44 lines
4.0 KiB
Factor
44 lines
4.0 KiB
Factor
USING: arrays assocs byte-arrays help.markup help.syntax io.encodings.utf8
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kernel math serialize trees.cb.private ;
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IN: trees.cb
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ARTICLE: "trees.cb" "Binary crit-bit trees"
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"The " { $vocab-link "trees.cb" } " vocabulary is a library for binary critical bit trees, a variant of PATRICIA tries. A crit-bit tree stores each element of a non-empty set of keys " { $snippet "K" } " in a leaf node. Each leaf node is attached to the tree of internal split nodes for bit strings " { $snippet "x" } " such that " { $snippet "x0" } " and " { $snippet "x1" } " are prefixes of (serialized byte arrays of) elements in " { $snippet "K" } " and ancestors of other bit strings higher up in the tree. Split nodes store the prefix compressed as two values, the byte number and bit position, in the subset of " { $snippet "K" } " at which the prefixes of all ancestors to the left differ from all ancestors to the right."
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$nl
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"Serialization of keys is implemented using " { $link key>bytes } ". Crit-bit trees can store arbitrary keys and values, even mixed (but see implementation notes to " { $link key>bytes* } "). Due to the nature of crit-bit trees, for any given input key set that shares a common prefix, the tree compresses the common prefix into the split node at the joint extending the lookup by one node for arbitrarily long prefixes."
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$nl
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"Keys are serialized once for every lookup and insertion not adding a new leaf node. Two keys are serialized for every insertion adding a new leaf node to the tree."
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$nl
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"Due to ordering ancestors at split nodes into crit-bit '0' (left) and crit-bit '1' (right), the order of the elements in a crit-bit tree is total allowing efficient suffix searches and minimum searches."
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$nl
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"Crit-bit trees consume 2 * " { $emphasis "n" } " - 1 nodes in total for storing " { $emphasis "n" } " elements; each internal split node consumes two pointers and a fixnum and an integer; each leaf node two pointers to the key and value. Their shape is unique for any given set of keys, which also means lookup times are deterministic for a known set of keys regardless of insertion order or the tree having been cloned."
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$nl
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"Compared to hash tables, crit-bit trees provide fast access without being prone to malicious input (but see limitations of the standard implementation of " { $link key>bytes* } ") and also provide ordered operations (e.g. finding minimums). Compared to heaps, they support exact searches and suffix searches in addition. Compared to other ordered trees (AVL, B-), they support the same set of operations while keeping a simpler inner structure."
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$nl
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"Crit-bit trees conform to the assoc protocol."
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;
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ABOUT: "trees.cb"
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HELP: CB{
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{ $syntax "CB{ { key value }... }" }
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{ $values { "key" "a key" } { "value" "a value" } }
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{ $description "Literal syntax for a crit-bit tree." } ;
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HELP: <cb>
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{ $values { "tree" cb } }
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{ $description "Creates an empty crit-bit tree" } ;
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HELP: >cb
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{ $values { "assoc" assoc } { "tree" cb } }
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{ $description "Converts any " { $link assoc } " into a crit-bit tree. If the input assoc is a " { $link cb } ", the elements are cloned before insertion. The resulting tree is, then, identical to the input, as crit-bit trees are unique for any given content." } ;
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HELP: cb
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{ $class-description "This is the class for binary crit-bit trees (i.e. discriminating on a single critical bit)." } ;
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HELP: key>bytes*
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{ $values { "key" object } { "bytes" byte-array } }
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{ $description "Converts a key, which can be any " { $link object } ", into a " { $link byte-array } ". Standard methods convert strings into its " { $link utf8 } " byte sequences and " { $link float } " values into byte arrays representing machine-specific doubles. Integrals are converted into a byte sequence of at least machine word size in little endian byte order."
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$nl
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"All other objects are serialized using " { $link object>bytes } ". In the standard implementation, this maps " { $link f } " to the byte array " { $snippet "B{ 110 }" } " and " { $link t } " to " { $snippet "B{ 116 }" } ", which is identical to using the respective literal byte arrays as inputs." } ;
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