USING: accessors kernel math ;
IN: project-euler.215

TUPLE: block two three ;
TUPLE: end { ways integer } ;

: <block> ( l r -- t ) block boa ; inline
: <end> ( n -- t ) end boa ; inline
: <failure> end new ; inline
: <success> 1 <end> ; inline

: failure? ( t -- ? ) ways>> zero? ; inline

: add-ends ( t t -- t ) [ ways>> ] bi@ + <end> ; inline

: choice ( t p q -- t t ) [ [ two>> ] [ three>> ] bi ] 2dip bi* ; inline

: merge ( t t -- t )
   over block? over block? [
     [ [ [ two>>   ] bi@ merge ]
       [ [ three>> ] bi@ merge ] 2bi <block>
     ] [ nip ] if
   ] [
     [ drop ] [ add-ends ] if
   ] if ;

GENERIC: h-1 ( t -- t )
GENERIC: h0 ( t -- t )
GENERIC: h1 ( t -- t )
GENERIC: h2 ( t -- t )

M: block h-1 [ h1 ] [ h2 ] choice merge ;
M: block h0 drop <failure> ;
M: block h1 [ [ h1 ] [ h2 ] choice merge ]
            [ [ h0 ] [ h1 ] choice merge ] bi <block> ;
M: block h2 [ h1 ] [ h2 ] choice merge <failure> swap <block> ;

M: end h-1 drop <failure> ;
M: end h0 ;
M: end h1 drop <failure> ;
M: end h2 dup failure? [ <failure> <block> ] unless ;

: next-row [ h-1 ] [ h1 ] choice swap <block> ;

: first-row
  [ <failure> <success> <failure> ] dip
  1- [ over roll <block> ] times 2nip ;

GENERIC: total ( t -- n )
M: block total [ total ] dup choice + ;
M: end   total ways>> ;

: solve ( width height -- ways )
  [ first-row ] dip 1- [ next-row ] times total ;

: euler215 32 10 solve ;