1 ! Copyright (c) 2007-2009 Aaron Schaefer.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: accessors arrays kernel lists make math math.functions math.matrices
4 math.primes.miller-rabin math.order math.parser math.primes.factors
5 math.primes.lists math.ranges math.ratios namespaces parser prettyprint
6 quotations sequences sorting strings unicode.case vocabs vocabs.parser
8 IN: project-euler.common
10 ! A collection of words used by more than one Project Euler solution
11 ! and/or related words that could be useful for future problems.
13 ! Problems using each public word
14 ! -------------------------------
15 ! alpha-value - #22, #42
16 ! cartesian-product - #4, #27, #29, #32, #33, #43, #44, #56
21 ! nth-triangle - #12, #42
22 ! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56, #92
23 ! palindrome? - #4, #36, #55
24 ! pandigital? - #32, #38
25 ! pentagonal? - #44, #45
26 ! penultimate - #69, #71
27 ! propagate-all - #18, #67
28 ! sum-proper-divisors - #21
30 ! [uad]-transform - #39, #75
33 : nth-pair ( seq n -- nth next )
36 : perfect-square? ( n -- ? )
41 : max-children ( seq -- seq )
42 [ dup length 1 - [ nth-pair max , ] with each ] { } make ;
44 ! Propagate one row into the upper one
45 : propagate ( bottom top -- newtop )
46 [ over rest rot first2 max rot + ] map nip ;
48 : (sum-divisors) ( n -- sum )
49 dup sqrt >integer [1,b] [
50 [ 2dup divisor? [ 2dup / + , ] [ drop ] if ] each
51 dup perfect-square? [ sqrt >fixnum neg , ] [ drop ] if
54 : transform ( triple matrix -- new-triple )
55 [ 1array ] dip m. first ;
59 : alpha-value ( str -- n )
60 >lower [ CHAR: a - 1 + ] map-sum ;
62 : cartesian-product ( seq1 seq2 -- seq1xseq2 )
63 [ [ 2array ] with map ] curry map concat ;
65 : mediant ( a/c b/d -- (a+b)/(c+d) )
66 2>fraction [ + ] 2bi@ / ;
68 : max-path ( triangle -- n )
70 2 cut* first2 max-children [ + ] 2map suffix max-path
75 : number>digits ( n -- seq )
76 [ dup 0 = not ] [ 10 /mod ] produce reverse nip ;
78 : number-length ( n -- m )
83 [ [ 10 * ] [ 1 + ] bi* ] while 2nip
86 : nth-prime ( n -- n )
89 : nth-triangle ( n -- n )
92 : palindrome? ( n -- ? )
93 number>string dup reverse = ;
95 : pandigital? ( n -- ? )
96 number>string natural-sort >string "123456789" = ;
98 : pentagonal? ( n -- ? )
99 dup 0 > [ 24 * 1 + sqrt 1 + 6 / 1 mod zero? ] [ drop f ] if ; inline
101 : penultimate ( seq -- elt )
102 dup length 2 - swap nth ;
104 ! Not strictly needed, but it is nice to be able to dump the triangle after the
106 : propagate-all ( triangle -- new-triangle )
107 reverse [ first dup ] [ rest ] bi
108 [ propagate dup ] map nip reverse swap suffix ;
110 : sum-divisors ( n -- sum )
111 dup 4 < [ { 0 1 3 4 } nth ] [ (sum-divisors) ] if ;
113 : sum-proper-divisors ( n -- sum )
114 dup sum-divisors swap - ;
116 : abundant? ( n -- ? )
117 dup sum-proper-divisors < ;
119 : deficient? ( n -- ? )
120 dup sum-proper-divisors > ;
122 : perfect? ( n -- ? )
123 dup sum-proper-divisors = ;
125 ! The divisor function, counts the number of divisors
127 group-factors flip second 1 [ 1 + * ] reduce ;
129 ! Optimized brute-force, is often faster than prime factorization
131 factor-2s dup [ 1 + ]
132 [ perfect-square? -1 0 ? ]
133 [ dup sqrt >fixnum [1,b] ] tri* [
134 dupd divisor? [ [ 2 + ] dip ] when
137 ! These transforms are for generating primitive Pythagorean triples
138 : u-transform ( triple -- new-triple )
139 { { 1 2 2 } { -2 -1 -2 } { 2 2 3 } } transform ;
140 : a-transform ( triple -- new-triple )
141 { { 1 2 2 } { 2 1 2 } { 2 2 3 } } transform ;
142 : d-transform ( triple -- new-triple )
143 { { -1 -2 -2 } { 2 1 2 } { 2 2 3 } } transform ;
147 [ name>> "-main" append create-in ] keep
148 [ drop current-vocab (>>main) ]
149 [ [ . ] swap prefix (( -- )) define-declared ]