* Trie key-value traversal *)
(************************************************************)
Clear[TrieKeyValueTraverse];
SyntaxInformation[TrieKeyValueTraverse] = { "ArgumentsPattern" -> { _, _., _., _. } };
TrieKeyValueTraverse::args = "The first argument is expected to be a trie.";
TrieKeyValueTraverse[tr_?TrieQ, composeFunc_ : List, joinFunc_ : List, nodeFunc_ : Identity] :=
TrieKeyValueTraverseRec[Normal[tr][[1]], composeFunc, joinFunc, nodeFunc, 1];
TrieKeyValueTraverse[___] :=
Block[{},
Message[TrieKeyValueTraverse::args];
$Failed
];
TrieKeyValueTraverseRec[trRule_?TrieValueRuleQ, composeFunc_, joinFunc_, nodeFunc_, lvl_Integer] := nodeFunc[trRule];
TrieKeyValueTraverseRec[trRule_?TrieRuleQ, composeFunc_, joinFunc_, nodeFunc_, lvl_Integer] :=
Block[{res},
res = Map[TrieKeyValueTraverseRec[#, composeFunc, joinFunc, nodeFunc, lvl + 1] &, Normal@trRule[[2]]];
composeFunc[trRule[[1]], joinFunc @@ res]
];
(************************************************************)
(* Trie keys traversal *)
(************************************************************)
Clear[TrieKeyTraverse];
SyntaxInformation[TrieKeyTraverse] = { "ArgumentsPattern" -> { _, _., _. } };
TrieKeyTraverse::args = "The first argument is expected to be a trie.";
TrieKeyTraverse[tr_?TrieQ, composeFunc_ : List, joinFunc_ : List] :=
TrieKeyTraverseRec[Normal[tr][[1]], composeFunc, joinFunc, 1];
TrieKeyTraverse[___] :=
Block[{},
Message[TrieKeyTraverse::args];
$Failed
];
TrieKeyTraverseRec[trRule_?TrieValueRuleQ, composeFunc_, joinFunc_, lvl_Integer] := {};
TrieKeyTraverseRec[trRule_?TrieRuleQ, composeFunc_, joinFunc_, lvl_Integer] :=
Block[{res},
res = Map[TrieKeyTraverseRec[#, composeFunc, joinFunc, lvl + 1] &, Normal@trRule[[2]]];
res = DeleteCases[res, {}];
If[Length[res] == 0,
trRule[[1]],
(*ELSE*)
composeFunc[trRule[[1]], joinFunc @@ res]
]
];
(************************************************************)
(* Trie random choice *)
(************************************************************)
Clear[TrieRandomChoice];
SyntaxInformation[TrieRandomChoice] = { "ArgumentsPattern" -> { _, _. } };
TrieRandomChoice::args = "The first argument is expected to be a trie. \
The second, optional argument is expected to be a positive integer.";
Clear[TrieRandomChoice];
TrieRandomChoice[tr_?TrieQ] :=
First @ TrieRandomChoice[tr,1];
TrieRandomChoice[tr_?TrieQ, n_Integer] :=
Table[TrieRandomChoiceRec[Normal[tr][[1]]][[1]], n];
Clear[TrieRandomChoiceRec];
TrieRandomChoiceRec[trRule_?TrieValueRuleQ] := trRule;
TrieRandomChoiceRec[trRule_?TrieRuleQ] :=
Block[{recurseQ, res, childrenProb},
childrenProb = TrieValueTotal[trRule[[2]]];
If[ 1.0 - childrenProb < 0,
(* This might happen around the $MachineEpsilon .*)
childrenProb = 1.0
];
recurseQ = RandomChoice[{childrenProb, 1.0 - childrenProb} -> {True, False}];
If[! recurseQ,
{trRule[[1]]} -> trRule[[2]][$TrieValue],
(*ELSE*)
(* The choice over which element to recurse should happen beforehand. *)
res = TrieBodyElementRandomChoice[trRule[[2]]];
res = TrieRandomChoiceRec[ res -> trRule[[2]][res] ];
Flatten[{trRule[[1]], res[[1]]}] -> trRule[[2]][$TrieValue]
]
];
Clear[TrieBodyElementRandomChoice];
TrieBodyElementRandomChoice[trb_?TrieBodyQ] :=
Block[{res},
res = Map[#[$TrieValue] &, KeyDrop[trb, $TrieValue]];
RandomChoice[ Values[res] -> Keys[res] ]
];
(************************************************************)
(* Trie Map *)
(************************************************************)
Clear[TrieMap, TrieMapRec];
SyntaxInformation[TrieMap] = { "ArgumentsPattern" -> {_, _, _ } };
TrieMap::funcs = "At least one of the second and third argument has to be a function.";
TrieMap[ tr_?TrieQ, preFunc_, postFunc_ ] :=
Block[{},
If[ ( preFunc === Null || preFunc === None ) && ( postFunc === Null || postFunc === None ),
Message[TrieMap::funcs];
Return[tr]
];
Association[ TrieMapRec[ First @ Normal @ tr, preFunc, postFunc, 0 ] ]
];
TrieMapRec[tr_?TrieRuleQ, preFunc_, postFunc_, level_Integer ] :=
Block[{res, resChildren},
If[ Length[tr] == 0, Return[{}] ];
If[ ! ( TrueQ[preFunc === Null] || TrueQ[preFunc === None] ),
res = preFunc[tr],
(* ELSE *)
res = tr
];
(* Print @ Normal @ KeyDrop[ res[[2]], $TrieValue ] ;*)
If[ Length[res[[2]]] == 1,
resChildren = <||>,
(* ELSE *)
resChildren = Association @ Map[ TrieMapRec[#, preFunc, postFunc, level + 1]&, Normal @ KeyDrop[ res[[2]], $TrieValue ] ]
];
res = res[[1]] -> Join[ KeyTake[res[[2]], $TrieValue], resChildren ];
If[ !(TrueQ[postFunc === Null] || TrueQ[postFunc === None]),
res = postFunc[res]
];
res
];
(************************************************************)
(* Trie threshold removal *)
(************************************************************)
Clear[TrieThresholdRemove];
SyntaxInformation[TrieThresholdRemove] = { "ArgumentsPattern" -> {_, _, OptionsPattern[]} };
Options[TrieThresholdRemove] = {"Postfix" -> Anonymous, "BelowThreshold" -> True};
TrieThresholdRemove[ tr_?TrieQ, threshold_?NumberQ, opts : OptionsPattern[] ] :=
Block[{postfix, belowThresholdQ},
postfix = OptionValue[TrieThresholdRemove, "Postfix"];
belowThresholdQ = TrueQ[OptionValue[TrieThresholdRemove, "BelowThreshold"]];
TrieMap[ tr, ThresholdRemove[#, threshold, postfix, belowThresholdQ] &, None]
];
Clear[ThresholdRemove];
ThresholdRemove[tr_?TrieRuleQ, threshold_?NumberQ, postfix_, belowThresholdQ : (True | False) ] :=
Block[{resChildren, removeSum},
If[Length[KeyDrop[tr, $TrieValue]] == 0, Return[tr]];
If[ belowThresholdQ,
resChildren = Select[KeyDrop[tr[[2]], $TrieValue], #[$TrieValue] >= threshold &],
(* ELSE *)
resChildren = Select[KeyDrop[tr[[2]], $TrieValue], #[$TrieValue] <= threshold &]
];
If[! (TrueQ[postfix === None] || TrueQ[postfix === Null]) && Length[resChildren] < Length[tr[[2]]] - 1,
removeSum = Total @ Map[ #[$TrieValue] &, KeyDrop[tr[[2]], Prepend[ Keys[resChildren], $TrieValue] ] ];
resChildren = Append[resChildren, postfix -> <|$TrieValue -> removeSum|>]
];
tr[[1]] -> Join[KeyTake[tr[[2]], $TrieValue], resChildren]
];
(************************************************************)
(* Trie Pareto fraction removal *)
(************************************************************)
Clear[TrieParetoFractionRemove];
TrieParetoFractionRemove::pfrac = "The second argument is expected to be a number between 0 and 1.";
SyntaxInformation[TrieParetoFractionRemove] = { "ArgumentsPattern" -> {_, _, OptionsPattern[]} };
Options[TrieParetoFractionRemove] = {"Postfix" -> Anonymous, "RemoveBottomElements" -> True};
TrieParetoFractionRemove[ tr_?TrieQ, paretoFraction_?NumberQ, opts : OptionsPattern[] ] :=
Block[{postfix, removeBottomElementsQ},
postfix = OptionValue[TrieParetoFractionRemove, "Postfix"];
removeBottomElementsQ = TrueQ[OptionValue[TrieParetoFractionRemove, "RemoveBottomElements"]];
If[ !( 0 <= paretoFraction <= 1),
Message[TrieParetoFractionRemove::pfrac];
Return[$Failed]
];
TrieMap[ tr, ParetoThresholdRemove[#, paretoFraction, postfix, removeBottomElementsQ] &, None]
];
(* Essentially the same as ThresholdRemove, except here we have accumulation and threshold calculation. *)
Clear[ParetoThresholdRemove];
ParetoThresholdRemove[tr_?TrieRuleQ, paretoFraction_?NumberQ, postfix_, removeBottomElementsQ : (True | False) ] :=
Block[{children, acc, threshold, resChildren, removeSum},
children = KeyDrop[ tr[[2]], $TrieValue ];
If[Length[children] == 0, Return[tr]];
children = Reverse[ SortBy[ children, #[$TrieValue]& ] ];
acc = Accumulate[ Values @ Map[ #[$TrieValue]&, children ] ];
acc = AssociationThread[ Keys[children], acc ];
threshold = paretoFraction * Last[acc];
If[ removeBottomElementsQ,
resChildren = KeyTake[ children, Keys @ Select[ acc, # <= threshold &] ],
(* ELSE *)
resChildren = KeyTake[ children, Keys @ Select[ acc, # >= threshold &] ]
];
If[! (TrueQ[postfix === None] || TrueQ[postfix === Null]) && Length[resChildren] < Length[tr[[2]]] - 1,
removeSum = Total @ Map[ #[$TrieValue] &, KeyDrop[tr[[2]], Prepend[ Keys[resChildren], $TrieValue] ] ];
resChildren = Append[resChildren, postfix -> <|$TrieValue -> removeSum|>]
];
tr[[1]] -> Join[KeyTake[tr[[2]], $TrieValue], resChildren]
];
(************************************************************)
(* Trie conversion related functions *)
(************************************************************)
Clear[TrieToRules];
SyntaxInformation[TrieToRules] = { "ArgumentsPattern" -> { _, _. } };
TrieToRules[tree_?TrieQ] := Block[{ORDER = 0}, TrieToRules[tree, 0, 0]];
TrieToRules[tree_, level_, order_] :=
Block[{nodeRules, k, v},
Which[
tree === <||>, {},
Keys[tree] === {$TrieValue}, {},
True,