From fe2125399ca86acff53290fc7df888850c082496 Mon Sep 17 00:00:00 2001 From: Guillaume Nargeot Date: Sat, 26 Sep 2009 19:07:31 +0900 Subject: [PATCH 1/4] Slightly modified project euler 72, and added some comments --- extra/project-euler/072/072.factor | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/extra/project-euler/072/072.factor b/extra/project-euler/072/072.factor index de6312f2a7..9fab6788bd 100644 --- a/extra/project-euler/072/072.factor +++ b/extra/project-euler/072/072.factor @@ -30,7 +30,7 @@ IN: project-euler.072 ! The answer can be found by adding totient(n) for 2 ≤ n ≤ 1e6 : euler072 ( -- answer ) - 2 1000000 [a,b] [ totient ] [ + ] map-reduce ; + 2 1000000 [a,b] [ totient ] sigma ; ! [ euler072 ] 100 ave-time ! 5274 ms ave run time - 102.7 SD (100 trials) From 6f87a9c4e42f3f34f351f291fa4b0e926abc2e35 Mon Sep 17 00:00:00 2001 From: Guillaume Nargeot Date: Sat, 26 Sep 2009 19:09:42 +0900 Subject: [PATCH 2/4] Solution to Project Euler problem 65 --- extra/project-euler/065/065-tests.factor | 4 ++ extra/project-euler/065/065.factor | 77 ++++++++++++++++++++++++ extra/project-euler/project-euler.factor | 18 +++--- 3 files changed, 90 insertions(+), 9 deletions(-) create mode 100644 extra/project-euler/065/065-tests.factor create mode 100644 extra/project-euler/065/065.factor diff --git a/extra/project-euler/065/065-tests.factor b/extra/project-euler/065/065-tests.factor new file mode 100644 index 0000000000..8d16cce32e --- /dev/null +++ b/extra/project-euler/065/065-tests.factor @@ -0,0 +1,4 @@ +USING: project-euler.065 tools.test ; +IN: project-euler.065.tests + +[ 272 ] [ euler065 ] unit-test diff --git a/extra/project-euler/065/065.factor b/extra/project-euler/065/065.factor new file mode 100644 index 0000000000..588c38c53d --- /dev/null +++ b/extra/project-euler/065/065.factor @@ -0,0 +1,77 @@ +! Copyright (c) 2009 Guillaume Nargeot. +! See http://factorcode.org/license.txt for BSD license. +USING: kernel math lists lists.lazy project-euler.common sequences ; +IN: project-euler.065 + +! http://projecteuler.net/index.php?section=problems&id=065 + +! DESCRIPTION +! ----------- + +! The square root of 2 can be written as an infinite continued fraction. + +! 1 +! √2 = 1 + ------------------------- +! 1 +! 2 + --------------------- +! 1 +! 2 + ----------------- +! 1 +! 2 + ------------- +! 2 + ... + +! The infinite continued fraction can be written, √2 = [1;(2)], (2) indicates +! that 2 repeats ad infinitum. In a similar way, √23 = [4;(1,3,1,8)]. + +! It turns out that the sequence of partial values of continued fractions for +! square roots provide the best rational approximations. Let us consider the +! convergents for √2. + +! 1 3 1 7 1 17 1 41 +! 1 + - = - ; 1 + ----- = - ; 1 + --------- = -- ; 1 + ------------- = -- +! 2 2 1 5 1 12 1 29 +! 2 + - 2 + ----- 2 + --------- +! 2 1 1 +! 2 + - 2 + ----- +! 2 1 +! 2 + - +! 2 + +! Hence the sequence of the first ten convergents for √2 are: +! 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408, 1393/985, 3363/2378, ... + +! What is most surprising is that the important mathematical constant, +! e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...]. + +! The first ten terms in the sequence of convergents for e are: +! 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ... + +! The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17. + +! Find the sum of digits in the numerator of the 100th convergent of the +! continued fraction for e. + + +! SOLUTION +! -------- + +array reverse 0 + [ + recip ] reduce 2 + ; + +PRIVATE> + +: euler065 ( -- answer ) + 100 e-frac numerator number>digits sum ; + +! [ euler065 ] 100 ave-time +! 4 ms ave run time - 0.33 SD (100 trials) + +SOLUTION: euler065 diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index 1bba3182d1..b67b07e06d 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -16,15 +16,15 @@ USING: definitions io io.files io.pathnames kernel math math.parser project-euler.045 project-euler.046 project-euler.047 project-euler.048 project-euler.049 project-euler.052 project-euler.053 project-euler.054 project-euler.055 project-euler.056 project-euler.057 project-euler.058 - project-euler.059 project-euler.063 project-euler.067 project-euler.069 - project-euler.071 project-euler.072 project-euler.073 project-euler.074 - project-euler.075 project-euler.076 project-euler.079 project-euler.085 - project-euler.092 project-euler.097 project-euler.099 project-euler.100 - project-euler.102 project-euler.112 project-euler.116 project-euler.117 - project-euler.124 project-euler.134 project-euler.148 project-euler.150 - project-euler.151 project-euler.164 project-euler.169 project-euler.173 - project-euler.175 project-euler.186 project-euler.190 project-euler.203 - project-euler.215 ; + project-euler.059 project-euler.063 project-euler.065 project-euler.067 + project-euler.069 project-euler.071 project-euler.072 project-euler.073 + project-euler.074 project-euler.075 project-euler.076 project-euler.079 + project-euler.085 project-euler.092 project-euler.097 project-euler.099 + project-euler.100 project-euler.102 project-euler.112 project-euler.116 + project-euler.117 project-euler.124 project-euler.134 project-euler.148 + project-euler.150 project-euler.151 project-euler.164 project-euler.169 + project-euler.173 project-euler.175 project-euler.186 project-euler.190 + project-euler.203 project-euler.215 ; IN: project-euler Date: Mon, 12 Oct 2009 21:38:34 +0900 Subject: [PATCH 3/4] Solution to Project Euler problem 188 --- extra/project-euler/188/188-tests.factor | 4 +++ extra/project-euler/188/188.factor | 43 ++++++++++++++++++++++++ extra/project-euler/project-euler.factor | 2 +- 3 files changed, 48 insertions(+), 1 deletion(-) create mode 100755 extra/project-euler/188/188-tests.factor create mode 100755 extra/project-euler/188/188.factor diff --git a/extra/project-euler/188/188-tests.factor b/extra/project-euler/188/188-tests.factor new file mode 100755 index 0000000000..aa0debbbe3 --- /dev/null +++ b/extra/project-euler/188/188-tests.factor @@ -0,0 +1,4 @@ +USING: project-euler.188 tools.test ; +IN: project-euler.188.tests + +[ 95962097 ] [ euler188 ] unit-test diff --git a/extra/project-euler/188/188.factor b/extra/project-euler/188/188.factor new file mode 100755 index 0000000000..559cd8c5c1 --- /dev/null +++ b/extra/project-euler/188/188.factor @@ -0,0 +1,43 @@ +! Copyright (c) 2009 Guillaume Nargeot. +! See http://factorcode.org/license.txt for BSD license. +USING: kernel math math.functions project-euler.common ; +IN: project-euler.188 + +! http://projecteuler.net/index.php?section=problems&id=188 + +! DESCRIPTION +! ----------- + +! The hyperexponentiation or tetration of a number a by a positive integer b, +! denoted by a↑↑b or ^(b)a, is recursively defined by: + +! a↑↑1 = a, +! a↑↑(k+1) = a^(a↑↑k). + +! Thus we have e.g. 3↑↑2 = 3^3 = 27, hence +! 3↑↑3 = 3^27 = 7625597484987 and +! 3↑↑4 is roughly 10^(3.6383346400240996*10^12). + +! Find the last 8 digits of 1777↑↑1855. + + +! SOLUTION +! -------- + +! Using modular exponentiation. +! http://en.wikipedia.org/wiki/Modular_exponentiation + + + +: euler188 ( -- answer ) + 1777 1855 10 8 ^ hyper-exp-mod ; + +! [ euler188 ] 100 ave-time +! 4 ms ave run time - 0.05 SD (100 trials) + +SOLUTION: euler188 diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index 41420da803..401e53d185 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -24,7 +24,7 @@ USING: definitions io io.files io.pathnames kernel math math.parser project-euler.116 project-euler.117 project-euler.124 project-euler.134 project-euler.148 project-euler.150 project-euler.151 project-euler.164 project-euler.169 project-euler.173 project-euler.175 project-euler.186 - project-euler.190 project-euler.203 project-euler.215 ; + project-euler.188 project-euler.190 project-euler.203 project-euler.215 ; IN: project-euler Date: Mon, 12 Oct 2009 22:01:29 +0900 Subject: [PATCH 4/4] Added author --- extra/project-euler/065/authors.txt | 1 + extra/project-euler/072/authors.txt | 1 + extra/project-euler/074/authors.txt | 1 + extra/project-euler/085/authors.txt | 1 + extra/project-euler/102/authors.txt | 1 + extra/project-euler/112/authors.txt | 1 + extra/project-euler/124/authors.txt | 1 + extra/project-euler/188/authors.txt | 1 + 8 files changed, 8 insertions(+) create mode 100644 extra/project-euler/065/authors.txt create mode 100644 extra/project-euler/072/authors.txt create mode 100644 extra/project-euler/074/authors.txt create mode 100644 extra/project-euler/085/authors.txt create mode 100644 extra/project-euler/102/authors.txt create mode 100644 extra/project-euler/112/authors.txt create mode 100644 extra/project-euler/124/authors.txt create mode 100644 extra/project-euler/188/authors.txt diff --git a/extra/project-euler/065/authors.txt b/extra/project-euler/065/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/065/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/072/authors.txt b/extra/project-euler/072/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/072/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/074/authors.txt b/extra/project-euler/074/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/074/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/085/authors.txt b/extra/project-euler/085/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/085/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/102/authors.txt b/extra/project-euler/102/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/102/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/112/authors.txt b/extra/project-euler/112/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/112/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/124/authors.txt b/extra/project-euler/124/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/124/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot diff --git a/extra/project-euler/188/authors.txt b/extra/project-euler/188/authors.txt new file mode 100644 index 0000000000..6eb6698c00 --- /dev/null +++ b/extra/project-euler/188/authors.txt @@ -0,0 +1 @@ +Guillaume Nargeot