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]
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
erlang
find_all_pythagorean_triangles(L) ->
lists:sort(fun({_, _, H1}, {_, _, H2}) -> H1 =< H2 end,
[ { X, Y, Z } ||
X <- lists:seq(1,L),
Y <- lists:seq(1,L),
Z <- lists:seq(1,2*L),
X*X + Y*Y =:= Z*Z,
Y > X,
Z > Y
]).
main(_) ->
List = find_all_pythagorean_triangles(20).
lists:sort(fun({_, _, H1}, {_, _, H2}) -> H1 =< H2 end,
[ { X, Y, Z } ||
X <- lists:seq(1,L),
Y <- lists:seq(1,L),
Z <- lists:seq(1,2*L),
X*X + Y*Y =:= Z*Z,
Y > X,
Z > Y
]).
main(_) ->
List = find_all_pythagorean_triangles(20).
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);;
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.
ruby
135.gcd(30)
# => 15
# => 15
erlang
-module(gcd).
-export([gcd/2]).
gcd(A, 0) -> A;
gcd(A, B) -> gcd(B, A rem B).
-export([gcd/2]).
gcd(A, 0) -> A;
gcd(A, B) -> gcd(B, A rem B).
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);
}
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)
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))
}
