Merge branch 'master' of git://projects.elasticdog.com/git/factor

db4
Slava Pestov 2008-02-12 12:21:54 -06:00
commit 3a5762b44c
25 changed files with 6751 additions and 6460 deletions

0
extra/math/primes/list/authors.txt Executable file → Normal file
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! Copyright (c) 2007 Aaron Schaefer, Daniel Ehrenberg.
! See http://factorcode.org/license.txt for BSD license.
USING: hashtables kernel math math.parser math.ranges project-euler.common
sequences sorting ;
USING: hashtables kernel math math.ranges project-euler.common sequences
sorting ;
IN: project-euler.004
! http://projecteuler.net/index.php?section=problems&id=4
@ -18,9 +18,6 @@ IN: project-euler.004
! SOLUTION
! --------
: palindrome? ( n -- ? )
number>string dup reverse = ;
<PRIVATE
: source-004 ( -- seq )

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@ -1,7 +1,7 @@
! Copyright (c) 2007 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math.ranges math.text.english sequences strings
ascii ;
USING: kernel math.ranges math.text.english sequences sequences.lib strings
ascii ;
IN: project-euler.017
! http://projecteuler.net/index.php?section=problems&id=17

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@ -1,7 +1,7 @@
! Copyright (c) 2007 Samuel Tardieu, Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: calendar combinators combinators.lib kernel math math.ranges namespaces
sequences ;
USING: calendar combinators kernel math math.ranges namespaces sequences
sequences.lib ;
IN: project-euler.019
! http://projecteuler.net/index.php?section=problems&id=19
@ -32,7 +32,7 @@ IN: project-euler.019
: euler019 ( -- answer )
1901 2000 [a,b] [
12 [1,b] [ 1 zeller-congruence ] 1 map-withn
12 [1,b] [ 1 zeller-congruence ] map-with
] map concat [ zero? ] count ;
! [ euler019 ] 100 ave-time

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@ -1,7 +1,7 @@
! Copyright (c) 2007 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.functions math.ranges namespaces
project-euler.common sequences ;
project-euler.common sequences sequences.lib ;
IN: project-euler.021
! http://projecteuler.net/index.php?section=problems&id=21

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@ -1,6 +1,6 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.ranges ;
USING: kernel math math.ranges sequences.lib ;
IN: project-euler.028
! http://projecteuler.net/index.php?section=problems&id=28

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@ -1,6 +1,6 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.functions project-euler.common sequences ;
USING: kernel math math.functions project-euler.common sequences sequences.lib ;
IN: project-euler.030
! http://projecteuler.net/index.php?section=problems&id=30

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@ -1,6 +1,6 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math.ranges project-euler.common sequences ;
USING: kernel math.ranges project-euler.common sequences sequences.lib ;
IN: project-euler.034
! http://projecteuler.net/index.php?section=problems&id=34

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@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.combinatorics math.parser math.primes
project-euler.common sequences ;
USING: kernel math math.combinatorics math.parser math.primes
project-euler.common sequences sequences.lib ;
IN: project-euler.035
! http://projecteuler.net/index.php?section=problems&id=35

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@ -1,6 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math.parser math.ranges sequences ;
USING: combinators.lib kernel math.parser math.ranges project-euler.common
sequences ;
IN: project-euler.036
! http://projecteuler.net/index.php?section=problems&id=36
@ -24,12 +25,9 @@ IN: project-euler.036
<PRIVATE
: palindrome? ( str -- ? )
dup reverse = ;
: both-bases? ( n -- ? )
{ [ dup number>string palindrome? ]
[ dup >bin palindrome? ] } && nip ;
{ [ dup palindrome? ]
[ dup >bin dup reverse = ] } && nip ;
PRIVATE>

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@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: arrays combinators.lib kernel math math.ranges namespaces
project-euler.common sequences ;
USING: arrays combinators.cleave combinators.lib kernel math math.ranges
namespaces project-euler.common sequences ;
IN: project-euler.039
! http://projecteuler.net/index.php?section=problems&id=39
@ -43,7 +43,7 @@ SYMBOL: p-count
: (count-perimeters) ( seq -- )
dup sum max-p < [
dup sum adjust-p-count
[ u-transform ] keep [ a-transform ] keep d-transform
[ u-transform ] [ a-transform ] [ d-transform ] tri
[ (count-perimeters) ] 3apply
] [
drop

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@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: ascii combinators.lib io.files kernel math math.functions namespaces
project-euler.common sequences splitting ;
USING: ascii io.files kernel math math.functions namespaces
project-euler.common sequences sequences.lib splitting ;
IN: project-euler.042
! http://projecteuler.net/index.php?section=problems&id=42

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@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib hashtables kernel math math.combinatorics math.parser
math.ranges project-euler.common sequences sorting ;
math.ranges project-euler.common sequences sequences.lib sorting ;
IN: project-euler.043
! http://projecteuler.net/index.php?section=problems&id=43

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@ -30,9 +30,6 @@ IN: project-euler.044
: nth-pentagonal ( n -- seq )
dup 3 * 1- * 2 / ;
: pentagonal? ( n -- ? )
dup 0 > [ 24 * 1+ sqrt 1+ 6 / 1 mod zero? ] [ drop f ] if ;
: sum-and-diff? ( m n -- ? )
2dup + -rot - [ pentagonal? ] 2apply and ;

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! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math project-euler.common ;
IN: project-euler.045
! http://projecteuler.net/index.php?section=problems&id=45
! DESCRIPTION
! -----------
! Triangle, pentagonal, and hexagonal numbers are generated by the following
! formulae:
! Triangle Tn = n(n + 1) / 2 1, 3, 6, 10, 15, ...
! Pentagonal Pn = n(3n 1) / 2 1, 5, 12, 22, 35, ...
! Hexagonal Hn = n(2n 1) 1, 6, 15, 28, 45, ...
! It can be verified that T285 = P165 = H143 = 40755.
! Find the next triangle number that is also pentagonal and hexagonal.
! SOLUTION
! --------
! All hexagonal numbers are also triangle numbers, so iterate through hexagonal
! numbers until you find one that is pentagonal as well.
<PRIVATE
: nth-hexagonal ( n -- m )
dup 2 * 1- * ;
DEFER: next-solution
: (next-solution) ( n hexagonal -- hexagonal )
dup pentagonal? [ nip ] [ drop next-solution ] if ;
: next-solution ( n -- m )
1+ dup nth-hexagonal (next-solution) ;
PRIVATE>
: euler045 ( -- answer )
143 next-solution ;
! [ euler045 ] 100 ave-time
! 18 ms run / 1 ms GC ave time - 100 trials
MAIN: euler045

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! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions math.primes math.ranges sequences ;
IN: project-euler.046
! http://projecteuler.net/index.php?section=problems&id=46
! DESCRIPTION
! -----------
! It was proposed by Christian Goldbach that every odd composite number can be
! written as the sum of a prime and twice a square.
! 9 = 7 + 2 * 1^2
! 15 = 7 + 2 * 2^2
! 21 = 3 + 2 * 3^2
! 25 = 7 + 2 * 3^2
! 27 = 19 + 2 * 2^2
! 33 = 31 + 2 * 1^2
! It turns out that the conjecture was false.
! What is the smallest odd composite that cannot be written as the sum of a
! prime and twice a square?
! SOLUTION
! --------
<PRIVATE
: perfect-squares ( n -- seq )
2 /i sqrt >integer [1,b] [ sq ] map ;
: fits-conjecture? ( n -- ? )
dup perfect-squares [ 2 * - ] with map [ prime? ] contains? ;
: next-odd-composite ( n -- m )
dup odd? [ 2 + ] [ 1+ ] if dup prime? [ next-odd-composite ] when ;
: disprove-conjecture ( n -- m )
dup fits-conjecture? [ next-odd-composite disprove-conjecture ] when ;
PRIVATE>
: euler046 ( -- answer )
9 disprove-conjecture ;
! [ euler046 ] 100 ave-time
! 150 ms run / 2 ms GC ave time - 100 trials
MAIN: euler046

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@ -1,6 +1,6 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.functions ;
USING: kernel math math.functions sequences.lib ;
IN: project-euler.048
! http://projecteuler.net/index.php?section=problems&id=48

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@ -0,0 +1,35 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.combinatorics math.ranges sequences.lib ;
IN: project-euler.053
! http://projecteuler.net/index.php?section=problems&id=53
! DESCRIPTION
! -----------
! There are exactly ten ways of selecting three from five, 12345:
! 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345
! In combinatorics, we use the notation, 5C3 = 10.
! In general,
! nCr = n! / r! * (n - r)!
! where r ≤ n, n! = n * (n 1) * ... * 3 * 2 * 1, and 0! = 1.
! It is not until n = 23, that a value exceeds one-million: 23C10 = 1144066.
! How many values of nCr, for 1 ≤ n ≤ 100, are greater than one-million?
! SOLUTION
! --------
: euler053 ( -- answer )
23 100 [a,b] [ dup [ nCk 1000000 > ] with count ] sigma ;
! [ euler053 ] 100 ave-time
! 64 ms run / 2 ms GC ave time - 100 trials
MAIN: euler053

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@ -0,0 +1,69 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.parser project-euler.common sequences sequences.lib ;
IN: project-euler.055
! http://projecteuler.net/index.php?section=problems&id=55
! DESCRIPTION
! -----------
! If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
! Not all numbers produce palindromes so quickly. For example,
! 349 + 943 = 1292,
! 1292 + 2921 = 4213
! 4213 + 3124 = 7337
! That is, 349 took three iterations to arrive at a palindrome.
! Although no one has proved it yet, it is thought that some numbers, like 196,
! never produce a palindrome. A number that never forms a palindrome through
! the reverse and add process is called a Lychrel number. Due to the
! theoretical nature of these numbers, and for the purpose of this problem, we
! shall assume that a number is Lychrel until proven otherwise. In addition you
! are given that for every number below ten-thousand, it will either (i) become a
! palindrome in less than fifty iterations, or, (ii) no one, with all the
! computing power that exists, has managed so far to map it to a palindrome. In
! fact, 10677 is the first number to be shown to require over fifty iterations
! before producing a palindrome: 4668731596684224866951378664 (53 iterations,
! 28-digits).
! Surprisingly, there are palindromic numbers that are themselves Lychrel
! numbers; the first example is 4994.
! How many Lychrel numbers are there below ten-thousand?
! NOTE: Wording was modified slightly on 24 April 2007 to emphasise the
! theoretical nature of Lychrel numbers.
! SOLUTION
! --------
<PRIVATE
: add-reverse ( n -- m )
dup number>digits reverse 10 digits>integer + ;
: (lychrel?) ( n iteration -- ? )
dup 50 < [
>r add-reverse dup palindrome?
[ r> 2drop f ] [ r> 1+ (lychrel?) ] if
] [
2drop t
] if ;
: lychrel? ( n -- ? )
1 (lychrel?) ;
PRIVATE>
: euler055 ( -- answer )
10000 [ lychrel? ] count ;
! [ euler055 ] 100 ave-time
! 1370 ms run / 31 ms GC ave time - 100 trials
MAIN: euler055

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@ -0,0 +1,31 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math.functions math.ranges project-euler.common sequences ;
IN: project-euler.056
! http://projecteuler.net/index.php?section=problems&id=56
! DESCRIPTION
! -----------
! A googol (10^100) is a massive number: one followed by one-hundred zeros;
! 100^100 is almost unimaginably large: one followed by two-hundred zeros.
! Despite their size, the sum of the digits in each number is only 1.
! Considering natural numbers of the form, a^b, where a, b < 100, what is the
! maximum digital sum?
! SOLUTION
! --------
! Through analysis, you only need to check when a and b > 90
: euler056 ( -- answer )
90 100 [a,b) dup cartesian-product
[ first2 ^ number>digits sum ] map supremum ;
! [ euler056 ] 100 ave-time
! 33 ms run / 1 ms GC ave time - 100 trials
MAIN: euler056

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@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: arrays combinators.lib kernel math math.ranges namespaces
project-euler.common sequences ;
USING: arrays combinators.cleave combinators.lib kernel math math.ranges
namespaces project-euler.common sequences sequences.lib ;
IN: project-euler.075
! http://projecteuler.net/index.php?section=problems&id=75
@ -56,7 +56,7 @@ SYMBOL: p-count
: (count-perimeters) ( seq -- )
dup sum max-p < [
dup sum adjust-p-count
[ u-transform ] keep [ a-transform ] keep d-transform
[ u-transform ] [ a-transform ] [ d-transform ] tri
[ (count-perimeters) ] 3apply
] [
drop

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@ -0,0 +1,54 @@
! Copyright (c) 2008 Aaron Schaefer, Slava Pestov.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.ranges sequences ;
IN: project-euler.092
! http://projecteuler.net/index.php?section=problems&id=92
! DESCRIPTION
! -----------
! A number chain is created by continuously adding the square of the digits in
! a number to form a new number until it has been seen before.
! For example,
! 44 -> 32 -> 13 -> 10 -> 1 -> 1
! 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89
! Therefore any chain that arrives at 1 or 89 will become stuck in an endless
! loop. What is most amazing is that EVERY starting number will eventually
! arrive at 1 or 89.
! How many starting numbers below ten million will arrive at 89?
! SOLUTION
! --------
<PRIVATE
: next-link ( n -- m )
0 swap [ dup zero? not ] [ 10 /mod sq -rot [ + ] dip ] [ ] while drop ;
: chain-ending ( n -- m )
dup 1 = over 89 = or [ next-link chain-ending ] unless ;
: lower-endings ( -- seq )
567 [1,b] [ chain-ending ] map ;
: fast-chain-ending ( seq n -- m )
dup 567 > [ next-link ] when 1- swap nth ;
: count ( seq quot -- n )
0 -rot [ rot >r call [ r> 1+ ] [ r> ] if ] curry each ; inline
PRIVATE>
: euler092 ( -- answer )
lower-endings 9999999 [1,b] [ fast-chain-ending 89 = ] with count ;
! [ euler092 ] 10 ave-time
! 11169 ms run / 0 ms GC ave time - 10 trials
MAIN: euler092

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@ -1,6 +1,6 @@
USING: arrays combinators.lib kernel math math.functions math.miller-rabin
math.matrices math.parser math.primes.factors math.ranges namespaces
sequences sorting unicode.case ;
USING: arrays kernel math math.functions math.miller-rabin math.matrices
math.parser math.primes.factors math.ranges namespaces sequences
sequences.lib sorting unicode.case ;
IN: project-euler.common
! A collection of words used by more than one Project Euler solution
@ -9,13 +9,15 @@ IN: project-euler.common
! Problems using each public word
! -------------------------------
! alpha-value - #22, #42
! cartesian-product - #4, #27, #29, #32, #33
! cartesian-product - #4, #27, #29, #32, #33, #43, #44, #56
! collect-consecutive - #8, #11
! log10 - #25, #134
! max-path - #18, #67
! nth-triangle - #12, #42
! number>digits - #16, #20, #30, #34
! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56
! palindrome? - #4, #36, #55
! pandigital? - #32, #38
! pentagonal? - #44, #45
! propagate-all - #18, #67
! sum-proper-divisors - #21
! tau* - #12
@ -76,14 +78,20 @@ PRIVATE>
] if ;
: number>digits ( n -- seq )
number>string string>digits ;
[ dup zero? not ] [ 10 /mod ] [ ] unfold reverse nip ;
: nth-triangle ( n -- n )
dup 1+ * 2 / ;
: palindrome? ( n -- ? )
number>string dup reverse = ;
: pandigital? ( n -- ? )
number>string natural-sort "123456789" = ;
: pentagonal? ( n -- ? )
dup 0 > [ 24 * 1+ sqrt 1+ 6 / 1 mod zero? ] [ drop f ] if ;
! Not strictly needed, but it is nice to be able to dump the triangle after the
! propagation
: propagate-all ( triangle -- newtriangle )

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@ -13,9 +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.048 project-euler.052 project-euler.067 project-euler.075
project-euler.079 project-euler.097 project-euler.134 project-euler.169
project-euler.173 project-euler.175 ;
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 ;
IN: project-euler
<PRIVATE