! Copyright (C) 2020 Michael Raitza
! See http://factorcode.org/license.txt for BSD license.
!
! * Crit-bit trees
! ** Rationale
! Critbit trees are described in [[https://cr.yp.to/critbit.html][djb's crit-bit tree]]. They are an evolution of
! PATRICIA trees showing that fast insertion, deletion, exact searching and suffix
! searching is possible with this data structure.

! The strength of this data structure, according to its author, lies in its
! simple design and its optimisation to be machine parsable using machine
! word-sized operations where possible. Like PATRICIA trees, crit-bit trees are
! prefix-compressed, with internal nodes storing next decision point (the
! critical bit) in a length field (encoded as an integer and a mask) and two
! successor pointers. Arbitrary data objects make up its leaves.

USING: accessors alien arrays assocs byte-arrays combinators.short-circuit fry
io.binary io.encodings.binary io.encodings.private io.encodings.string
io.encodings.utf8 kernel layouts locals make math math.private namespaces parser
prettyprint.custom sequences serialize strings trees trees.private vectors ;
IN: trees.cb

TUPLE: cb < tree ;

: <cb> ( -- tree ) cb new-tree ; inline

<PRIVATE

TUPLE: cb-node { byte# integer } { bits integer } left right ;

: new-node ( byte# bits class -- node )
    new
    swap >>bits
    swap >>byte# ; inline

: <cb-node> ( byte# bits -- node )
    cb-node new-node ;

: key-side ( bits byte -- side )
    bitor 1 + -8 shift 0 = left right ? ;

! Produce a byte with all bits set except the msb from bits*.
! See MAGIC Algorithms for rationale.
: msb0 ( bits* -- bits )
    dup -1 shift bitor
    dup -2 shift bitor
    dup -4 shift bitor
    dup -1 shift bitnot bitand 255 bitxor ;

! Calculate the direction and the critical bit for the differing byte.
: byte-diff ( newbyte oldbyte -- side bits )
    swap over
    bitxor msb0
    [ key-side ] keep ;

! For two byte strings, calculate the critical bit, byte and direction of
! difference (0 = left, 1 = right).
: bytes-diff ( newbytes oldbytes -- side bits byte# )
    2dup mismatch
    [
        [ '[ _ swap nth ] bi@ byte-diff ] keep
    ] [
        ! Equal prefix over full (shorter) byte sequence.
        [ 1 255 ] 2dip shorter length 1 -
    ] if* ;

PRIVATE>

GENERIC: key>bytes* ( key -- bytes )

M: object key>bytes*
    object>bytes ;

M: byte-array key>bytes* ;

M: string key>bytes* utf8 encode ;

M: fixnum key>bytes* cell >le ;

M: bignum key>bytes* dup (log2) 8 /i 1 + >le ;

! Assumes that a double is never larger than a pointer
M: float key>bytes* double>bits cell >le ;

<PRIVATE

: key>bytes ( key -- bytes )
    key>bytes* ;

! Keep the byte sequence of the current key in =key-bytes= and provide a working
! environment for it with =with-key=.
SYMBOL: key-bytes
SYMBOL: current-key
SYMBOL: new-side

: with-key ( key quot -- )
    [
        { current-key key-bytes new-side } swap
        dup key>bytes left 3array zip
    ] dip with-variables ; inline

! Extract the critical byte
: byte-at ( byte# -- byte/0 )
    key-bytes get ?nth [ 0 ] unless* ;

! For the current key and cb-node determin which side to go next
: select-side ( node -- node side )
    dup [ bits>> ] [ byte#>> ] bi
    byte-at key-side ;

! ** Insertion

! Tree insertion must be done by traversing the tree from the root, as it is
! ordered.

! ** Walking the tree for the best fit

GENERIC: cb-best-fit ( node -- node )

M: f cb-best-fit ;

M: node cb-best-fit ;

M: cb-node cb-best-fit
    select-side [
        node-link cb-best-fit
    ] with-side ;

GENERIC: cb-update ( value node -- node created? )

M: f cb-update
    drop current-key get swap <node> t ;

! Attach a new leaf node and record =new-side=. New leaf node is attached
! opposite of =new-side=.
: attach-node ( value side cb-node -- cb-node )
    swap [ new-side set ] keep
    [
        [ current-key get swap <node> ] dip
        [ set-node+link ] keep
    ] with-side ;

! Update the tree by either updating a leaf node with a new key object and value
! or create a new split node and attach a fresh leaf node with the new key and
! value.
M: node cb-update
    dup key>> current-key get = [
        current-key get >>key
        swap >>value f
    ] [
        key>> key>bytes key-bytes get swap
        bytes-diff swap <cb-node>
        attach-node t
    ] if ;

! Break off the search when:
! - the top node is no longer a split node
! - the top split node is larger than the new split node (i.e. refers to a later
!   byte or more significant bit in the current byte)
: break? ( new-node node -- ? )
    { [ nip cb-node? not ]
      [ [ byte#>> ] bi@ < ]
      [ { [ [ byte#>> ] bi@ = ]
          [ [ bits>> ] bi@ < ]
        } 2&& ]
    } 2|| ;

! Walk the tree and insert =new-node= at the pre-determined best place. We have
! to keep track of the parent instead of the current node, as we might need to
! relink from the parent to =new-node=.
GENERIC: cb-insert ( new-node parent -- )

M:: cb cb-insert ( n p -- )
    p root>> :> c
    n c break?
    [ n p root<<
      new-side get [
          c n set-node-link
      ] with-side
    ]
    [ n c cb-insert ] if ;

M:: cb-node cb-insert ( n p -- )
    p select-side [
        drop
        p node-link :> c
        n c break?
        [ n p set-node-link
          new-side get [
              c n set-node-link
          ] with-side
        ]
        [ n c cb-insert ] if
    ] with-side ;

M: cb set-at ( value key cb -- )
    [ swap [
        [ root>> cb-best-fit cb-update ]
        [ swap [ cb-insert t ] [ 2drop f ] if ] bi
    ] with-key ] keep
    swap [ dup inc-count ] when drop ;

! ** Deletion

GENERIC: cb-delete ( node -- node deleted? )

M: f cb-delete f ;

M: node cb-delete
    dup key>> current-key get = [ drop f t ] [ f ] if ;

M: cb-node cb-delete ( node -- node deleted? )
    select-side [
        dup node-link dup cb-delete [
            ! ( node old-child new-child -- )
            [
                ! ( node old new )
                ! Deleted a split node (received some node)
                tuck eq? [
                    drop t
                ] [
                    swap tuck set-node-link
                    t
                ] if
            ] [
                ! Deleted a leaf node return other child.
                drop
                node+link t
            ] if*
            f
        ] when drop
    ] with-side ;

M: cb delete-at ( key cb -- )
    [ swap [ cb-delete ] with-key swap ] change-root
    swap [ dup dec-count ] when drop ;

M: cb new-assoc
    2drop <cb> ;

GENERIC: (cb-node>alist) ( node -- )

M: node (cb-node>alist)
    entry, ;

: cb-node>entry ( node -- entry ) [ byte#>> ] [ bits>> ] bi 2array ;

: cb-entry, ( node -- ) cb-node>entry , ;

M: cb-node (cb-node>alist)
    [ left>> (cb-node>alist) ]
    [ cb-entry, ]
    [ right>> (cb-node>alist) ]
    tri ;

M: cb >alist
    [ root>> (cb-node>alist) ] { } make ;

! Post-order traversal
!
! Assumes =f= in =left= and =right= slots of leaf nodes and ≠ =f= in split
! nodes.
: each-leaf-node ( node quot: ( ... entry -- ... ) -- ... )
    [ [ dup left>> ] dip over [ each-leaf-node drop ] [ nip [ node>entry ] dip call ] if ]
    [ [ right>> ] dip over [ each-leaf-node ] [ 2drop ] if ]
    2bi ; inline recursive

: >cb-alist ( tree -- alist )
    dup assoc-size <vector> [
        [ push ] curry [ root>> ] dip each-leaf-node
    ] keep ;

M: cb assoc-clone-like
    [ dup cb? [ >cb-alist ] when ] dip call-next-method ;

PRIVATE>

: >cb ( assoc -- tree )
    <cb> assoc-clone-like ;

SYNTAX: CBTREE{
        \ } [ >cb ] parse-literal ;

<PRIVATE

M: cb assoc-like drop dup cb? [ >cb ] unless ;

M: cb pprint-delims drop \ CBTREE{ \ } ;
M: cb >pprint-sequence >alist ;
M: cb pprint-narrow? drop t ;

PRIVATE>