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April 28, 2011 14:54
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Euler Project 1-50 in a cool ruby dsl
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| # Usage example: | |
| # ruby -r/path/to/this/file 'Euler.execute 1' | |
| # library {{{ | |
| require 'benchmark' | |
| require 'fffs' | |
| fs = FFFS::FileSystem.parse(__FILE__ == $0 ? DATA : File.read(__FILE__).split(/^__END__$/, 2).last) #DATA doesn't work if required | |
| class NilClass | |
| def dup | |
| self | |
| end | |
| end | |
| class Object | |
| def redefine_method(meth) | |
| return unless block_given? | |
| oldmeth = self.instance_method(meth) | |
| self.send(:define_method, meth) {|*args| | |
| yield(oldmeth.bind(self), *args) | |
| } | |
| end | |
| end | |
| class Proc | |
| attr_accessor :require | |
| end | |
| $INCLUDED_HELPERS = [] | |
| def helper(x) | |
| Module.new { | |
| unless $INCLUDED_HELPERS.include?(x.to_s.to_sym) | |
| lambda { Euler.helper(x).require.flatten.uniq.select{|x|x}.each {|r| ::Kernel.require r.to_s }; Euler.helper(x).call }.call | |
| $INCLUDED_HELPERS << x.to_s.to_sym | |
| end | |
| } | |
| end | |
| def helpers(*y) | |
| Module.new { y.each {|x| include helper x } } | |
| end | |
| def catch_output | |
| stdout, stderr = IO.pipe, IO.pipe | |
| pid = fork { | |
| [stdout, stderr].each {|i| i[0].close } | |
| STDOUT.reopen(stdout[1]) | |
| STDERR.reopen(stderr[1]) | |
| begin | |
| yield | |
| rescue Exception => e | |
| STDERR.puts "#{e.class}: #{e}" | |
| STDERR.puts e.backtrace.map {|l| ' ' * 8 + l }.join("\n") | |
| end | |
| [stdout, stderr].each {|i| i[1].close } | |
| } | |
| [stdout, stderr].each {|io| io[1].close } | |
| Process.wait pid | |
| [stdout[0].read, stderr[0].read] | |
| ensure | |
| [stdout, stderr].each {|io| io[0].close } | |
| end | |
| module Euler | |
| class Exercise < Struct.new(:proc, :helper, :require) | |
| def caller | |
| lambda { | |
| self.proc.require.each {|r| ::Kernel.require(r.to_s) } if self.proc and self.proc.require.is_a?(Array) | |
| self.helper.require.each {|r| ::Kernel.require(r.to_s) } if self.helper and self.helper.require.is_a?(Array) | |
| self.helper.() if self.helper | |
| self.proc.() if self.proc | |
| } | |
| end | |
| end | |
| @exercises = {} | |
| class << self | |
| def exercise(number, *requires, &blk) | |
| number = number.to_s.to_sym | |
| if block_given? | |
| @exercises[number] ||= Euler::Exercise.new | |
| @exercises[number].proc = blk | |
| @exercises[number].proc.require = (@exercises[number].proc.require || []) + requires | |
| else | |
| @exercises[number].dup | |
| end | |
| end | |
| def helper(number, *requires, &blk) | |
| number = number.to_s.to_sym | |
| if block_given? | |
| @exercises[number] ||= Euler::Exercise.new | |
| @exercises[number].helper = blk | |
| @exercises[number].helper.require = requires | |
| else | |
| @exercises[number].helper rescue nil | |
| end | |
| end | |
| def execute(*numbers) | |
| numbers.each {|number| | |
| self.execute_single(number) | |
| } | |
| end | |
| protected | |
| def execute_single(number) | |
| number, stderr, stdout = number.to_s.to_sym, '', '' | |
| res = Benchmark.measure { stdout, stderr = catch_output(&Euler.exercise(number).caller) }.to_s.strip | |
| puts "\e[34mEuler ##{number}\e[0m " + '-' * (res.size - 8 - number.to_s.size) | |
| puts Benchmark::CAPTION[1..-1] | |
| puts res | |
| if !stdout.empty? | |
| puts "\e[32mAnswer\e[0m " + '-' * (res.size - 7) | |
| puts stdout | |
| end | |
| if !stderr.empty? | |
| puts "\e[31mError\e[0m " + '-' * (res.size - 6) | |
| puts stderr | |
| end | |
| puts '-' * res.size | |
| end | |
| end | |
| end | |
| # }}} | |
| # 1-10 {{{ | |
| Euler.helper 1 do | |
| module Enumerable | |
| def sum | |
| self.inject(:+) | |
| end | |
| end | |
| end | |
| Euler.exercise 1 do | |
| puts 1000.times.select {|i| i % 3 == 0 or i % 5 == 0 }.sum | |
| end | |
| Euler.helper 2 do | |
| class Fibonacci < Enumerator | |
| def initialize | |
| super {|x| | |
| a = b = 1 | |
| loop { | |
| x << a | |
| a, b = b, a + b | |
| } | |
| } | |
| end | |
| end | |
| end | |
| Euler.exercise 2 do | |
| include helper 1 | |
| puts Fibonacci.new.take_while {|x| x < 4_000_000 }.select(&:even?).sum | |
| end | |
| Euler.exercise 3, :prime do | |
| puts Prime.prime_division(600_851_475_143).map {|(b, e)| b }.max | |
| end | |
| Euler.helper 4 do | |
| class String | |
| def palindrom? | |
| self == self.reverse | |
| end | |
| end | |
| class Integer | |
| def palindrom? | |
| self.to_s.palindrom? | |
| end | |
| end | |
| end | |
| Euler.exercise 4 do | |
| puts (100..999).map {|a| (100..999).map {|b| a * b } }.flatten.select {|x| x.palindrom? }.max | |
| end | |
| Euler.exercise 5 do | |
| puts (12..19).inject(11) {|p, c| p.lcm(c) } | |
| end | |
| Euler.exercise 6 do | |
| include helper 1 | |
| puts ((1..100).sum ** 2) - (1..100).map {|x| x ** 2 }.sum | |
| end | |
| Euler.helper 7, :prime do | |
| Enumerable.module_eval { define_method(:[]) {|index| self.with_index {|x, i| break x if i == index - 1 } } } | |
| Primes = Prime.each | |
| end | |
| Euler.exercise 7 do | |
| puts Primes[10001] | |
| end | |
| Euler.helper 8 do | |
| def pythag?(a, b, c) | |
| a ** 2 + b ** 2 == c ** 2 | |
| end | |
| module Enumerable | |
| def mul | |
| self.inject(:*) | |
| end | |
| end | |
| class String | |
| redefine_method(:split) {|old, *args| | |
| if args.size.zero? | |
| old.(//) | |
| else | |
| old.(*args) | |
| end | |
| } | |
| end | |
| end | |
| Euler.exercise 8 do | |
| DIGITS = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" | |
| puts (0..(DIGITS.size - 1)).map {|i| DIGITS[i, 5].split.map(&:to_i).mul }.max | |
| end | |
| Euler.exercise 9 do | |
| include helper 8 | |
| puts (0..1000).map {|a| (0..(1000 - a)).map {|b| [a, b, 1000 - a - b] } }.flatten.each_slice(3).select {|(a,b,c)| pythag?(a, b, c) and a != 0 and b != 0 and c != 0 }.map {|x| x.sort }.uniq.first.mul | |
| end | |
| Euler.exercise 10, :prime do | |
| include helper 1 | |
| puts Prime.each(2_000_000).sum | |
| end | |
| # }}} | |
| # 11-20 {{{ | |
| Euler.helper 11 do | |
| include helper 8 | |
| class Matrix | |
| def max_prod(x, y) | |
| %w{up down left right up_left up_right down_left down_right}.map {|m| | |
| self.send(m, x, y) | |
| }.max | |
| end | |
| protected | |
| def prod(&blk) | |
| return 0 if !block_given? | |
| (0..3).map(&blk).mul | |
| rescue | |
| 0 | |
| end | |
| def up(x, y) | |
| self.prod {|i| self[x, y + i] } | |
| end | |
| def down(x, y) | |
| self.prod {|i| self[x, y - i] } | |
| end | |
| def left(x, y) | |
| self.prod {|i| self[x - i, y] } | |
| end | |
| def right(x, y) | |
| self.prod {|i| self[x + i, y] } | |
| end | |
| def up_left(x, y) | |
| self.prod {|i| self[x - i, y + i] } | |
| end | |
| def up_right(x, y) | |
| self.prod {|i| self[x + i, y + i] } | |
| end | |
| def down_left(x, y) | |
| self.prod {|i| self[x - i, y - i] } | |
| end | |
| def down_right(x, y) | |
| self.prod {|i| self[x + i, y - i] } | |
| end | |
| end | |
| end | |
| Euler.exercise 11, :matrix do | |
| puts Matrix[*"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 | |
| 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 | |
| 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 | |
| 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 | |
| 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 | |
| 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 | |
| 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 | |
| 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 | |
| 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 | |
| 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 | |
| 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 | |
| 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 | |
| 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 | |
| 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 | |
| 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 | |
| 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 | |
| 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 | |
| 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 | |
| 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 | |
| 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48".lines.map {|l| l.split(' ').map(&:to_i) }].tap {|m| | |
| break (0..(m.row_size)).map {|x| (0..(m.column_size)).map {|y| m.max_prod(x, y) } }.flatten.max | |
| } | |
| end | |
| Euler.helper 12 do | |
| include helpers 1, 8 | |
| class Integer | |
| def factors | |
| (1..(Math.sqrt(self).floor)).map {|x| [x, self / x].uniq if self % x == 0 }.flatten.select{|x|x} | |
| end | |
| def fact | |
| (1..self).mul | |
| end | |
| alias factorial fact | |
| def loop(&blk) | |
| if block_given? | |
| self.upto(Float::INFINITY, &blk) | |
| else | |
| (self..Float::INFINITY) | |
| end | |
| end | |
| def loop_while(&blk) | |
| if block_given? | |
| self.loop {|__x| | |
| res = blk.(__x) | |
| break res if res | |
| } | |
| else | |
| self.loop | |
| end | |
| end | |
| end | |
| end | |
| Euler.exercise 12 do | |
| puts 1.loop_while {|i, n = (1..i).sum| n if n.factors.size > 500 } | |
| end | |
| Euler.exercise 13 do | |
| include helpers 1, 8 | |
| puts "37107287533902102798797998220837590246510135740250 | |
| 46376937677490009712648124896970078050417018260538 | |
| 74324986199524741059474233309513058123726617309629 | |
| 91942213363574161572522430563301811072406154908250 | |
| 23067588207539346171171980310421047513778063246676 | |
| 89261670696623633820136378418383684178734361726757 | |
| 28112879812849979408065481931592621691275889832738 | |
| 44274228917432520321923589422876796487670272189318 | |
| 47451445736001306439091167216856844588711603153276 | |
| 70386486105843025439939619828917593665686757934951 | |
| 62176457141856560629502157223196586755079324193331 | |
| 64906352462741904929101432445813822663347944758178 | |
| 92575867718337217661963751590579239728245598838407 | |
| 58203565325359399008402633568948830189458628227828 | |
| 80181199384826282014278194139940567587151170094390 | |
| 35398664372827112653829987240784473053190104293586 | |
| 86515506006295864861532075273371959191420517255829 | |
| 71693888707715466499115593487603532921714970056938 | |
| 54370070576826684624621495650076471787294438377604 | |
| 53282654108756828443191190634694037855217779295145 | |
| 36123272525000296071075082563815656710885258350721 | |
| 45876576172410976447339110607218265236877223636045 | |
| 17423706905851860660448207621209813287860733969412 | |
| 81142660418086830619328460811191061556940512689692 | |
| 51934325451728388641918047049293215058642563049483 | |
| 62467221648435076201727918039944693004732956340691 | |
| 15732444386908125794514089057706229429197107928209 | |
| 55037687525678773091862540744969844508330393682126 | |
| 18336384825330154686196124348767681297534375946515 | |
| 80386287592878490201521685554828717201219257766954 | |
| 78182833757993103614740356856449095527097864797581 | |
| 16726320100436897842553539920931837441497806860984 | |
| 48403098129077791799088218795327364475675590848030 | |
| 87086987551392711854517078544161852424320693150332 | |
| 59959406895756536782107074926966537676326235447210 | |
| 69793950679652694742597709739166693763042633987085 | |
| 41052684708299085211399427365734116182760315001271 | |
| 65378607361501080857009149939512557028198746004375 | |
| 35829035317434717326932123578154982629742552737307 | |
| 94953759765105305946966067683156574377167401875275 | |
| 88902802571733229619176668713819931811048770190271 | |
| 25267680276078003013678680992525463401061632866526 | |
| 36270218540497705585629946580636237993140746255962 | |
| 24074486908231174977792365466257246923322810917141 | |
| 91430288197103288597806669760892938638285025333403 | |
| 34413065578016127815921815005561868836468420090470 | |
| 23053081172816430487623791969842487255036638784583 | |
| 11487696932154902810424020138335124462181441773470 | |
| 63783299490636259666498587618221225225512486764533 | |
| 67720186971698544312419572409913959008952310058822 | |
| 95548255300263520781532296796249481641953868218774 | |
| 76085327132285723110424803456124867697064507995236 | |
| 37774242535411291684276865538926205024910326572967 | |
| 23701913275725675285653248258265463092207058596522 | |
| 29798860272258331913126375147341994889534765745501 | |
| 18495701454879288984856827726077713721403798879715 | |
| 38298203783031473527721580348144513491373226651381 | |
| 34829543829199918180278916522431027392251122869539 | |
| 40957953066405232632538044100059654939159879593635 | |
| 29746152185502371307642255121183693803580388584903 | |
| 41698116222072977186158236678424689157993532961922 | |
| 62467957194401269043877107275048102390895523597457 | |
| 23189706772547915061505504953922979530901129967519 | |
| 86188088225875314529584099251203829009407770775672 | |
| 11306739708304724483816533873502340845647058077308 | |
| 82959174767140363198008187129011875491310547126581 | |
| 97623331044818386269515456334926366572897563400500 | |
| 42846280183517070527831839425882145521227251250327 | |
| 55121603546981200581762165212827652751691296897789 | |
| 32238195734329339946437501907836945765883352399886 | |
| 75506164965184775180738168837861091527357929701337 | |
| 62177842752192623401942399639168044983993173312731 | |
| 32924185707147349566916674687634660915035914677504 | |
| 99518671430235219628894890102423325116913619626622 | |
| 73267460800591547471830798392868535206946944540724 | |
| 76841822524674417161514036427982273348055556214818 | |
| 97142617910342598647204516893989422179826088076852 | |
| 87783646182799346313767754307809363333018982642090 | |
| 10848802521674670883215120185883543223812876952786 | |
| 71329612474782464538636993009049310363619763878039 | |
| 62184073572399794223406235393808339651327408011116 | |
| 66627891981488087797941876876144230030984490851411 | |
| 60661826293682836764744779239180335110989069790714 | |
| 85786944089552990653640447425576083659976645795096 | |
| 66024396409905389607120198219976047599490197230297 | |
| 64913982680032973156037120041377903785566085089252 | |
| 16730939319872750275468906903707539413042652315011 | |
| 94809377245048795150954100921645863754710598436791 | |
| 78639167021187492431995700641917969777599028300699 | |
| 15368713711936614952811305876380278410754449733078 | |
| 40789923115535562561142322423255033685442488917353 | |
| 44889911501440648020369068063960672322193204149535 | |
| 41503128880339536053299340368006977710650566631954 | |
| 81234880673210146739058568557934581403627822703280 | |
| 82616570773948327592232845941706525094512325230608 | |
| 22918802058777319719839450180888072429661980811197 | |
| 77158542502016545090413245809786882778948721859617 | |
| 72107838435069186155435662884062257473692284509516 | |
| 20849603980134001723930671666823555245252804609722 | |
| 53503534226472524250874054075591789781264330331690".gsub(/[^\d]+/, '').split.each_slice(50).map {|x| x.join.to_i }.sum.to_s[0, 10] | |
| end | |
| Euler.exercise 14 do | |
| include helper 12 | |
| puts (3..999999).map {|x| [x, 0.loop.inject([1, x]) {|res, k| res[0] += 1; res[1].odd? ? res[1] = 3 * res[1] + 1 : res[1] /= 2; break res[0] if res[1] == 1; res }] }.sort {|a, b| a[1] <=> b[1] }.last[0] | |
| end | |
| Euler.exercise 15 do | |
| include helper 12 | |
| puts 40.fact / 20.fact ** 2 | |
| end | |
| Euler.exercise 16 do | |
| include helpers 1, 8 | |
| puts (2 ** 1000).to_s.split.map(&:to_i).sum | |
| end | |
| Euler.exercise 17, :linguistics do | |
| include helper 1 | |
| Linguistics.use(:en) | |
| puts 1.upto(1000).map {|x| x.en.numwords.gsub(/\W/, '').size }.sum | |
| end | |
| Euler.exercise 18 do | |
| puts "75 | |
| 95 64 | |
| 17 47 82 | |
| 18 35 87 10 | |
| 20 04 82 47 65 | |
| 19 01 23 75 03 34 | |
| 88 02 77 73 07 63 67 | |
| 99 65 04 28 06 16 70 92 | |
| 41 41 26 56 83 40 80 70 33 | |
| 41 48 72 33 47 32 37 16 94 29 | |
| 53 71 44 65 25 43 91 52 97 51 14 | |
| 70 11 33 28 77 73 17 78 39 68 17 57 | |
| 91 71 52 38 17 14 91 43 58 50 27 29 48 | |
| 63 66 04 68 89 53 67 30 73 16 69 87 40 31 | |
| 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23".lines.map {|l| l.split(' ').map(&:to_i) }.tap {|triangle| | |
| (triangle.size - 1).downto(0) {|a| | |
| 0.upto(a - 1) {|b| | |
| triangle[a - 1][b] += [triangle[a][b], triangle[a][b + 1]].max | |
| } | |
| } | |
| break triangle [0][0] | |
| } | |
| end | |
| Euler.exercise 19 do | |
| puts (1901..2000).map {|y| (1..12).map {|m| Time.new(y, m, 1) } }.flatten.select {|d| d.sunday? }.size | |
| end | |
| Euler.exercise 20 do | |
| include helpers 1, 8 | |
| puts (2..100).mul.to_s.split.map(&:to_i).sum | |
| end | |
| # }}} | |
| # 21-30 {{{ | |
| Euler.helper 21 do | |
| include helper 1 | |
| class Integer | |
| def divisors | |
| [1] + (2..(Math.sqrt(self).floor)).map {|x| [x, self / x].uniq if self % x == 0 }.flatten.select {|x| x } | |
| end | |
| end | |
| def d(x) | |
| x.divisors.sum | |
| end | |
| end | |
| Euler.exercise 21 do | |
| puts (1..9_999).select {|a| a != (b = d(a)) and d(b) == a }.sum | |
| end | |
| Euler.exercise 22 do | |
| include helper 1 | |
| puts fs.names.content.scan(/"((?:[^"]|\\")+)"(?:,|$)/).flatten.sort.each_with_index.map {|n, i| n.split(//).map {|c| c.ord - 64 }.sum * (i + 1) }.sum | |
| end | |
| Euler.helper 23 do | |
| include helper 21 | |
| class Integer | |
| def aboundant? | |
| self < self.divisors.sum | |
| end | |
| end | |
| end | |
| Euler.exercise 23 do | |
| puts (1..28123).select {|i| i.aboundant? }.repeated_combination(2).inject((0..28123).to_a) {|res, x, i = x.sum| res[i] = 0 if i < res.size; res }.sum | |
| end | |
| Euler.exercise 24 do | |
| puts (?0..?9).to_a.permutation.take(1_000_000).last.join | |
| end | |
| Euler.exercise 25 do | |
| include helper 12 | |
| puts 2.loop.inject([0, 1]) {|f, n| f[0], f[1] = f[1], f.sum; break n if f[1].to_s.size >= 1000; f } | |
| end | |
| Euler.helper 26 do | |
| class Integer | |
| def longdiv(a) | |
| integer, r = self.divmod(a) | |
| seen, digits = {r => 0}, [] | |
| loop do | |
| r *= 10 | |
| digits << (r / a) | |
| r = r % a | |
| if seen[r] | |
| w = seen[r] | |
| return [integer, | |
| (digits[0, w].map(&:to_s).join.gsub(/0+$/, '') rescue []), | |
| digits[w, digits.size - w].map(&:to_s).join.gsub(/0+$/, '') | |
| ] | |
| else | |
| seen[r] = digits.size | |
| end | |
| end | |
| end | |
| end | |
| end | |
| Euler.exercise 26 do | |
| puts (1..999).map {|x| 1.longdiv(x) + [x] }.sort {|a, b| a[2].size <=> b[2].size }.last[3] | |
| end | |
| Euler.exercise 27, :prime do | |
| puts (-999..999).map {|a| (-999..999).map {|b| loop.inject({0 => 0, 1 => 0}) {|v| break v.merge(2 => a * b) unless ((v[0] ** 2 + a * v[0] + b).prime? rescue false) | |
| v[0] += 1; v[1] += 1; v } } }.flatten.sort {|a, b| a[0] <=> b[0] }.last[2] | |
| end | |
| Euler.helper 28 do | |
| class Matrix | |
| attr_accessor :x, :y | |
| redefine_method(:initialize) {|old, *args| | |
| old.(*args) | |
| @dir = nil | |
| @x = 0 | |
| @y = 0 | |
| } | |
| def val | |
| self[@x, @y] | |
| end | |
| def val=(x) | |
| self[@x, @y] = x if self[@x, @y] | |
| end | |
| def valid?(x = nil, y = nil) | |
| ![nil, 0].include?(self[x || @x, y || @y]) | |
| end | |
| def complete?(x = nil, y = nil) | |
| self.valid?(nil, @y - 1) and self.valid?(nil, @y + 1) and | |
| self.valid?(@x - 1) and self.valid?(@x + 1) | |
| end | |
| def down | |
| @dir = :down | |
| @y -= 1 | |
| end | |
| def up | |
| @dir = :up | |
| @y += 1 | |
| end | |
| def left | |
| @dir = :left | |
| @x -= 1 | |
| end | |
| def right | |
| @dir = :right | |
| @x += 1 | |
| end | |
| public :[]= | |
| [:up, :right, :left, :down].each {|pos| | |
| define_method "#{pos}?" do | |
| @dir == pos | |
| end | |
| } | |
| end | |
| end | |
| Euler.exercise 28, :matrix do | |
| MAX = 1001 | |
| m = Matrix[*([[]] * MAX).map {|x| | |
| [0] * MAX | |
| }] | |
| m.x, m.y = [MAX / 2] * 2 | |
| m.val = 1 | |
| m.x, m.y = m.x + 1, m.y + 1 | |
| m.down | |
| m.val = 2 | |
| 1.upto(MAX ** 2 - 1) do | |
| old = m.val | |
| if m.down? then m.valid?(m.x - 1) ? m.down : m.left | |
| elsif m.up? then m.valid?(m.x + 1) ? m.up : m.right | |
| elsif m.right? then m.valid?(nil, m.y - 1) ? m.right : m.down | |
| elsif m.left? then m.valid?(nil, m.y + 1) ? m.left : m.up | |
| end | |
| m.val = old + 1 | |
| end | |
| m = Matrix[*m.transpose.to_a.reverse] | |
| sum = m.trace | |
| m = Matrix[*m.to_a.map {|x|x.reverse}] | |
| puts sum + m.trace - 1 | |
| end | |
| Euler.exercise 29 do | |
| puts (2..100).map {|x| (2..100).map {|y| x ** y } }.flatten.uniq.size | |
| end | |
| Euler.exercise 30 do | |
| include helpers 1, 8 | |
| puts (10..354294).select {|x| x.to_s.split.map {|d| d.to_i ** 5}.sum == x }.sum | |
| end | |
| # }}} | |
| # 31-40 {{{ | |
| Euler.exercise 31 do | |
| target = 200 | |
| coins = [1, 2, 5, 10, 20, 50, 100, 200] | |
| ways = [1] | |
| coins.each {|coin| | |
| coin.upto(target + 1) {|i| | |
| ways[i] = (ways[i] || 0) + (ways[i - coin] || 0) | |
| } | |
| } | |
| puts ways[target] | |
| end | |
| Euler.helper 32 do | |
| include helpers 1, 8 | |
| def pandigital?(*args) | |
| str = args.map(&:to_s).join.split.sort.join | |
| str == (str[0]..str[-1]).to_a.join | |
| end | |
| end | |
| Euler.exercise 32 do | |
| puts (2..100).map {|i| ((i > 9 ? 123 : 1234)..(10000 / i + 1)).map {|j| pandigital?(i, j, i * j) ? i * j : 0 } }.flatten.uniq.sum | |
| end | |
| Euler.exercise 33 do | |
| include helper 8 | |
| puts ((1..10).map {|i| (1..i).map {|j| (1..j).map {|k, ki = (k * 10 + i), ij = (i.to_f * 10 + j)| ij/ki == j.to_f / k ? ij / ki : 0 } } }.flatten - [0]).mul.to_i | |
| end | |
| Euler.exercise 34 do | |
| include helpers 1, 8 | |
| fact = [1, 1, 2, 6, 24, 120, 720, 5_040, 40_320, 362_880] | |
| puts (10..50000).map {|n, x = (n.to_s.split.map {|i| fact[i.to_i] }.sum)| n == x ? n : 0 }.sum | |
| end | |
| Euler.exercise 35, :prime do | |
| include helper 8 | |
| puts Prime.each(1_000_000).select {|x, n = x.to_s.split| (0..(n.size)).map { n.rotate!; break false unless n.join.to_i.prime? } }.size | |
| end | |
| Euler.exercise 36 do | |
| include helpers 1, 4 | |
| puts (1..1_000_000).select {|x| x.palindrom? and x.to_s(2).palindrom? }.sum | |
| end | |
| Euler.exercise 37, :prime do | |
| include helper 12 | |
| puts (1..11).inject({ last: 10, sum: 0 }) {|v, k| v[:last] = v[:last].loop {|k, x = (k.to_s)| break k if ((0..(x.size - 1)).map {|i| x[i..-1] } + (2..(x.size)).map {|i| x[0..-i] }).each {|i| break false unless i.to_i.prime? } } + 1; v[:sum] += v[:last] - 1; v }[:sum] | |
| end | |
| Euler.exercise 38 do | |
| include helpers 12, 32 | |
| puts (9123..9876).reverse_each {|r| break $_ if pandigital?($_ = 1.loop.inject('') {|p, i| p << (r * i).to_s; break (i > 1 ? p : ?0) if p.size >= 9; p }) } | |
| end | |
| Euler.exercise 39 do | |
| include helper 8 | |
| puts (1..999).map {|p| [p, (1..(p / 3)).map {|a| (a..((p - a) / 2)).select {|b, c = (p - a - b)| pythag?(a, b, c) } }.flatten.size] }.sort {|a, b| a[1] <=> b[1] }.last[0] | |
| end | |
| Euler.exercise 40 do | |
| include helpers 8 | |
| puts ('1'..'1000000').to_a.join.split.tap {|str| break (1..6).map {|i| str[10 ** i - 1].to_i }.mul } | |
| end | |
| # }}} | |
| # 41-50 {{{ | |
| Euler.exercise 41, :prime do | |
| puts (1..9).map {|i| (1..i).to_a.permutation(i).map{|x| x.join.to_i } }.flatten.reverse_each {|x| break x if x.prime? } | |
| end | |
| Euler.helper 42 do | |
| include helper 1 | |
| Triangle = Enumerator.new {|x, i = 0| | |
| loop { | |
| x << (i += 1).triangle | |
| } | |
| } | |
| class Integer | |
| def triangle? | |
| self == Triangle.take_while {|x| x <= self }.max | |
| end | |
| def triangle | |
| self * (self + 1) / 2 | |
| end | |
| end | |
| class String | |
| def triangle? | |
| self.chars.map {|x| x.ord - 64 }.sum.triangle? | |
| end | |
| end | |
| end | |
| Euler.exercise 42 do | |
| puts fs.words.content.scan(/"((?:[^"]|\\")+)"(?:,|$)/).flatten.select(&:triangle?).size | |
| end | |
| Euler.helper 43 do | |
| include helper 8 | |
| class Array | |
| def subst_div? | |
| self.join.subst_div? | |
| end | |
| def to_i | |
| self.join.to_i | |
| end | |
| end | |
| class String | |
| def subst_div? | |
| return false if self[0] == ?0 | |
| primes = [2, 3, 5, 7, 11, 13, 17] | |
| digs = self.split | |
| 0.upto(6) {|i| | |
| digs.rotate! | |
| break false if digs[0, 3].join.to_i % primes[i] != 0 | |
| } ? true : false | |
| end | |
| end | |
| end | |
| Euler.exercise 43 do | |
| include helper 1 | |
| puts (?0..?9).to_a.permutation(10).select(&:subst_div?).map(&:to_i).sum | |
| end | |
| Euler.helper 44 do | |
| class Integer | |
| def pentagonal | |
| (self * (3 * self - 1)) / 2 | |
| end | |
| def pentagonal? | |
| (Math.sqrt(24 * self + 1) + 1) % 6 == 0 | |
| end | |
| end | |
| Pentagonal = Enumerator.new {|x, i = 0| | |
| loop { | |
| x << (i += 1).pentagonal | |
| } | |
| } | |
| end | |
| Euler.exercise 44 do | |
| puts Pentagonal.take(3000).each_with_index.map {|p, i| Pentagonal.take(i).select {|q| (p + q).pentagonal? }.map {|q| p - q }.select(&:pentagonal?) }.flatten.min | |
| end | |
| Euler.helper 45 do | |
| include helpers 42, 44 | |
| class Integer | |
| def hexagonal | |
| self * (2 * self - 1) | |
| end | |
| end | |
| Hexagonal = Enumerator.new {|x, i = 0| | |
| loop { | |
| x << (i += 1).hexagonal | |
| } | |
| } | |
| end | |
| Euler.exercise 45 do | |
| puts [Pentagonal, Hexagonal].map {|x| x.take(100000) }.inject(:&).drop_while {|x| x <= 40755 }.min | |
| end | |
| Euler.helper 46, :prime do | |
| class Integer | |
| def odd_composite? | |
| self.odd? and !self.prime? and self != 1 | |
| end | |
| def goldbach? | |
| Prime.each(self - 1).map {|p| Math.sqrt((self - p) / 2).tap {|x| break x == x.to_i } }.inject(:|) | |
| end | |
| end | |
| Composites = Enumerator.new {|x, i = -1| | |
| loop { | |
| next unless (i += 2).odd_composite? | |
| x << i | |
| } | |
| } | |
| end | |
| Euler.exercise 46 do | |
| puts Composites.each {|x| break x if !x.goldbach? } | |
| end | |
| Euler.helper 47, :prime do | |
| include helper 1 | |
| class Array | |
| def four_distinct_factors? | |
| self.map {|x| x.prime_division }.tap {|f| break false if f.map {|f| f.size } != [4] * 4 }.sum.tap {|x| break x == x.uniq } | |
| rescue | |
| false | |
| end | |
| end | |
| ForFour = Enumerator.new {|x, i = [1000, 1001, 1002, 1003]| | |
| loop { | |
| x << (i = i[1, 3] << (i[3] + 1)) | |
| } | |
| } | |
| end | |
| Euler.exercise 47 do | |
| puts ForFour.each {|g| break g[0] if g.four_distinct_factors? } | |
| end | |
| Euler.exercise 48 do | |
| include helper 1 | |
| puts (1..1000).map {|x| x ** x }.sum.to_s[-10, 10] | |
| end | |
| Euler.exercise 49, :prime do | |
| puts Prime.each {|a, b = (a + 3330), c = (a + 6660)| | |
| next if a == 1487 or !b.prime? or !c.prime? | |
| break [a, b, c].map(&:to_s).join if a.to_s.chars.to_a.permutation(4).map {|p| p.join.to_i }.tap {|p| break false if !p.include?(b) or !p.include?(c) } | |
| } | |
| end | |
| Euler.exercise 50, :prime do | |
| puts Prime.each(1_000_000).to_a.tap {|p| break p.each_with_index.map {|v, i| p[i..-1].inject([0, 0]){|(sum, max), n| | |
| break [sum, max] if sum + n > 1_000_000; sum += n; max += 1; [sum, max] } } }.select {|x| x[0].prime? }.sort {|a, b| a[1] <=> b[1] }.last[0] | |
| end | |
| # }}} | |
| __END__ | |
| --- | |
| --- names --- | |
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