Solving problems using trees

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solving problems using Trees @tmmx

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No content

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Tree?

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unidirectional acyclic graph

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binary red-black B-tree T-tree 2-3-4 tree AVL

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data structure

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recursion

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tree with other data structures

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tree-linear correspondence

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Why?

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context reduction

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extensibility

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Examples

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AST

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simple PHP obfuscator nikic/PHP-Parser

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format('Y'); $isCurrentYear = '2017' === $currentYear; return $isCurrentYear && in_array($currentYear, ['2016', '2018']); } } $validator = new AllowedYearsValidator(); $dt = DateTimeImmutable::createFromFormat('Y', '2016'); assert(false === $validator->isYearAllowed($dt));

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AllowedYearsValidator isYearAllowed $dt $currentYear $isCurrentYear $validator $dt AST

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format('Y'); $v2 = '2017' === $v1; return $v2 && in_array($v1, ['2016', '2018']); } } $v3 = new c0(); $v0 = DateTimeImmutable::createFromFormat('Y', '2016'); assert(false === $v3->m0($v0));

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format('Y'); $v2 = '2017' === $v1; return $v2 && in_array($v1, ['2016', '2018']); }} $v3 = new c0(); $v0 = DateTimeImmutable::createFromFormat('Y', '2016'); assert(false === $v3->m0($v0));

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search tree

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N non-overlapping ranges and a number find matching range

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004604-004660 213674-213701 ... 960101-961999 962387-962414 004651? 213702? 961446?

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naive approach linear search

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O(1) memory-heavy approach precomputed list

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tree approach trie / radix tree

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retrieval

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t r i e trie e e tree

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0 0 4 6 0 6 4 0 2 1 3 6 7 0 4 1 7 9 6 0 1 0 9 1 9 9 1 2 8 7 3 1 4 4 start end start end start end start end

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0 0 4 6 0 6 4 0 2 1 3 6 7 0 4 1 7 9 6 0 1 0 9 1 9 9 1 2 8 7 3 1 4 4 004651 213702 961446 962001 start end start end start end start end

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trie vs radix tree vs PATRICIA vs ...

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tr ie ee trie tree

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parser

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shortcode parser thunderer/shortcode

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[foo arg=val] data [inner=x /] code [/foo]

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shortcode name BBCode parameters content arg value

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shortcode “foo” null parameters data [inner /] code “arg” “val”

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shortcode “inner” “x” parameters null null

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$handlers = new HandlerContainer(); $handlers->add('foo', function(ShortcodeInterface $s) { return ''.$s->getContent().''; }); $handlers->add('inner', function(ShortcodeInterface $s) { return date('Y.m.d'); }); $processor = new Processor(new RegularParser(), $handlers); $text = '[foo arg=val] data [inner=x /] code [/foo]'; $expected = ' data 2017.04.03 code '; assert($expected === $processor->process($text));

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XML structure

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say hello to

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$schemaDir = __DIR__.'/xsd'; $targetDir = __DIR__.'/xml'; $log = new NullLogger(); $ctr = new Counter(); $fs = new FilePutContentsFilesystem($targetDir); $ns = new CustomNamespaceResolver(); $analyzer = new XsdAnalyzer($log); $schemas = $analyzer->createFromDirectories([$schemaDir]); $generator = new PrimitivePhpGenerator($fs, $ns, $log, $ctr); $generator->generate($schemas);

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approval tree

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A B C D E A requires B and C B requires D and E E requires F and G ...but D and E can’t confirm before B, F and G must wait for E, so... Who can vote? Did vote pass? F G

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recursive approach recursive node traversal

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A B C D E Check B and C, when in B check D and E, when in E check F and G… and if something failed somewhere then return all the information down. F G failed

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linear approach sequential node traversal

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A B C D E filter root nodes filter already decided nodes filter already notified nodes map to contact information F G failed

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object graph

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User Category Tag Article Category Tag User Hydration Normalization

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Summary

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?$questions

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treehanks! @tmmx

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Resources https://en.wikipedia.org/wiki/Radix_tree https://en.wikipedia.org/wiki/Trie http://stackoverflow.com/questions/14708134/what-is-the-difference-between-trie-and-radix-trie-data-structures Repositories https://github.com/nikic/PHP-Parser https://github.com/thunderer/Shortcode https://github.com/thunderer/Serializard https://github.com/thunderer/XSDragon Images https://www.flickr.com/photos/ghor/8394379683 (forest) https://www.flickr.com/photos/skyseeker/14404947216 (lightning)