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common.factor
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common.factor
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! Copyright (c) 2007-2010 Aaron Schaefer.
! The contents of this file are licensed under the Simplified BSD License
! A copy of the license is available at https://factorcode.org/license.txt
USING: accessors arrays byte-arrays hints kernel lists make
math math.functions math.matrices math.order math.parser
math.primes.factors math.primes.lists ranges math.ratios
math.vectors parser prettyprint sequences sorting strings
unicode vocabs.parser words ;
IN: project-euler.common
! A collection of words used by more than one Project Euler solution
! and/or related words that could be useful for future problems.
! Problems using each public word
! -------------------------------
! alpha-value - #22, #42
! cartesian-product - #4, #27, #29, #32, #33, #43, #44, #56
! log10 - #25, #134
! max-path - #18, #67
! mediant - #71, #73
! nth-prime - #7, #69
! nth-triangle - #12, #42
! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56, #92, #206
! palindrome? - #4, #36, #55
! pandigital? - #32, #38
! pentagonal? - #44, #45
! penultimate - #69, #71
! propagate-all - #18, #67
! permutations? - #49, #70
! sum-proper-divisors - #21
! tau* - #12
! [uad]-transform - #39, #75
: nth-pair ( seq n -- nth next )
tail-slice first2 ;
: perfect-square? ( n -- ? )
dup sqrt mod zero? ;
: alpha-value ( str -- n )
>lower [ CHAR: a - 1 + ] map-sum ;
: mediant ( a/c b/d -- (a+b)/(c+d) )
2>fraction [ + ] 2bi@ / ;
<PRIVATE
: max-children ( seq -- seq )
[ dup length 1 - <iota> [ nth-pair max , ] with each ] { } make ;
PRIVATE>
: max-path ( triangle -- n )
dup length 1 > [
2 cut* first2 max-children v+ suffix max-path
] [
first first
] if ;
: number>digits ( n -- seq )
[ dup 0 = not ] [ 10 /mod ] produce reverse! nip ;
: digits>number ( seq -- n )
0 [ [ 10 * ] [ + ] bi* ] reduce ;
: number-length ( n -- m )
abs [
1
] [
1 0 [ 2over >= ]
[ [ 10 * ] [ 1 + ] bi* ] while 2nip
] if-zero ;
: nth-place ( x n -- y )
10^ [ * round >integer ] keep /f ;
: nth-prime ( n -- n )
1 - lprimes lnth ;
: nth-triangle ( n -- n )
dup 1 + * 2 / ;
: palindrome? ( n -- ? )
number>string dup reverse = ;
: pandigital? ( n -- ? )
number>string sort >string "123456789" = ;
: pentagonal? ( n -- ? )
dup 0 > [ 24 * 1 + sqrt 1 + 6 / 1 mod zero? ] [ drop f ] if ; inline
: penultimate ( seq -- elt )
dup length 2 - swap nth ;
<PRIVATE
! Propagate one row into the upper one
: propagate ( bottom top -- newtop )
[ over rest rot first2 max rot + ] map nip ;
PRIVATE>
! Not strictly needed, but it is nice to be able to dump the
! triangle after the propagation
: propagate-all ( triangle -- new-triangle )
reverse unclip dup rot
[ propagate dup ] map nip
reverse swap suffix ;
<PRIVATE
: count-digits ( n -- byte-array )
10 <byte-array> [
'[ 10 /mod _ [ 1 + ] change-nth dup 0 > ] loop drop
] keep ;
HINTS: count-digits fixnum ;
PRIVATE>
: permutations? ( n m -- ? )
[ count-digits ] same? ;
<PRIVATE
: (sum-divisors) ( n -- sum )
dup sqrt >integer [1..b] [
[ 2dup divisor? [ 2dup / + , ] [ drop ] if ] each
dup perfect-square? [ sqrt >fixnum neg , ] [ drop ] if
] { } make sum ;
PRIVATE>
: sum-divisors ( n -- sum )
dup 4 < [ { 0 1 3 4 } nth ] [ (sum-divisors) ] if ;
: sum-proper-divisors ( n -- sum )
[ sum-divisors ] keep - ;
: abundant? ( n -- ? )
dup sum-proper-divisors < ;
: deficient? ( n -- ? )
dup sum-proper-divisors > ;
: perfect? ( n -- ? )
dup sum-proper-divisors = ;
! The divisor function, counts the number of divisors
: tau ( m -- n )
group-factors flip second 1 [ 1 + * ] reduce ;
! Optimized brute-force, is often faster than prime factorization
: tau* ( m -- n )
factor-2s dup [ 1 + ]
[ perfect-square? -1 0 ? ]
[ dup sqrt >fixnum [1..b] ] tri* [
dupd divisor? [ [ 2 + ] dip ] when
] each drop * ;
<PRIVATE
: transform ( triple matrix -- new-triple )
[ 1array ] dip mdot first ;
PRIVATE>
! These transforms are for generating primitive Pythagorean triples
: u-transform ( triple -- new-triple )
{ { 1 2 2 } { -2 -1 -2 } { 2 2 3 } } transform ;
: a-transform ( triple -- new-triple )
{ { 1 2 2 } { 2 1 2 } { 2 2 3 } } transform ;
: d-transform ( triple -- new-triple )
{ { -1 -2 -2 } { 2 1 2 } { 2 2 3 } } transform ;
SYNTAX: SOLUTION:
scan-word
[ name>> "-main" append create-word-in ] keep
[ drop current-vocab main<< ]
[ [ . ] swap prefix ( -- ) define-declared ]
2bi ;