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Ruby On Rails in UA/Code Review, Вопросы по теории программирования/Работа с числами

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2008-06-08 12:08:26	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Работа с числами
	1000.class # => Fixnum 10000000000.class # => Bignum (230 - 1).class # => Fixnum (230).class # => Bignum #--- small = 1000 big = small ** 5 # => 1000000000000000 big.class # => Bignum smaller = big / big # => 1 smaller.class # => Fixnum #--- 0.01.class # => Float 1.0.class # => Float 10000000000.00000000001.class # => Float #---
	numbers, числа

2008-06-10 04:55:11	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Извлечение чисел из строк
	'400'.to_i # => 400 '3.14'.to_f # => 3.14 '1.602e-19'.to_f # => 1.602e-19 #--- '405'.oct # => 261 '405'.to_i(8) # => 261 '405'.hex # => 1029 '405'.to_i(16) # => 1029 'fed'.hex # => 4077 'fed'.to_i(16) # => 4077 #--- "13: a baker's dozen".to_i # => 13 '1001 Nights'.to_i # => 1001 'The 1000 Nights and a Night'.to_i # => 0 '60.50 Misc. Agricultural Equipment'.to_f # => 60.5 '$60.50'.to_f # => 0.0 'Feed the monster!'.hex # => 65261 'I fed the monster at Canoga Park Waterslides'.hex # => 0 '0xA2Z'.hex # => 162 '-10'.oct # => -8 '-109'.oct # => -8 '3.14'.to_i # => 3 #--- Integer('1001') # => 1001 Integer('1001 nights') # ArgumentError: invalid value for Integer: "1001 nights" Float('99.44') # => 99.44 Float('99.44% pure') # ArgumentError: invalid value for Float(): "99.44% pure" #--- class NumberParser @@number_regexps = { :to_i => /([+-]?[0-9]+)/, :to_f => /([+-]?([0-9]*\.)?[0-9]+(e[+-]?[0-9]+)?)/i, :oct => /([+-]?[0-7]+)/, :hex => /\b([+-]?(0x)?[0-9a-f]+)\b/i #The \b characters prevent every letter A-F in a word from being #considered a hexadecimal number. } def NumberParser.re(parsing_method=:to_i) re = @@number_regexps[parsing_method] raise ArgumentError, "No regexp for #{parsing_method.inspect}!" unless re return re end def extract(s, parsing_method=:to_i) numbers = [] s.scan(NumberParser.re(parsing_method)) do \|match\| numbers << match[0].send(parsing_method) end numbers end end #--- p = NumberParser.new pw = "Today's numbers are 104 and 391." NumberParser.re(:to_i).match(pw).captures # => ["104"] p.extract(pw, :to_i) # => [104, 391] p.extract('The 1000 nights and a night') # => [1000] p.extract('$60.50', :to_f) # => [60.5] p.extract('I fed the monster at Canoga Park Waterslides', :hex) # => [4077] p.extract('In octal, fifteen is 017.', :oct) # => [15] p.extract('From 0 to 10e60 in -2.4 seconds', :to_f) # => [0.0, 1.0e+61, -2.4] p.extract('From 0 to 10e60 in -2.4 seconds') # => [0, 10, 60, -2, 4] #--- require 'scanf' s = '0x10 4.44 10'.scanf('%x %f %d') # => [16, 4.44, 10] #---
	hex, numbers from string, oct, Parsing A Number From A String, to_f, to_i, to_i(16), to_i(8)

2008-06-08 12:21:26	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Сравнение дробных чисел
	1.8 + 0.1 # => 1.9 1.8 + 0.1 == 1.9 # => false 1.8 + 0.1 > 1.9 # => true #--- class Float def approx(other, relative_epsilon=Float::EPSILON, epsilon=Float::EPSILON) difference = other - self return true if difference.abs <= epsilon relative_error = (difference / (self > other ? self : other)).abs return relative_error <= relative_epsilon end end 100.2.approx(100.1 + 0.1) # => true 10e10.approx(10e10+1e-5) # => true 100.0.approx(100+1e-5) # => false #--- printf("%.55f", 1.9) # 1.8999999999999999111821580299874767661094665527343750000 printf("%.55f", 1.8 + 0.1) # 1.9000000000000001332267629550187848508358001708984375000 #--- Float::EPSILON # => 2.22044604925031e-16 (1.8 + 0.1) - 1.9 # => 2.22044604925031e-16 #--- class Float def absolute_approx(other, epsilon=Float::EPSILON) puts((other-self).abs) return (other-self).abs <= epsilon end end (1.8 + 0.1).absolute_approx(1.9) # => true 10e10.absolute_approx(10e10+1e-5) # => false #--- 98.6.approx(98.66) # => false 98.6.approx(98.66, 0.001) # => true #---
	Comparing Floating-Point Numbers

2008-06-06 19:42:03	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Изменение точности вывода дробный чисел
	require 'bigdecimal' BigDecimal("10").to_s # => "0.1E2" BigDecimal("1000").to_s # => "0.1E4" BigDecimal("1000").to_s("F") # => "1000.0" BigDecimal("0.123456789").to_s # => "0.123456789E0" #--- nm = "0.123456789012345678901234567890123456789" nm.to_f # => 0.123456789012346 BigDecimal(nm).to_s # => "0.123456789012345678901234567890123456789E0" #--- BigDecimal("105000").split # => [1, "105", 10, 6] # That is, 0.105(106) BigDecimal("-0.005").split # => [-1, "5", 10, -2] # That is, -1 (0.5(10-2)) #--- (BigDecimal("2") / BigDecimal("3")).to_s # => "0.6666666666666667E0" 2.0/3 # => 0.666666666666667 #--- def two_thirds(precision) (BigDecimal("2", precision) / BigDecimal("3")).to_s end two_thirds(1) # => "0.6666666666666667E0" two_thirds(4) # => "0.6666666666666667E0" two_thirds(5) # => "0.66666666666666666667E0" two_thirds(9) # => "0.666666666666666666666667E0" two_thirds(13) # => "0.6666666666666666666666666667E0" #--- BigDecimal("2").precs # => [4, 8] BigDecimal("2.000000000000").precs # => [4, 20] BigDecimal("2.000000000001").precs # => [16, 20] #--- (a = BigDecimal("2.01")).precs # => [8, 8] (b = BigDecimal("3.01")).precs # => [8, 8] (product = a b).to_s("F") # => "6.0501" product.precs # => [8, 24] #--- two_thirds = (BigDecimal("2", 13) / 3) two_thirds.to_s # => "0.666666666666666666666666666666666667E0" (two_thirds + 1).to_s # => "0.1666666666666666666666666666666666667E1" two_thirds.add(1, 1).to_s # => "0.2E1" two_thirds.add(1, 4).to_s # => "0.1667E1" #--- require 'bigdecimal/math' include BigMath two = BigDecimal("2") BigMath::sqrt(two, 10).to_s("F") # => "1.4142135623730950488016883515" #--- BigMath::sqrt(two, 10).round(10).to_s("F") # => "1.4142135624" #--- BigMath::sqrt(two, 28).round(28).to_s("F") # => "1.4142135623730950488016887242" #--- Math::PI # => 3.14159265358979 Math::PI.class # => Float BigDecimal.PI(1).to_s # => "0.31415926535897932364198143965603E1" BigDecimal.PI(20).to_s # => "0.3141592653589793238462643383279502883919859293521427E1" #---
	BigDecimal, BigDecimal, Math, sqrt, точность дробных чисел

2008-06-10 07:01:47	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Рациональные числа
	float = 2.0/3.0 # => 0.666666666666667 float * 100 # => 66.6666666666667 float * 100 / 42 # => 1.58730158730159 require 'rational' rational = Rational(2, 3) # => Rational(2, 3) rational.to_f # => 0.666666666666667 rational * 100 # => Rational(200, 3) rational * 100 / 42 # => Rational(100, 63) #--- 10 + Rational(2,3) # => Rational(32, 3) require 'bigdecimal' BigDecimal('10') + Rational(2,3) # => 10.6666666666667 #--- Math::sqrt(Rational(2,3)) # => 0.816496580927726 Math::sqrt(Rational(25,1)) # => 5.0 Math::log10(Rational(100, 1)) # => 2.0 #--- require 'mathn' Math::sqrt(Rational(2,3)) # => 0.816496580927726 Math::sqrt(Rational(25,1)) # => 5 Math::sqrt(25) # => 5 Math::sqrt(25.0) # => 5.0 #---
	rational, Representing Rational Numbers, рациональные фисла, рецепт

2008-06-07 10:37:06	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Конвертация между числами по основанию
	0b100 # => 4 0o100 # => 64 0x100 # => 256 #--- "1045".to_i(10) # => 1045 "-1001001".to_i(2) # => -73 "abc".to_i(16) # => 2748 "abc".to_i(20) # => 4232 "number".to_i(36) # => 1442151747 "zz1z".to_i(36) # => 1678391 "abcdef".to_i(16) # => 11259375 "AbCdEf".to_i(16) # => 11259375 #--- 42.to_s(10) # => "42" -100.to_s(2) # => "-1100100" 255.to_s(16) # => "ff" 1442151747.to_s(36) # => "number" #--- "6".to_i(2) # => 0 "0".to_i(1) # ArgumentError: illegal radix 1 40.to_s(37) # ArgumentError: illegal radix 37 #---
	конвертация между числами

2008-06-10 15:43:36	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Берем логарифмы на руби
	Math.log(1) # => 0.0 Math.log(Math::E) # => 1.0 Math.log(10) # => 2.30258509299405 Math::E Math.log(25) # => 25.0 #--- Math.log10(1) # => 0.0 Math.log10(10) # => 1.0 Math.log10(10.1) # => 1.00432137378264 Math.log10(1000) # => 3.0 10 Math.log10(25) # => 25.0 #--- module Math def Math.logb(num, base) log(num) / log(base) end end #--- dividend = Math.log(2) (1..6).collect { \|x\| Math.log(x) / dividend } # => [0.0, 1.0, 1.58496250072116, 2.0, 2.32192809488736, 2.58496250072116] #--- require 'bigdecimal' require 'bigdecimal/math' require 'bigdecimal/util' module BigMath alias :log_slow :log def log(x, prec) if x <= 0 \|\| prec <= 0 raise ArgumentError, "Zero or negative argument for log" end return x if x.infinite? \|\| x.nan? sign, fraction, power, exponent = x.split fraction = BigDecimal(".#{fraction}") power = power.to_s.to_d log_slow(fraction, prec) + (log_slow(power, prec) * exponent) end end #--- include BigMath number = BigDecimal("1234.5678") Math.log(number) # => 7.11847622829779 prec = 50 BigMath.log_slow(number, prec).round(prec).to_s("F") # => "7.11847622829778629250879253638708184134073214145175" BigMath.log(number, prec).round(prec).to_s("F") # => "7.11847622829778629250879253638708184134073214145175" BigMath.log(number 1000, prec).round(prec).to_s("F") # => "7118.47622829778629250879253638708184134073214145175161" #--- huge_number = BigDecimal("1000") 1000 base = BigDecimal("10") (BigMath.log(huge_number, 100) / BigMath.log(base, 100)).to_f # => 3000.0 #---
	Math.log10, берем логарифмы на руби

2008-06-08 22:25:23	Ответить
Ruslan Voloshin Адрес: odessa Сообщений: 1201 Регистр: 2007-03-13 его блог 40 сообщ.	Взятие среднего, по основанию и медианы
	def mean(array) array.inject(0) { \|sum, x\| sum += x } / array.size.to_f end mean([1,2,3,4]) # => 2.5 mean([100,100,100,100.1]) # => 100.025 mean([-100, 100]) # => 0.0 mean([3,3,3,3]) # => 3.0 #--- def median(array, already_sorted=false) return nil if array.empty? array = array.sort unless already_sorted m_pos = array.size / 2 return array.size % 2 == 1 ? array[m_pos] : mean(array[m_pos-1..m_pos]) end median([1,2,3,4,5]) # => 3 median([5,3,2,1,4]) # => 3 median([1,2,3,4]) # => 2.5 median([1,1,2,3,4]) # => 2 median([2,3,-100,100]) # => 2.5 median([1, 1, 10, 100, 1000]) # => 10 #--- def modes(array, find_all=true) histogram = array.inject(Hash.new(0)) { \|h, n\| h[n] += 1; h } modes = nil histogram.each_pair do \|item, times\| modes << item if modes && times == modes[0] and find_all modes = [times, item] if (!modes && times>1) or (modes && times>modes[0]) end return modes ? modes[1...modes.size] : modes end modes([1,2,3,4]) # => nil modes([1,1,2,3,4]) # => [1] modes([1,1,2,2,3,4]) # => [1, 2] modes([1,1,2,2,3,4,4]) # => [1, 2, 4] modes([1,1,2,2,3,4,4], false) # => [1] modes([1,1,2,2,3,4,4,4,4,4]) # => [4] #--- def mean_without_float_conversion(array) array.inject(0) { \|x, sum\| sum += x } / array.size end require 'rational' numbers = [Rational(2,3), Rational(3,4), Rational(6,7)] mean(numbers) # => 0.757936507936508 mean_without_float_conversion(numbers) # => Rational(191, 252) #--- mean([1, 100, 100000]) # => 33367.0 median([1, 100, 100000]) # => 100 mean([1, 100, -1000000]) # => -333299.666666667 median([1, 100, -1000000]) # => 1 #--- median(["a", "z", "b", "l", "m", "j", "b"]) # => "j" median(["a", "b", "c", "d"]) # TypeError: String can't be coerced into Fixnum #--- def mean_and_standard_deviation(array) m = mean(array) variance = array.inject(0) { \|variance, x\| variance += (x - m) ** 2 } return m, Math.sqrt(variance/(array.size-1)) end #All the items in the list are close to the mean, so the standard #deviation is low. mean_and_standard_deviation([1,2,3,1,1,2,1]) # => [1.57142857142857, 0.786795792469443] #The outlier increases the mean, but also increases the standard deviation. mean_and_standard_deviation([1,2,3,1,1,2,1000]) # => [144.285714285714, 377.33526837801] #---
	median, mode

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