View Category
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]
fsharp
let getGoodTri (a,b) =
let h = int(System.Math.Sqrt(float(a*a + b*b)))
if a*a + b*b = h*h then Some(a,b,h)
else None
seq{ for i in 1..20 do yield! seq{for j in i..20 do yield i,j} } |> Seq.choose(getGoodTri) |> Seq.sortBy(fun (_,_,c) -> c);;
let h = int(System.Math.Sqrt(float(a*a + b*b)))
if a*a + b*b = h*h then Some(a,b,h)
else None
seq{ for i in 1..20 do yield! seq{for j in i..20 do yield i,j} } |> Seq.choose(getGoodTri) |> Seq.sortBy(fun (_,_,c) -> c);;
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)
groovy
Set results = []
for (x in 1..20)
for (y in x..20) {
def z = sqrt(x*x + y*y)
if (z.toInteger() == z) results << [x, y, z.toInteger()]
}
println results.sort{it[2]}.join('\n')
for (x in 1..20)
for (y in x..20) {
def z = sqrt(x*x + y*y)
if (z.toInteger() == z) results << [x, y, z.toInteger()]
}
println results.sort{it[2]}.join('\n')
Set results = []
for (x in 1..20)
for (y in x..20) {
def z = sqrt(x*x + y*y)
if (z.toInteger() == z) results << [x, y, z.toInteger()]
}
println results.sort{it[2]}.join('\n')
for (x in 1..20)
for (y in x..20) {
def z = sqrt(x*x + y*y)
if (z.toInteger() == z) results << [x, y, z.toInteger()]
}
println results.sort{it[2]}.join('\n')
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.
fsharp
let rec gcd x y =
if y = 0 then x
else gcd y (x % y)
if y = 0 then x
else gcd y (x % y)
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
groovy
static def gcd(int i, int j) {
if (Math.min(i,j)==0) return Math.max(i,j)
else return gcd(Math.min(i,j),Math.abs(i-j))
}
if (Math.min(i,j)==0) return Math.max(i,j)
else return gcd(Math.min(i,j),Math.abs(i-j))
}
