! Copyright (C) 2009 Jon Harper.
! See http://factorcode.org/license.txt for BSD license.
USING: assocs kernel math math.combinatorics math.functions
math.parser math.primes namespaces project-euler.common
sequences sets strings ;
IN: project-euler.051

SYMBOL: family-count
SYMBOL: large-families
: reset-globals ( -- ) 
    H{ } clone family-count set
    H{ } clone large-families set ;


: *-if-index ( char index combination -- char )
    swap member? [ drop CHAR: * ] when ;

: family ( combination seq -- family )
    [ *-if-index ] with map-index ;

: family-with-n-stars ( stra n -- seq )
    [ [ length iota ] keep ] dip swap [ family ] curry map-combinations ;

: possible-family? ( stra family -- ? )
    [ CHAR: * = [ drop 0 ] unless ] 2map [ 0 = not ] filter prune length 1 = ; 
: families ( stra -- seq )
    dup 
    dup length iota rest [ family-with-n-stars ] with map concat
    [ possible-family? ] with filter ;

: 10^n ( n -- 10^n ) 10 swap ^ ; inline

: n-digits-primes ( n -- primes )
    [ 1 - 10^n [ <= ] curry ] [ 10^n ] bi primes-upto swap trim-head ; 


: save-family ( family -- )
    family-count get dupd at 8 = [ large-families get conjoin ] [ drop ] if ;
: increment-family ( family -- )
    family-count get dupd at* [ 1 + ] [ drop 1 ] if swap family-count get set-at ;
: handle-family ( family -- )
    [ increment-family ] [ save-family ] bi ;

! Test all primes that have length n
: test-n-digits-primes ( n -- seq )
    reset-globals 
    n-digits-primes 
    [ number>string families [ handle-family ] each ] each
    large-families get ;

: fill-*-with-ones ( str -- str )
    [ dup CHAR: * = [ drop CHAR: 1 ] when ] map ;

! recursively test all primes by length until we find an answer
: (euler051) ( i -- answer )
    dup test-n-digits-primes 
    dup assoc-size 0 > 
    [ nip values [ fill-*-with-ones string>number ] map infimum ]
    [ drop 1 + (euler051) ] if ;

: euler051 ( -- answer )
    2 (euler051) ;