Merge branch 'master' of git://projects.elasticdog.com/git/factor
Slava Pestov
commit
05b915f8af
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@ -17,9 +17,6 @@ IN: project-euler.007
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! SOLUTION
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! --------
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: nth-prime ( n -- n )
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1- lprimes lnth ;
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: euler007 ( -- answer )
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10001 nth-prime ;
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@ -0,0 +1,4 @@
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USING: project-euler.069 tools.test ;
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{ 510510 } [ euler069 ] unit-test
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{ 510510 } [ euler069a ] unit-test
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@ -0,0 +1,87 @@
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! Copyright (c) 2009 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators fry kernel math math.primes math.primes.factors math.ranges
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project-euler.common sequences ;
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IN: project-euler.069
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! http://projecteuler.net/index.php?section=problems&id=69
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! DESCRIPTION
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! -----------
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! Euler's Totient function, φ(n) [sometimes called the phi function], is used
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! to determine the number of numbers less than n which are relatively prime to
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! n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and
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! relatively prime to nine, φ(9)=6.
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! +----+------------------+------+-----------+
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! | n | Relatively Prime | φ(n) | n / φ(n) |
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! +----+------------------+------+-----------+
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! | 2 | 1 | 1 | 2 |
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! | 3 | 1,2 | 2 | 1.5 |
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! | 4 | 1,3 | 2 | 2 |
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! | 5 | 1,2,3,4 | 4 | 1.25 |
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! | 6 | 1,5 | 2 | 3 |
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! | 7 | 1,2,3,4,5,6 | 6 | 1.1666... |
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! | 8 | 1,3,5,7 | 4 | 2 |
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! | 9 | 1,2,4,5,7,8 | 6 | 1.5 |
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! | 10 | 1,3,7,9 | 4 | 2.5 |
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! +----+------------------+------+-----------+
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! It can be seen that n = 6 produces a maximum n / φ(n) for n ≤ 10.
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! Find the value of n ≤ 1,000,000 for which n / φ(n) is a maximum.
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! SOLUTION
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! --------
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! Brute force
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<PRIVATE
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: totient-ratio ( n -- m )
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dup totient / ;
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PRIVATE>
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: euler069 ( -- answer )
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2 1000000 [a,b] [ totient-ratio ] map
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[ supremum ] keep index 2 + ;
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! [ euler069 ] 10 ave-time
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! 25210 ms ave run time - 115.37 SD (10 trials)
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! ALTERNATE SOLUTIONS
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! -------------------
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! In order to obtain maximum n / φ(n), φ(n) needs to be low and n needs to be
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! high. Hence we need a number that has the most factors. A number with the
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! most unique factors would have fewer relatively prime.
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<PRIVATE
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: primorial ( n -- m )
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{
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{ [ dup 0 = ] [ drop V{ 1 } ] }
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{ [ dup 1 = ] [ drop V{ 2 } ] }
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[ nth-prime primes-upto ]
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} cond product ;
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: (primorial-upto) ( count limit -- m )
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'[ dup primorial _ <= ] [ 1+ dup primorial ] produce
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nip penultimate ;
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: primorial-upto ( limit -- m )
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1 swap (primorial-upto) ;
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PRIVATE>
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: euler069a ( -- answer )
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1000000 primorial-upto ;
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! [ euler069a ] 100 ave-time
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! 0 ms ave run time - 0.01 SD (100 trials)
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SOLUTION: euler069a
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@ -32,13 +32,6 @@ IN: project-euler.071
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! repeatedly until the denominator is as close to 1000000 as possible without
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! going over.
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<PRIVATE
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: penultimate ( seq -- elt )
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dup length 2 - swap nth ;
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PRIVATE>
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: euler071 ( -- answer )
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2/5 [ dup denominator 1000000 <= ] [ 3/7 mediant dup ] produce
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nip penultimate numerator ;
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@ -1,9 +1,10 @@
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! Copyright (c) 2007-2008 Aaron Schaefer.
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! Copyright (c) 2007-2009 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel make math math.functions math.matrices math.miller-rabin
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math.order math.parser math.primes.factors math.ranges math.ratios
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sequences sorting strings unicode.case parser accessors vocabs.parser
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namespaces vocabs words quotations prettyprint ;
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USING: accessors arrays kernel lists make math math.functions math.matrices
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math.miller-rabin math.order math.parser math.primes.factors
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math.primes.lists math.ranges math.ratios namespaces parser prettyprint
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quotations sequences sorting strings unicode.case vocabs vocabs.parser
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words ;
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IN: project-euler.common
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! A collection of words used by more than one Project Euler solution
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@ -16,11 +17,13 @@ IN: project-euler.common
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! log10 - #25, #134
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! max-path - #18, #67
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! mediant - #71, #73
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! nth-prime - #7, #69
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! nth-triangle - #12, #42
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! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56, #92
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! palindrome? - #4, #36, #55
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! pandigital? - #32, #38
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! pentagonal? - #44, #45
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! penultimate - #69, #71
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! propagate-all - #18, #67
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! sum-proper-divisors - #21
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! tau* - #12
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@ -78,6 +81,9 @@ PRIVATE>
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: number-length ( n -- m )
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log10 floor 1+ >integer ;
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: nth-prime ( n -- n )
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1- lprimes lnth ;
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: nth-triangle ( n -- n )
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dup 1+ * 2 / ;
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@ -90,6 +96,9 @@ PRIVATE>
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: pentagonal? ( n -- ? )
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dup 0 > [ 24 * 1+ sqrt 1+ 6 / 1 mod zero? ] [ drop f ] if ;
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: penultimate ( seq -- elt )
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dup length 2 - swap nth ;
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! Not strictly needed, but it is nice to be able to dump the triangle after the
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! propagation
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: propagate-all ( triangle -- new-triangle )
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@ -1,4 +1,4 @@
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! Copyright (c) 2007, 2008, 2009 Aaron Schaefer, Samuel Tardieu.
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! Copyright (c) 2007-2009 Aaron Schaefer, Samuel Tardieu.
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! See http://factorcode.org/license.txt for BSD license.
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USING: definitions io io.files io.pathnames kernel math math.parser
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prettyprint project-euler.ave-time sequences vocabs vocabs.loader
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@ -16,13 +16,13 @@ USING: definitions io io.files io.pathnames kernel math math.parser
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project-euler.045 project-euler.046 project-euler.047 project-euler.048
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project-euler.049 project-euler.052 project-euler.053 project-euler.054
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project-euler.055 project-euler.056 project-euler.057 project-euler.058
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project-euler.059 project-euler.063 project-euler.067 project-euler.071
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project-euler.073 project-euler.075 project-euler.076 project-euler.079
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project-euler.092 project-euler.097 project-euler.099 project-euler.100
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project-euler.116 project-euler.117 project-euler.134 project-euler.148
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project-euler.150 project-euler.151 project-euler.164 project-euler.169
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project-euler.173 project-euler.175 project-euler.186 project-euler.190
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project-euler.203 project-euler.215 ;
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project-euler.059 project-euler.063 project-euler.067 project-euler.069
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project-euler.071 project-euler.073 project-euler.075 project-euler.076
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project-euler.079 project-euler.092 project-euler.097 project-euler.099
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project-euler.100 project-euler.116 project-euler.117 project-euler.134
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project-euler.148 project-euler.150 project-euler.151 project-euler.164
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project-euler.169 project-euler.173 project-euler.175 project-euler.186
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project-euler.190 project-euler.203 project-euler.215 ;
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IN: project-euler
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<PRIVATE
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