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Find all Pythagorean triangles with length or height less than or equal to 20
Pythagorean triangles are right angle triangles whose sides comply with the following equation:
a * a + b * b = c * c
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:
a * a + b * b = c * c
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Find all such triangles where a, b and c are non-zero integers with a and b less than or equal to 20. Sort your results by the size of the hypotenuse. The expected answer is:
[3, 4, 5]
[6, 8, 10]
[5, 12, 13]
[9, 12, 15]
[8, 15, 17]
[12, 16, 20]
[15, 20, 25]
ruby
results=[]
1.upto(20) do |a|
1.upto(20) do |b|
c=Math.sqrt(a**2+b**2)
results<<[a, b, c.to_i] if c.to_i==c && !results.index([b, a, c.to_i])
end
end
results=results.sort_by{|r| r[2]}
puts results
1.upto(20) do |a|
1.upto(20) do |b|
c=Math.sqrt(a**2+b**2)
results<<[a, b, c.to_i] if c.to_i==c && !results.index([b, a, c.to_i])
end
end
results=results.sort_by{|r| r[2]}
puts results
def find_pythag( max=20 )
r = []
1.upto max do |n|
n.upto max do |m|
h = Math.sqrt( n**2 + m**2)
r << [n,m,h.to_i] if (h.round - h).zero?
end
end
r.sort_by { |a| a[2] }
end
r = []
1.upto max do |n|
n.upto max do |m|
h = Math.sqrt( n**2 + m**2)
r << [n,m,h.to_i] if (h.round - h).zero?
end
end
r.sort_by { |a| a[2] }
end
fantom
triangles := [,]
(1..20).each |Int a|
{
(a..20).each |Int b|
{
c := (a.pow(2) + b.pow(2)).toFloat.sqrt
if (c % c.toInt == 0.0f && !triangles.contains([b,a,c]))
triangles.add([a,b,c.toInt])
}
}
triangles.sort |Int[] x, Int[] y -> Int| { x[2]-y[2] }
echo(triangles)
(1..20).each |Int a|
{
(a..20).each |Int b|
{
c := (a.pow(2) + b.pow(2)).toFloat.sqrt
if (c % c.toInt == 0.0f && !triangles.contains([b,a,c]))
triangles.add([a,b,c.toInt])
}
}
triangles.sort |Int[] x, Int[] y -> Int| { x[2]-y[2] }
echo(triangles)
Greatest Common Divisor
Find the largest positive integer that divides two given numbers without a remainder. For example, the GCD of 8 and 12 is 4.
ruby
135.gcd(30)
# => 15
# => 15
csharp
public static int gcd(int a, int b)
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
{
if (b == 0)
return a;
else
return gcd(b, a % b);
}
fantom
gcd := |Int a, Int b -> Int| {
pair := [a, b].sort
while (pair.first != 0)
pair.set(1, pair.last % pair.first).swap(0, 1)
return pair.last
}
echo(gcd(12, 8)) // a>b, result == 4
echo(gcd(1029, 1071)) // a<b, result == 21
pair := [a, b].sort
while (pair.first != 0)
pair.set(1, pair.last % pair.first).swap(0, 1)
return pair.last
}
echo(gcd(12, 8)) // a>b, result == 4
echo(gcd(1029, 1071)) // a<b, result == 21
