Merge branch 'master' of git://projects.elasticdog.com/git/factor
Slava Pestov
commit
50e300c080
|
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@ -1,5 +1,4 @@
|
|||
USING: accessors kernel math math.order poker poker.private
|
||||
tools.test ;
|
||||
USING: accessors kernel math math.order poker poker.private tools.test ;
|
||||
IN: poker.tests
|
||||
|
||||
[ 134236965 ] [ "KD" >ckf ] unit-test
|
||||
|
|
|
|||
|
|
@ -1,5 +1,4 @@
|
|||
! Copyright (c) 2009 Aaron Schaefer. All rights reserved.
|
||||
! Copyright (c) 2009 Doug Coleman.
|
||||
! Copyright (c) 2009 Aaron Schaefer, Doug Coleman. All rights reserved.
|
||||
! The contents of this file are licensed under the Simplified BSD License
|
||||
! A copy of the license is available at http://factorcode.org/license.txt
|
||||
USING: accessors arrays ascii assocs binary-search combinators
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
! Copyright (c) 2009 Aaron Schaefer.
|
||||
! See http://factorcode.org/license.txt for BSD license.
|
||||
USING: arrays byte-arrays fry hints kernel math math.combinatorics
|
||||
math.functions math.parser math.primes project-euler.common sequences sets ;
|
||||
USING: arrays byte-arrays fry kernel math math.combinatorics math.functions
|
||||
math.parser math.primes project-euler.common sequences sets ;
|
||||
IN: project-euler.049
|
||||
|
||||
! http://projecteuler.net/index.php?section=problems&id=49
|
||||
|
|
@ -25,16 +25,6 @@ IN: project-euler.049
|
|||
|
||||
<PRIVATE
|
||||
|
||||
: count-digits ( n -- byte-array )
|
||||
10 <byte-array> [
|
||||
'[ 10 /mod _ [ 1 + ] change-nth dup 0 > ] loop drop
|
||||
] keep ;
|
||||
|
||||
HINTS: count-digits fixnum ;
|
||||
|
||||
: permutations? ( n m -- ? )
|
||||
[ count-digits ] bi@ = ;
|
||||
|
||||
: collect-permutations ( seq -- seq )
|
||||
[ V{ } clone ] [ dup ] bi* [
|
||||
dupd '[ _ permutations? ] filter
|
||||
|
|
|
|||
|
|
@ -0,0 +1,4 @@
|
|||
USING: project-euler.070 tools.test ;
|
||||
IN: project-euler.070.tests
|
||||
|
||||
[ 8319823 ] [ euler070 ] unit-test
|
||||
|
|
@ -0,0 +1,67 @@
|
|||
! Copyright (c) 2010 Aaron Schaefer. All rights reserved.
|
||||
! The contents of this file are licensed under the Simplified BSD License
|
||||
! A copy of the license is available at http://factorcode.org/license.txt
|
||||
USING: arrays assocs combinators.short-circuit kernel math math.combinatorics
|
||||
math.functions math.primes math.ranges project-euler.common sequences ;
|
||||
IN: project-euler.070
|
||||
|
||||
! http://projecteuler.net/index.php?section=problems&id=70
|
||||
|
||||
! DESCRIPTION
|
||||
! -----------
|
||||
|
||||
! Euler's Totient function, φ(n) [sometimes called the phi function], is used
|
||||
! to determine the number of positive numbers less than or equal to n which are
|
||||
! relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less
|
||||
! than nine and relatively prime to nine, φ(9)=6. The number 1 is considered to
|
||||
! be relatively prime to every positive number, so φ(1)=1.
|
||||
|
||||
! Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation
|
||||
! of 79180.
|
||||
|
||||
! Find the value of n, 1 < n < 10^(7), for which φ(n) is a permutation of n and
|
||||
! the ratio n/φ(n) produces a minimum.
|
||||
|
||||
|
||||
! SOLUTION
|
||||
! --------
|
||||
|
||||
! For n/φ(n) to be minimised, φ(n) must be as close to n as possible; that is,
|
||||
! we want to maximise φ(n). The minimal solution for n/φ(n) would be if n was
|
||||
! prime giving n/(n-1) but since n-1 never is a permutation of n it cannot be
|
||||
! prime.
|
||||
|
||||
! The next best thing would be if n only consisted of 2 prime factors close to
|
||||
! (in this case) sqrt(10000000). Hence n = p1*p2 and we only need to search
|
||||
! through a list of known prime pairs. In addition:
|
||||
|
||||
! φ(p1*p2) = p1*p2*(1-1/p1)(1-1/p2) = (p1-1)(p2-1)
|
||||
|
||||
! ...so we can compute φ(n) more efficiently.
|
||||
|
||||
<PRIVATE
|
||||
|
||||
! NOTE: ±1000 is an arbitrary range
|
||||
: likely-prime-factors ( -- seq )
|
||||
7 10^ sqrt >integer 1000 [ - ] [ + ] 2bi primes-between ; inline
|
||||
|
||||
: n-and-phi ( seq -- seq' )
|
||||
#! ( seq = { p1, p2 } -- seq' = { n, φ(n) } )
|
||||
[ product ] [ [ 1 - ] map product ] bi 2array ;
|
||||
|
||||
: fit-requirements? ( seq -- ? )
|
||||
first2 { [ drop 7 10^ < ] [ permutations? ] } 2&& ;
|
||||
|
||||
: minimum-ratio ( seq -- n )
|
||||
[ [ first2 / ] map [ infimum ] keep index ] keep nth first ;
|
||||
|
||||
PRIVATE>
|
||||
|
||||
: euler070 ( -- answer )
|
||||
likely-prime-factors 2 all-combinations [ n-and-phi ] map
|
||||
[ fit-requirements? ] filter minimum-ratio ;
|
||||
|
||||
! [ euler070 ] 100 ave-time
|
||||
! 379 ms ave run time - 1.15 SD (100 trials)
|
||||
|
||||
SOLUTION: euler070
|
||||
|
|
@ -0,0 +1,4 @@
|
|||
USING: project-euler.206 tools.test ;
|
||||
IN: project-euler.206.tests
|
||||
|
||||
[ 1389019170 ] [ euler206 ] unit-test
|
||||
|
|
@ -0,0 +1,46 @@
|
|||
! Copyright (c) 2010 Aaron Schaefer. All rights reserved.
|
||||
! The contents of this file are licensed under the Simplified BSD License
|
||||
! A copy of the license is available at http://factorcode.org/license.txt
|
||||
USING: grouping kernel math math.ranges project-euler.common sequences ;
|
||||
IN: project-euler.206
|
||||
|
||||
! http://projecteuler.net/index.php?section=problems&id=206
|
||||
|
||||
! DESCRIPTION
|
||||
! -----------
|
||||
|
||||
! Find the unique positive integer whose square has the form
|
||||
! 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit.
|
||||
|
||||
|
||||
! SOLUTION
|
||||
! --------
|
||||
|
||||
! Through mathematical analysis, we know that the number must end in 00, and
|
||||
! the only way to get the last digits to be 900, is for our answer to end in
|
||||
! 30 or 70.
|
||||
|
||||
<PRIVATE
|
||||
|
||||
! 1020304050607080900 sqrt, rounded up to the nearest 30 ending
|
||||
CONSTANT: lo 1010101030
|
||||
|
||||
! 1929394959697989900 sqrt, rounded down to the nearest 70 ending
|
||||
CONSTANT: hi 1389026570
|
||||
|
||||
: form-fitting? ( n -- ? )
|
||||
number>digits 2 group [ first ] map
|
||||
{ 1 2 3 4 5 6 7 8 9 0 } = ;
|
||||
|
||||
: candidates ( -- seq )
|
||||
lo lo 40 + [ hi 100 <range> ] bi@ append ;
|
||||
|
||||
PRIVATE>
|
||||
|
||||
: euler206 ( -- answer )
|
||||
candidates [ sq form-fitting? ] find-last nip ;
|
||||
|
||||
! [ euler206 ] 100 ave-time
|
||||
! 321 ms ave run time - 8.33 SD (100 trials)
|
||||
|
||||
SOLUTION: euler206
|
||||
|
|
@ -1,49 +1,64 @@
|
|||
! Copyright (C) 2009 Jon Harper.
|
||||
! Copyright (c) 2009 Jon Harper.
|
||||
! See http://factorcode.org/license.txt for BSD license.
|
||||
USING: project-euler.common math kernel sequences math.functions math.ranges prettyprint io threads math.parser locals arrays namespaces ;
|
||||
USING: arrays io kernel locals math math.functions math.parser math.ranges
|
||||
namespaces prettyprint project-euler.common sequences threads ;
|
||||
IN: project-euler.255
|
||||
|
||||
! http://projecteuler.net/index.php?section=problems&id=255
|
||||
|
||||
! DESCRIPTION
|
||||
! -----------
|
||||
! We define the rounded-square-root of a positive integer n as the square root of n rounded to the nearest integer.
|
||||
!
|
||||
! The following procedure (essentially Heron's method adapted to integer arithmetic) finds the rounded-square-root of n:
|
||||
!
|
||||
! Let d be the number of digits of the number n.
|
||||
! If d is odd, set x_(0) = 2×10^((d-1)⁄2).
|
||||
! If d is even, set x_(0) = 7×10^((d-2)⁄2).
|
||||
! Repeat:
|
||||
!
|
||||
! until x_(k+1) = x_(k).
|
||||
!
|
||||
|
||||
! We define the rounded-square-root of a positive integer n as the square root
|
||||
! of n rounded to the nearest integer.
|
||||
|
||||
! The following procedure (essentially Heron's method adapted to integer
|
||||
! arithmetic) finds the rounded-square-root of n:
|
||||
|
||||
! Let d be the number of digits of the number n.
|
||||
! If d is odd, set x_(0) = 2×10^((d-1)⁄2).
|
||||
! If d is even, set x_(0) = 7×10^((d-2)⁄2).
|
||||
|
||||
! Repeat: [see URL for figure ]
|
||||
|
||||
! until x_(k+1) = x_(k).
|
||||
|
||||
! As an example, let us find the rounded-square-root of n = 4321.
|
||||
! n has 4 digits, so x_(0) = 7×10^((4-2)⁄2) = 70.
|
||||
!
|
||||
! Since x_(2) = x_(1), we stop here.
|
||||
! So, after just two iterations, we have found that the rounded-square-root of 4321 is 66 (the actual square root is 65.7343137…).
|
||||
!
|
||||
! The number of iterations required when using this method is surprisingly low.
|
||||
! For example, we can find the rounded-square-root of a 5-digit integer (10,000 ≤ n ≤ 99,999) with an average of 3.2102888889 iterations (the average value was rounded to 10 decimal places).
|
||||
!
|
||||
! Using the procedure described above, what is the average number of iterations required to find the rounded-square-root of a 14-digit number (10^(13) ≤ n < 10^(14))?
|
||||
! Give your answer rounded to 10 decimal places.
|
||||
!
|
||||
! Note: The symbols ⌊x⌋ and ⌈x⌉ represent the floor function and ceiling function respectively.
|
||||
!
|
||||
<PRIVATE
|
||||
|
||||
: round-to-10-decimals ( a -- b ) 1.0e10 * round 1.0e10 / ;
|
||||
! [ see URL for figure ]
|
||||
|
||||
! Since x_(2) = x_(1), we stop here.
|
||||
|
||||
! So, after just two iterations, we have found that the rounded-square-root of
|
||||
! 4321 is 66 (the actual square root is 65.7343137…).
|
||||
|
||||
! The number of iterations required when using this method is surprisingly low.
|
||||
! For example, we can find the rounded-square-root of a 5-digit integer
|
||||
! (10,000 ≤ n ≤ 99,999) with an average of 3.2102888889 iterations (the average
|
||||
! value was rounded to 10 decimal places).
|
||||
|
||||
! Using the procedure described above, what is the average number of iterations
|
||||
! required to find the rounded-square-root of a 14-digit number
|
||||
! (10^(13) ≤ n < 10^(14))? Give your answer rounded to 10 decimal places.
|
||||
|
||||
! Note: The symbols ⌊x⌋ and ⌈x⌉ represent the floor function and ceiling
|
||||
! function respectively.
|
||||
|
||||
! SOLUTION
|
||||
! --------
|
||||
|
||||
<PRIVATE
|
||||
|
||||
! same as produce, but outputs the sum instead of the sequence of results
|
||||
: produce-sum ( id pred quot -- sum )
|
||||
[ 0 ] 2dip [ [ dip swap ] curry ] [ [ dip + ] curry ] bi* while ; inline
|
||||
|
||||
: x0 ( i -- x0 )
|
||||
number-length dup even?
|
||||
number-length dup even?
|
||||
[ 2 - 2 / 10 swap ^ 7 * ]
|
||||
[ 1 - 2 / 10 swap ^ 2 * ] if ;
|
||||
|
||||
: ⌈a/b⌉ ( a b -- ⌈a/b⌉ )
|
||||
[ 1 - + ] keep /i ;
|
||||
|
||||
|
|
@ -56,38 +71,37 @@ IN: project-euler.255
|
|||
DEFER: iteration#
|
||||
! Gives the number of iterations when xk+1 has the same value for all a<=i<=n
|
||||
:: (iteration#) ( i xi a b -- # )
|
||||
a xi xk+1 dup xi =
|
||||
[ drop i b a - 1 + * ]
|
||||
[ i 1 + swap a b iteration# ] if ;
|
||||
a xi xk+1 dup xi =
|
||||
[ drop i b a - 1 + * ]
|
||||
[ i 1 + swap a b iteration# ] if ;
|
||||
|
||||
! Gives the number of iterations in the general case by breaking into intervals
|
||||
! in which xk+1 is the same.
|
||||
:: iteration# ( i xi a b -- # )
|
||||
a
|
||||
a xi next-multiple
|
||||
[ dup b < ]
|
||||
[
|
||||
a
|
||||
a xi next-multiple
|
||||
[ dup b < ]
|
||||
[
|
||||
! set up the values for the next iteration
|
||||
[ nip [ 1 + ] [ xi + ] bi ] 2keep
|
||||
! set up the arguments for (iteration#)
|
||||
[ i xi ] 2dip (iteration#)
|
||||
] produce-sum
|
||||
[ i xi ] 2dip (iteration#)
|
||||
] produce-sum
|
||||
! deal with the last numbers
|
||||
[ drop b [ i xi ] 2dip (iteration#) ] dip
|
||||
+ ;
|
||||
|
||||
: 10^ ( a -- 10^a ) 10 swap ^ ; inline
|
||||
|
||||
: (euler255) ( a b -- answer )
|
||||
: (euler255) ( a b -- answer )
|
||||
[ 10^ ] bi@ 1 -
|
||||
[ [ drop x0 1 swap ] 2keep iteration# ] 2keep
|
||||
swap - 1 + /f ;
|
||||
|
||||
|
||||
PRIVATE>
|
||||
|
||||
: euler255 ( -- answer )
|
||||
13 14 (euler255) round-to-10-decimals ;
|
||||
: euler255 ( -- answer )
|
||||
13 14 (euler255) 10 nth-place ;
|
||||
|
||||
! [ euler255 ] gc time
|
||||
! Running time: 37.468911341 seconds
|
||||
|
||||
SOLUTION: euler255
|
||||
|
||||
|
|
|
|||
|
|
@ -1,10 +1,11 @@
|
|||
! Copyright (c) 2007-2009 Aaron Schaefer.
|
||||
! See http://factorcode.org/license.txt for BSD license.
|
||||
USING: accessors arrays kernel lists make math math.functions math.matrices
|
||||
math.primes.miller-rabin math.order math.parser math.primes.factors
|
||||
math.primes.lists math.ranges math.ratios namespaces parser prettyprint
|
||||
quotations sequences sorting strings unicode.case vocabs vocabs.parser
|
||||
words ;
|
||||
! 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 http://factorcode.org/license.txt
|
||||
USING: accessors arrays byte-arrays fry hints kernel lists make math
|
||||
math.functions math.matrices math.order math.parser math.primes.factors
|
||||
math.primes.lists math.primes.miller-rabin math.ranges math.ratios
|
||||
namespaces parser prettyprint quotations sequences sorting strings
|
||||
unicode.case vocabs vocabs.parser words ;
|
||||
IN: project-euler.common
|
||||
|
||||
! A collection of words used by more than one Project Euler solution
|
||||
|
|
@ -19,12 +20,13 @@ IN: project-euler.common
|
|||
! mediant - #71, #73
|
||||
! nth-prime - #7, #69
|
||||
! nth-triangle - #12, #42
|
||||
! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56, #92
|
||||
! 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
|
||||
|
|
@ -38,6 +40,13 @@ IN: project-euler.common
|
|||
|
||||
<PRIVATE
|
||||
|
||||
: count-digits ( n -- byte-array )
|
||||
10 <byte-array> [
|
||||
'[ 10 /mod _ [ 1 + ] change-nth dup 0 > ] loop drop
|
||||
] keep ;
|
||||
|
||||
HINTS: count-digits fixnum ;
|
||||
|
||||
: max-children ( seq -- seq )
|
||||
[ dup length 1 - iota [ nth-pair max , ] with each ] { } make ;
|
||||
|
||||
|
|
@ -83,6 +92,9 @@ PRIVATE>
|
|||
[ [ 10 * ] [ 1 + ] bi* ] while 2nip
|
||||
] if-zero ;
|
||||
|
||||
: nth-place ( x n -- y )
|
||||
10^ [ * round >integer ] keep /f ;
|
||||
|
||||
: nth-prime ( n -- n )
|
||||
1 - lprimes lnth ;
|
||||
|
||||
|
|
@ -107,6 +119,9 @@ PRIVATE>
|
|||
reverse [ first dup ] [ rest ] bi
|
||||
[ propagate dup ] map nip reverse swap suffix ;
|
||||
|
||||
: permutations? ( n m -- ? )
|
||||
[ count-digits ] bi@ = ;
|
||||
|
||||
: sum-divisors ( n -- sum )
|
||||
dup 4 < [ { 0 1 3 4 } nth ] [ (sum-divisors) ] if ;
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
! Copyright (c) 2007-2009 Aaron Schaefer, Samuel Tardieu.
|
||||
! Copyright (c) 2007-2010 Aaron Schaefer, Samuel Tardieu.
|
||||
! See http://factorcode.org/license.txt for BSD license.
|
||||
USING: definitions io io.files io.pathnames kernel math math.parser
|
||||
prettyprint project-euler.ave-time sequences vocabs vocabs.loader
|
||||
|
|
@ -14,18 +14,19 @@ USING: definitions io io.files io.pathnames kernel math math.parser
|
|||
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.049 project-euler.051 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.062 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.081 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.188 project-euler.190
|
||||
project-euler.203 project-euler.215 ;
|
||||
project-euler.049 project-euler.050 project-euler.051 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.062
|
||||
project-euler.063 project-euler.065 project-euler.067 project-euler.069
|
||||
project-euler.070 project-euler.071 project-euler.072 project-euler.073
|
||||
project-euler.074 project-euler.075 project-euler.076 project-euler.079
|
||||
project-euler.081 project-euler.085 project-euler.089 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.188 project-euler.190 project-euler.203
|
||||
project-euler.206 project-euler.215 project-euler.255 ;
|
||||
IN: project-euler
|
||||
|
||||
<PRIVATE
|
||||
|
|
|
|||
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Reference in New Issue