Heronian triangles: Difference between revisions
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(7, 65, 68) perim: 140 area: 210 |
(7, 65, 68) perim: 140 area: 210 |
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(3, 148, 149) perim: 300 area: 210</pre> |
(3, 148, 149) perim: 300 area: 210</pre> |
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=={{header|Ruby}}== |
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<lang ruby>Triangle = Struct.new(:a, :b, :c) do |
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include Comparable |
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def self.valid?(a,b,c) # class method |
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short, middle, long = [a, b, c].sort |
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short + middle > long |
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end |
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def sides |
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@sides ||= [a, b, c].sort |
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end |
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def perimeter |
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@perimeter ||= a + b + c |
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end |
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def semiperimeter |
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@semiperimeter ||= perimeter/2.0 |
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end |
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def area |
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s = semiperimeter |
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@area ||= Math.sqrt(s*(s - a)*(s - b)*(s - c)) |
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end |
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def heronian? |
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area == area.to_i |
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end |
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def <=>(other) |
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[area, perimeter, sides] <=> [other.area, other.perimeter, other.sides] |
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end |
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def to_s |
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"#{sides.join("x").ljust(10)}\t#{perimeter}\t#{area}" |
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end |
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end |
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max, area = 200, 210 |
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prim_triangles = [] |
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1.upto(max) do |a| |
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a.upto(max) do |b| |
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b.upto(max) do |c| |
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next if a.gcd(b).gcd(c) > 1 |
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prim_triangles << Triangle.new(a, b, c) if Triangle.valid?(a, b, c) |
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end |
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end |
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end |
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sorted = prim_triangles.select(&:heronian?).sort |
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puts "Primitive heronian triangles with sides upto #{max}: #{sorted.size}" |
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puts "\nsides \tperim.\tarea" |
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sorted.first(10).each{|tr| puts tr } |
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puts "\nTriangles with an area of: #{area}" |
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sorted.select{|tr| tr.area == area}.each{|tr| puts tr } |
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</lang> |
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{{out}} |
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<pre> |
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Primitive heronian triangles with sides upto 200: 517 |
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sides perim. area |
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3x4x5 12 6.0 |
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5x5x6 16 12.0 |
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5x5x8 18 12.0 |
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4x13x15 32 24.0 |
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5x12x13 30 30.0 |
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9x10x17 36 36.0 |
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3x25x26 54 36.0 |
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7x15x20 42 42.0 |
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10x13x13 36 60.0 |
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8x15x17 40 60.0 |
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Triangles with an area of: 210 |
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17x25x28 70 210.0 |
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20x21x29 70 210.0 |
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12x35x37 84 210.0 |
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17x28x39 84 210.0 |
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7x65x68 140 210.0 |
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3x148x149 300 210.0 |
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</pre> |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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| Line 591: | Line 508: | ||
5 area: 210 perimeter: 140 sides: 7 65 68 |
5 area: 210 perimeter: 140 sides: 7 65 68 |
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6 area: 210 perimeter: 300 sides: 3 148 149 |
6 area: 210 perimeter: 300 sides: 3 148 149 |
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</pre> |
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=={{header|Ruby}}== |
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<lang ruby>Triangle = Struct.new(:a, :b, :c) do |
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include Comparable |
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def self.valid?(a,b,c) # class method |
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short, middle, long = [a, b, c].sort |
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short + middle > long |
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end |
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def sides |
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@sides ||= [a, b, c].sort |
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end |
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def perimeter |
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@perimeter ||= a + b + c |
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end |
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def semiperimeter |
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@semiperimeter ||= perimeter/2.0 |
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end |
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def area |
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s = semiperimeter |
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@area ||= Math.sqrt(s*(s - a)*(s - b)*(s - c)) |
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end |
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def heronian? |
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area == area.to_i |
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end |
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def <=>(other) |
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[area, perimeter, sides] <=> [other.area, other.perimeter, other.sides] |
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end |
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def to_s |
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"#{sides.join("x").ljust(10)}\t#{perimeter}\t#{area}" |
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end |
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end |
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max, area = 200, 210 |
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prim_triangles = [] |
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1.upto(max) do |a| |
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a.upto(max) do |b| |
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b.upto(max) do |c| |
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next if a.gcd(b).gcd(c) > 1 |
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prim_triangles << Triangle.new(a, b, c) if Triangle.valid?(a, b, c) |
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end |
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end |
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end |
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sorted = prim_triangles.select(&:heronian?).sort |
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puts "Primitive heronian triangles with sides upto #{max}: #{sorted.size}" |
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puts "\nsides \tperim.\tarea" |
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sorted.first(10).each{|tr| puts tr } |
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puts "\nTriangles with an area of: #{area}" |
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sorted.select{|tr| tr.area == area}.each{|tr| puts tr } |
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</lang> |
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{{out}} |
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<pre> |
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Primitive heronian triangles with sides upto 200: 517 |
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sides perim. area |
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3x4x5 12 6.0 |
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5x5x6 16 12.0 |
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5x5x8 18 12.0 |
|||
4x13x15 32 24.0 |
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5x12x13 30 30.0 |
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9x10x17 36 36.0 |
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3x25x26 54 36.0 |
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7x15x20 42 42.0 |
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10x13x13 36 60.0 |
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8x15x17 40 60.0 |
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Triangles with an area of: 210 |
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17x25x28 70 210.0 |
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20x21x29 70 210.0 |
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12x35x37 84 210.0 |
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17x28x39 84 210.0 |
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7x65x68 140 210.0 |
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3x148x149 300 210.0 |
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</pre> |
</pre> |
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