From 84901e6dbcec870d3cb62b54200433cde2e43341 Mon Sep 17 00:00:00 2001 From: Aaron Schaefer Date: Tue, 12 Feb 2008 23:02:33 -0500 Subject: [PATCH 1/4] Solution to Project Euler problem 47 --- extra/project-euler/047/047.factor | 95 ++++++++++++++++++++++++ extra/project-euler/project-euler.factor | 8 +- 2 files changed, 99 insertions(+), 4 deletions(-) create mode 100644 extra/project-euler/047/047.factor diff --git a/extra/project-euler/047/047.factor b/extra/project-euler/047/047.factor new file mode 100644 index 0000000000..ab4d206ddc --- /dev/null +++ b/extra/project-euler/047/047.factor @@ -0,0 +1,95 @@ +! Copyright (c) 2008 Aaron Schaefer. +! See http://factorcode.org/license.txt for BSD license. +USING: arrays combinators.lib kernel math math.primes math.primes.factors math.ranges namespaces sequences ; +IN: project-euler.047 + +! http://projecteuler.net/index.php?section=problems&id=47 + +! DESCRIPTION +! ----------- + +! The first two consecutive numbers to have two distinct prime factors are: + +! 14 = 2 * 7 +! 15 = 3 * 5 + +! The first three consecutive numbers to have three distinct prime factors are: + +! 644 = 2² * 7 * 23 +! 645 = 3 * 5 * 43 +! 646 = 2 * 17 * 19. + +! Find the first four consecutive integers to have four distinct primes +! factors. What is the first of these numbers? + + +! SOLUTION +! -------- + +! Brute force, not sure why it's incredibly slow compared to other languages + + + +: euler047 ( -- answer ) + 4 646 consecutive ; + +! [ euler047 ] time +! 542708 ms run / 60548 ms GC time + + +! ALTERNATE SOLUTIONS +! ------------------- + +! Use a sieve to generate prime factor counts up to a limit, then look for a +! repetition of the specified number of factors. + + >array sieve set ; + +: is-prime? ( index -- ? ) + sieve get nth zero? ; + +: multiples ( n -- seq ) + sieve get length 1- over ; + +: increment-counts ( n -- ) + multiples [ sieve get [ 1+ ] change-nth ] each ; + +: prime-tau-upto ( limit -- seq ) + dup initialize-sieve 2 swap [a,b) [ + dup is-prime? [ increment-counts ] [ drop ] if + ] each sieve get ; + +: consecutive-under ( m limit -- n/f ) + prime-tau-upto [ dup ] dip start ; + +PRIVATE> + +: euler047a ( -- answer ) + 4 1000000 consecutive-under ; + +! [ euler047a ] 100 ave-time +! 2589 ms run / 45 ms GC ave time - 100 trials + +! TODO: I don't like that you have to specify the upper bound, maybe try making +! this lazy so it will also short-circuit when it finds the answer? + +MAIN: euler047a diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index a322f69e90..5f5ffa959e 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -13,10 +13,10 @@ USING: definitions io io.files kernel math math.parser project-euler.ave-time project-euler.033 project-euler.034 project-euler.035 project-euler.036 project-euler.037 project-euler.038 project-euler.039 project-euler.040 project-euler.041 project-euler.042 project-euler.043 project-euler.044 - project-euler.045 project-euler.046 project-euler.048 project-euler.052 - project-euler.053 project-euler.056 project-euler.067 project-euler.075 - project-euler.079 project-euler.092 project-euler.097 project-euler.134 - project-euler.169 project-euler.173 project-euler.175 ; + project-euler.045 project-euler.046 project-euler.047 project-euler.048 + project-euler.052 project-euler.053 project-euler.056 project-euler.067 + project-euler.075 project-euler.079 project-euler.092 project-euler.097 + project-euler.134 project-euler.169 project-euler.173 project-euler.175 ; IN: project-euler Date: Tue, 12 Feb 2008 23:31:10 -0500 Subject: [PATCH 2/4] Tweak Project Euler solutions to use existing words --- extra/project-euler/022/022.factor | 5 +++-- extra/project-euler/047/047.factor | 13 +++++++------ 2 files changed, 10 insertions(+), 8 deletions(-) diff --git a/extra/project-euler/022/022.factor b/extra/project-euler/022/022.factor index 5bd1797272..f3a9828e01 100644 --- a/extra/project-euler/022/022.factor +++ b/extra/project-euler/022/022.factor @@ -1,6 +1,7 @@ ! Copyright (c) 2007 Aaron Schaefer. ! See http://factorcode.org/license.txt for BSD license. -USING: ascii io.files kernel math project-euler.common sequences sorting splitting ; +USING: ascii io.files kernel math project-euler.common sequences sequences.lib + sorting splitting ; IN: project-euler.022 ! http://projecteuler.net/index.php?section=problems&id=22 @@ -31,7 +32,7 @@ IN: project-euler.022 file-contents [ quotable? ] subset "," split ; : name-scores ( seq -- seq ) - dup length [ 1+ swap alpha-value * ] 2map ; + [ 1+ swap alpha-value * ] map-index ; PRIVATE> diff --git a/extra/project-euler/047/047.factor b/extra/project-euler/047/047.factor index ab4d206ddc..98e819a7db 100644 --- a/extra/project-euler/047/047.factor +++ b/extra/project-euler/047/047.factor @@ -1,6 +1,7 @@ ! Copyright (c) 2008 Aaron Schaefer. ! See http://factorcode.org/license.txt for BSD license. -USING: arrays combinators.lib kernel math math.primes math.primes.factors math.ranges namespaces sequences ; +USING: arrays combinators.lib kernel math math.primes math.primes.factors + math.ranges namespaces sequences ; IN: project-euler.047 ! http://projecteuler.net/index.php?section=problems&id=47 @@ -54,8 +55,8 @@ PRIVATE> ! ALTERNATE SOLUTIONS ! ------------------- -! Use a sieve to generate prime factor counts up to a limit, then look for a -! repetition of the specified number of factors. +! Use a sieve to generate prime factor counts up to an arbitrary limit, then +! look for a repetition of the specified number of factors. : euler047a ( -- answer ) - 4 1000000 consecutive-under ; + 4 200000 consecutive-under ; ! [ euler047a ] 100 ave-time -! 2589 ms run / 45 ms GC ave time - 100 trials +! 503 ms run / 5 ms GC ave time - 100 trials ! TODO: I don't like that you have to specify the upper bound, maybe try making -! this lazy so it will also short-circuit when it finds the answer? +! this lazy so it could also short-circuit when it finds the answer? MAIN: euler047a From 5aedba482ecd4050a65759068cbb2e501c0992af Mon Sep 17 00:00:00 2001 From: Aaron Schaefer Date: Thu, 6 Mar 2008 21:46:25 -0500 Subject: [PATCH 3/4] Fix encoding specification for Project Euler problem 22 --- extra/project-euler/022/022.factor | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/extra/project-euler/022/022.factor b/extra/project-euler/022/022.factor index f3a9828e01..c0a48ec055 100644 --- a/extra/project-euler/022/022.factor +++ b/extra/project-euler/022/022.factor @@ -1,7 +1,7 @@ ! Copyright (c) 2007 Aaron Schaefer. ! See http://factorcode.org/license.txt for BSD license. -USING: ascii io.files kernel math project-euler.common sequences sequences.lib - sorting splitting ; +USING: ascii io.encodings.ascii io.files kernel math project-euler.common + sequences sequences.lib sorting splitting ; IN: project-euler.022 ! http://projecteuler.net/index.php?section=problems&id=22 @@ -29,7 +29,7 @@ IN: project-euler.022 : source-022 ( -- seq ) "extra/project-euler/022/names.txt" resource-path - file-contents [ quotable? ] subset "," split ; + ascii file-contents [ quotable? ] subset "," split ; : name-scores ( seq -- seq ) [ 1+ swap alpha-value * ] map-index ; From b204473c8f3fd101fdc9f36bca358edba7a9a12e Mon Sep 17 00:00:00 2001 From: Aaron Schaefer Date: Fri, 7 Mar 2008 21:38:16 -0500 Subject: [PATCH 4/4] Solution to Project Euler problem 59 --- extra/project-euler/059/059.factor | 92 ++++++++++++++++++++++++ extra/project-euler/059/cipher1.txt | 1 + extra/project-euler/project-euler.factor | 7 +- 3 files changed, 97 insertions(+), 3 deletions(-) create mode 100644 extra/project-euler/059/059.factor create mode 100644 extra/project-euler/059/cipher1.txt diff --git a/extra/project-euler/059/059.factor b/extra/project-euler/059/059.factor new file mode 100644 index 0000000000..1c20d1ab34 --- /dev/null +++ b/extra/project-euler/059/059.factor @@ -0,0 +1,92 @@ +! Copyright (c) 2008 Aaron Schaefer, Slava Pestov. +! See http://factorcode.org/license.txt for BSD license. +USING: arrays ascii assocs hashtables io.encodings.ascii io.files kernel math + math.parser namespaces sequences sequences.lib sequences.private sorting + splitting strings ; +IN: project-euler.059 + +! http://projecteuler.net/index.php?section=problems&id=59 + +! DESCRIPTION +! ----------- + +! Each character on a computer is assigned a unique code and the preferred +! standard is ASCII (American Standard Code for Information Interchange). For +! example, uppercase A = 65, asterisk (*) = 42, and lowercase k = 107. + +! A modern encryption method is to take a text file, convert the bytes to +! ASCII, then XOR each byte with a given value, taken from a secret key. The +! advantage with the XOR function is that using the same encryption key on the +! cipher text, restores the plain text; for example, 65 XOR 42 = 107, then 107 +! XOR 42 = 65. + +! For unbreakable encryption, the key is the same length as the plain text +! message, and the key is made up of random bytes. The user would keep the +! encrypted message and the encryption key in different locations, and without +! both "halves", it is impossible to decrypt the message. + +! Unfortunately, this method is impractical for most users, so the modified +! method is to use a password as a key. If the password is shorter than the +! message, which is likely, the key is repeated cyclically throughout the +! message. The balance for this method is using a sufficiently long password +! key for security, but short enough to be memorable. + +! Your task has been made easy, as the encryption key consists of three lower +! case characters. Using cipher1.txt (right click and 'Save Link/Target +! As...'), a file containing the encrypted ASCII codes, and the knowledge that +! the plain text must contain common English words, decrypt the message and +! find the sum of the ASCII values in the original text. + + +! SOLUTION +! -------- + +! Assume that the space character will be the most common, so XOR the input +! text with a space character then group the text into three "columns" since +! that's how long our key is. Then do frequency analysis on each column to +! find out what the most likely candidate is for the key. + +! NOTE: This technique would probably not work well in all cases, but luckily +! it did for this particular problem. + +number ] map ; + +TUPLE: rollover seq n ; + +C: rollover + +M: rollover length rollover-n ; + +M: rollover nth-unsafe rollover-seq [ length mod ] keep nth-unsafe ; + +INSTANCE: rollover immutable-sequence + +: decrypt ( seq key -- seq ) + over length swap [ bitxor ] 2map ; + +: frequency-analysis ( seq -- seq ) + dup prune [ + [ 2dup [ = ] curry count 2array , ] each + ] { } make nip ; inline + +: most-frequent ( seq -- elt ) + frequency-analysis sort-values keys peek ; + +: crack-key ( seq key-length -- key ) + [ " " decrypt ] dip group 1 head-slice* + flip [ most-frequent ] map ; + +PRIVATE> + +: euler059 ( -- answer ) + source-059 dup 3 crack-key decrypt sum ; + +! [ euler059 ] 100 ave-time +! 13 ms run / 0 ms GC ave time - 100 trials + +MAIN: euler059 diff --git a/extra/project-euler/059/cipher1.txt b/extra/project-euler/059/cipher1.txt new file mode 100644 index 0000000000..08cee2dba4 --- /dev/null +++ b/extra/project-euler/059/cipher1.txt @@ -0,0 +1 @@ +79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73 diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index 5f5ffa959e..25ddd9a60b 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -14,9 +14,10 @@ USING: definitions io io.files kernel math math.parser project-euler.ave-time project-euler.037 project-euler.038 project-euler.039 project-euler.040 project-euler.041 project-euler.042 project-euler.043 project-euler.044 project-euler.045 project-euler.046 project-euler.047 project-euler.048 - project-euler.052 project-euler.053 project-euler.056 project-euler.067 - project-euler.075 project-euler.079 project-euler.092 project-euler.097 - project-euler.134 project-euler.169 project-euler.173 project-euler.175 ; + project-euler.052 project-euler.053 project-euler.056 project-euler.059 + project-euler.067 project-euler.075 project-euler.079 project-euler.092 + project-euler.097 project-euler.134 project-euler.169 project-euler.173 + project-euler.175 ; IN: project-euler