Set of real numbers: Difference between revisions

Content added Content deleted
(→‎{{header|Ruby}}: add methods (new_Rset, valid?, ^, ==))
(→‎{{header|Ruby}}: add length method and Optional work)
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=={{header|Ruby}}==
=={{header|Ruby}}==
{{works with|Ruby|1.9.3}}
<lang ruby>class Rset
<lang ruby>class Rset
Set = Struct.new(:lo, :hi, :inc_lo, :inc_hi) do
Set = Struct.new(:lo, :hi, :inc_lo, :inc_hi) do
def include?(x)
def include?(x)
(inc_lo ? lo<=x : lo<x) and (inc_hi ? x<=hi : x<hi)
(inc_lo ? lo<=x : lo<x) and (inc_hi ? x<=hi : x<hi)
end
def length
hi - lo
end
end
def to_s
def to_s
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raise TypeError unless lo.is_a?(Numeric) and hi.is_a?(Numeric)
raise TypeError unless lo.is_a?(Numeric) and hi.is_a?(Numeric)
raise ArgumentError unless valid?(lo, hi, inc_lo, inc_hi)
raise ArgumentError unless valid?(lo, hi, inc_lo, inc_hi)
@sets = [Set[lo, hi, inc_lo, inc_hi]]
@sets = [Set[lo, hi, !!inc_lo, !!inc_hi]] # !! -> Boolean values
end
end
end
end
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else
else
lo = [set.lo, oset.lo].max
lo = [set.lo, oset.lo].max
if set.lo < oset.lo
if set.lo == oset.lo
inc_lo = oset.inc_lo
inc_lo = set.inc_lo && oset.inc_lo
elsif set.lo > oset.lo
inc_lo = set.inc_lo
else
else
inc_lo = set.inc_lo && oset.inc_lo
inc_lo = (set.lo < oset.lo) ? oset.inc_lo : set.inc_lo
end
end
hi = [set.hi, oset.hi].min
hi = [set.hi, oset.hi].min
if set.hi < oset.hi
if set.hi == oset.hi
inc_hi = set.inc_hi
inc_hi = set.inc_hi && oset.inc_hi
elsif set.hi > oset.hi
inc_hi = oset.inc_hi
else
else
inc_hi = set.inc_hi && oset.inc_hi
inc_hi = (set.hi < oset.hi) ? set.inc_hi : oset.inc_hi
end
end
work << Set[lo, hi, inc_lo, inc_hi] if valid?(lo, hi, inc_lo, inc_hi)
work << Set[lo, hi, inc_lo, inc_hi] if valid?(lo, hi, inc_lo, inc_hi)
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return false if self.class != other.class
return false if self.class != other.class
@sets == other.sets
@sets == other.sets
end
def length
@sets.inject(0){|len, set| len + set.length}
end
end
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test_set.each do |sa,ope,sb|
test_set.each do |sa,ope,sb|
str = "#{sa} #{ope} #{sb}"
str = "#{sa} #{ope} #{sb}"
a = Rset.from_s(sa)
e = eval("Rset.from_s(sa) #{ope} Rset.from_s(sb)")
⚫
puts "%s -> %s" % [str, e]
⚫
b = Rset.from_s(sb)
⚫
(0..2).each{|i| puts " #{i} : #{e.include?(i)}"}
c = eval("a #{ope} b")
⚫
puts "%s -> %s" % [str, c]
⚫
(0..2).each{|i| puts " #{i} : #{c.include?(i)}"}
end
end


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test_set = ["x = Rset[0,2] | Rset(3,7) | Rset[8,10]",
test_set = ["x = Rset[0,2] | Rset(3,7) | Rset[8,10]",
"y = Rset(7,9) | Rset(5,6) | Rset[1,4]",
"y = Rset(7,9) | Rset(5,6) | Rset[1,4]",
"x | y", "x & y", "x - y", "y - x", "x ^ y"]
"x | y", "x & y", "x - y", "y - x", "x ^ y",
"y ^ x == (x | y) - (x & y)"]
x = y = nil
x = y = nil
test_set.each {|str| puts "#{str} -> #{eval(str)}"}
test_set.each {|str| puts "#{str} -> #{eval(str)}"}
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puts "a = #{a = Rset(-inf,inf)}"
puts "a = #{a = Rset(-inf,inf)}"
puts "b = #{b = Rset.from_s('[1/3,11/7)')}"
puts "b = #{b = Rset.from_s('[1/3,11/7)')}"
puts "a - b -> #{a - b}"
puts "a - b -> #{a - b}"</lang>
⚫
puts "create empty set : #{Rset.new}"</lang>


{{out}}
{{out}}
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y - x -> Rset(2,3],(7,8)
y - x -> Rset(2,3],(7,8)
x ^ y -> Rset[0,1),(2,3],(4,5],[6,7),(7,8),[9,10]
x ^ y -> Rset[0,1),(2,3],(4,5],[6,7),(7,8),[9,10]
y ^ x == (x | y) - (x & y) -> true


a = Rset(-Infinity,Infinity)
a = Rset(-Infinity,Infinity)
b = Rset[1/3,11/7)
b = Rset[1/3,11/7)
a - b -> Rset(-Infinity,1/3),[11/7,Infinity)
a - b -> Rset(-Infinity,1/3),[11/7,Infinity)
</pre>
create empty set : Rset

'''Optional work:'''
{{works with|Ruby|2.1+}}
<lang ruby>str, e = "e = Rset.new", nil
puts "#{str} -> #{eval(str)}\t\t# create empty set"
str = "e.empty?"
puts "#{str} -> #{eval(str)}"
puts

include Math
lohi = Enumerator.new do |y|
t = 1 / sqrt(6)
0.step do |n|
y << [sqrt(12*n+1) * t, sqrt(12*n+5) * t]
y << [sqrt(12*n+7) * t, sqrt(12*n+11) * t]
end
end

a = Rset.new
loop do
lo, hi = lohi.next
break if 10 <= lo
⚫
a |= Rset(lo, hi)
end
a &= Rset(0,10)

b = (0...10).inject(Rset.new){|res,i| res |= Rset(i+1/6r,i+5/6r)}

puts "a : #{a}"
puts "a.length : #{a.length}"
puts "b : #{b}"
puts "b.length : #{b.length}"
puts "a - b : #{a - b}"
⚫
puts "(a-b).length : #{(a-b).length}"</lang>

{{out}}
<pre>
e = Rset.new -> Rset # create empty set
e.empty? -> true

a : Rset(0.4082482904638631,0.912870929175277),(1.0801234497346435,1.3540064007726602),(1.4719601443879746,1.6832508230603467), ... (9.907909298467901,9.941495528004495),(9.958246164193106,9.991663191547909)
a.length : 6.50103079235655
b : Rset(1/6,5/6),(7/6,11/6),(13/6,17/6),(19/6,23/6),(25/6,29/6),(31/6,35/6),(37/6,41/6),(43/6,47/6),(49/6,53/6),(55/6,59/6)
b.length : 20/3
a - b : Rset[5/6,0.912870929175277),(1.0801234497346435,7/6],[11/6,1.9578900207451218),(2.041241452319315,13/6], ... (9.907909298467901,9.941495528004495),(9.958246164193106,9.991663191547909)
(a-b).length : 2.0758648411846745
</pre>
</pre>


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