USING: accessors arrays combinators combinators.short-circuit
kernel make math math.order sequences sequences.private typed ;
IN: lcs

<PRIVATE

: levenshtein-step ( insert delete change same? -- next )
    [ [ 1 + ] bi@ ] 2dip [ 1 + ] unless min min ;

: lcs-step ( insert delete change same? -- next )
    1 -1/0. ? + max max ; ! -1/0. is -inf (float)

TYPED:: loop-step ( i j matrix: array old new step -- )
    i j 1 + matrix nth-unsafe nth-unsafe ! insertion
    i 1 + j matrix nth-unsafe nth-unsafe ! deletion
    i j matrix nth-unsafe nth-unsafe ! replace/retain
    i old nth-unsafe j new nth-unsafe = ! same?
    step call
    i 1 + j 1 + matrix nth-unsafe set-nth-unsafe ; inline

: lcs-initialize ( |str1| |str2| -- matrix )
    <iota> [ drop 0 <array> ] with map ;

: levenshtein-initialize ( |str1| |str2| -- matrix )
    [ <iota> ] bi@ [ [ + ] curry map ] with map ;

:: run-lcs ( old new init step -- matrix )
    old length 1 + new length 1 + init call :> matrix
    old length <iota> [| i |
        new length <iota> [| j |
            i j matrix old new step loop-step
        ] each
    ] each matrix ; inline

PRIVATE>

: levenshtein ( old new -- n )
    [ levenshtein-initialize ] [ levenshtein-step ]
    run-lcs last last ;

TUPLE: retain item ;
TUPLE: delete item ;
TUPLE: insert item ;

<PRIVATE

TUPLE: trace-state old new table i j ;

: old-nth ( state -- elt )
    [ i>> 1 - ] [ old>> ] bi nth-unsafe ;

: new-nth ( state -- elt )
    [ j>> 1 - ] [ new>> ] bi nth-unsafe ;

: top-beats-side? ( state -- ? )
    [ [ i>> ] [ j>> 1 - ] [ table>> ] tri nth-unsafe nth-unsafe ]
    [ [ i>> 1 - ] [ j>> ] [ table>> ] tri nth-unsafe nth-unsafe ] bi > ;

: retained? ( state -- ? )
    {
        [ i>> 0 > ] [ j>> 0 > ]
        [ [ old-nth ] [ new-nth ] bi = ]
    } 1&& ;

: do-retain ( state -- state )
    dup old-nth retain boa ,
    [ 1 - ] change-i [ 1 - ] change-j ;

: inserted? ( state -- ? )
    {
        [ j>> 0 > ]
        [ { [ i>> zero? ] [ top-beats-side? ] } 1|| ]
    } 1&& ;

: do-insert ( state -- state )
    dup new-nth insert boa , [ 1 - ] change-j ;

: deleted? ( state -- ? )
    {
        [ i>> 0 > ]
        [ { [ j>> zero? ] [ top-beats-side? not ] } 1|| ]
    } 1&& ;

: do-delete ( state -- state )
    dup old-nth delete boa , [ 1 - ] change-i ;

: (trace-diff) ( state -- )
    {
        { [ dup retained? ] [ do-retain (trace-diff) ] }
        { [ dup inserted? ] [ do-insert (trace-diff) ] }
        { [ dup deleted? ] [ do-delete (trace-diff) ] }
        [ drop ] ! i=j=0
    } cond ;

: trace-diff ( old new table -- diff )
    [ ] [ first length 1 - ] [ length 1 - ] tri trace-state boa
    [ (trace-diff) ] { } make reverse! ;

PRIVATE>

: lcs-diff ( old new -- diff )
    2dup [ lcs-initialize ] [ lcs-step ] run-lcs trace-diff ;

: lcs ( seq1 seq2 -- lcs )
    [ lcs-diff [ retain? ] filter ] keep [ item>> ] swap map-as ;