Solving problems using trees

Tree is one of the most powerful data structures, and it is present in various kinds of problems. I want to show you how trees helped me design certain solutions so that you can do the same when the right time comes.

Transcript

1. solving problems using Trees @tmmx
3. Tree?
4. unidirectional acyclic graph
5. binary red-black B-tree T-tree 2-3-4 tree AVL
6. data structure
7. recursion
8. tree with other data structures
9. tree-linear correspondence
10. Why?
11. context reduction
12. extensibility
13. Examples
14. AST
15. simple PHP obfuscator nikic/PHP-Parser
16. <?php declare(strict_types=1); final class AllowedYearsValidator { public function isYearAllowed(DateTimeImmutable $dt): bool { $currentYear = $dt->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));
17. <?php declare(strict_types=1); final class AllowedYearsValidator { public function isYearAllowed(DateTimeImmutable $dt): bool { $currentYear = $dt->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));
18. AllowedYearsValidator isYearAllowed $dt $currentYear $isCurrentYear $validator $dt AST
19. <?php declare(strict_types=1); final class c0 { public function m0(DateTimeImmutable $v0): bool { $v1 = $v0->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));
20. <?php declare(strict_types=1); final class c0 { public function m0(DateTimeImmutable $v0): bool { $v1 = $v0->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));
21. search tree
22. N non-overlapping ranges and a number find matching range
23. 004604-004660 213674-213701 ... 960101-961999 962387-962414 004651? 213702? 961446?
24. naive approach linear search
25. O(1) memory-heavy approach precomputed list
26. tree approach trie / radix tree
27. retrieval
28. t r i e trie e e tree
29. 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
30. 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
31. trie vs radix tree vs PATRICIA vs ...
32. tr ie ee trie tree
33. parser
34. shortcode parser thunderer/shortcode
35. [foo arg=val] data [inner=x /] code [/foo]
36. shortcode name BBCode parameters content arg value
37. shortcode “foo” null parameters data [inner /] code “arg” “val”
38. shortcode “inner” “x” parameters null null
39. $handlers = new HandlerContainer(); $handlers->add('foo', function(ShortcodeInterface $s) { return '<foo>'.$s->getContent().'</foo>'; }); $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]'; $expected = '<foo> data 2017.04.03 code </foo>'; assert($expected === $processor->process($text));
40. XML structure
41. <root> <level attr=”val” /> <item /> </root>
42. <xsd:element name="root"> <xsd:complexType> <xsd:sequence> <xsd:element name="level"> <xsd:complexType> <xsd:attribute name="attr"/> </xsd:complexType> </xsd:element> <xsd:element name="item"/> </xsd:sequence> </xsd:complexType> </xsd:element>
43. <root> <level attr=”val” /> <item /> </root>
44. <xsd:element name="root"> <xsd:complexType> <xsd:sequence> <xsd:element name="level"> <xsd:complexType> <xsd:attribute name="attr"/> </xsd:complexType> </xsd:element> <xsd:element name="item"/> </xsd:sequence> </xsd:complexType> </xsd:element>
45. <XSDragon/> say hello to
46. $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);
47. approval tree
48. 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
49. recursive approach recursive node traversal
50. 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
51. linear approach sequential node traversal
52. A B C D E filter root nodes filter already decided nodes filter already notified nodes map to contact information F G failed
53. object graph
54. User Category Tag Article Category Tag User Hydration Normalization
55. Summary
56. ?$questions
57. treehanks! @tmmx
58. 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)