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
   

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3. Tree?
   

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4. unidirectional
   acyclic graph
   

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

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6. data structure
   

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7. recursion
   

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8. tree with other
   data structures
   

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9. tree-linear
   correspondence
   

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10. Why?
    

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11. context
    reduction
    

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12. extensibility
    

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13. Examples
    

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14. AST
    

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15. simple PHP obfuscator
    nikic/PHP-Parser
    

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16. 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));
    

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17. 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));
    

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

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19. 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));
    

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20. 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));
    

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21. search tree
    

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22. N non-overlapping ranges
    and a number
    find matching range
    

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23. 004604-004660
    213674-213701
    ...
    960101-961999
    962387-962414
    004651? 213702? 961446?
    

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24. naive approach
    linear search
    

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25. O(1) memory-heavy approach
    precomputed list
    

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26. tree approach
    trie / radix tree
    

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27. retrieval
    

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28. t
    r
    i e
    trie
    e e
    tree
    

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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
    

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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
    

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31. trie vs radix tree vs PATRICIA vs ...
    

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32. tr
    ie ee
    trie tree
    

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33. parser
    

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34. shortcode parser
    thunderer/shortcode
    

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

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36. shortcode
    name BBCode parameters content
    arg value
    

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

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38. shortcode
    “inner” “x” parameters null
    null
    

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39. $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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40. XML structure
    

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41. 
    
    
    
    

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42. 
    
    
    
    
    
    
    
    
    
    
    
    

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43. 
    
    
    
    

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44. 
    
    
    
    
    
    
    
    
    
    
    
    

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45. 
    say hello to
    

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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);
    

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47. approval tree
    

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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
    

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49. recursive approach
    recursive node traversal
    

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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
    

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51. linear approach
    sequential node traversal
    

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52. 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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53. object graph
    

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54. User
    Category Tag Article
    Category Tag User
    Hydration
    Normalization
    

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55. Summary
    

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56. ?$questions
    

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57. treehanks!
    @tmmx
    

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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)
    

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