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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:
java 1.5
erlang
cpp C++11 (gcc 4.6/VC++ 2010)
fsharp
haskell
haskell
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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]
SortedSet<List<Integer>> results = new TreeSet<List<Integer>>(new Comparator<List<Integer>>() {
public int compare(List<Integer> o1, List<Integer> o2) {
return o1.get(2).compareTo(o2.get(2));
}
});
for (int x = 1; x <= 20; x++) {
for (int y = 1; y <= 20; y++) {
double z = Math.hypot(x, y) ;
if ((int) z == z)
results.add(Arrays.asList( new Integer[] { x, y, (int) z }));
}
}
public int compare(List<Integer> o1, List<Integer> o2) {
return o1.get(2).compareTo(o2.get(2));
}
});
for (int x = 1; x <= 20; x++) {
for (int y = 1; y <= 20; y++) {
double z = Math.hypot(x, y) ;
if ((int) z == z)
results.add(Arrays.asList( new Integer[] { x, y, (int) z }));
}
}
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).
vector<solution> solutions;
for (int a = 1; a <= 20; ++a)
for (int b = a + 1; b <= 20; ++b)
{
int c_squared = a*a + b*b;
int c = b + 1;
while (c * c < c_squared)
++c;
if (c * c == c_squared)
solutions.push_back(make_tuple(a, b, c));
}
sort(begin(solutions), end(solutions),
[](const solution& s1, const solution& s2) { return get<2>(s1) < get<2>(s2); });
for (const auto &s: solutions)
cout << '[' << get<0>(s) << ", " << get<1>(s) << ", " << get<2>(s) << ']' << endl;
for (int a = 1; a <= 20; ++a)
for (int b = a + 1; b <= 20; ++b)
{
int c_squared = a*a + b*b;
int c = b + 1;
while (c * c < c_squared)
++c;
if (c * c == c_squared)
solutions.push_back(make_tuple(a, b, c));
}
sort(begin(solutions), end(solutions),
[](const solution& s1, const solution& s2) { return get<2>(s1) < get<2>(s2); });
for (const auto &s: solutions)
cout << '[' << get<0>(s) << ", " << get<1>(s) << ", " << get<2>(s) << ']' << endl;
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);;
import Data.List
import Control.Monad
pythTriangles :: [(Int,Int,Int)]
pythTriangles = do
a <- [1..20]
b <- [a+1..20]
c <- [1..2*b]
guard (a*a + b*b == c*c)
return (a,b,c)
cmpThird (_,_,a) (_,_,b)
| a < b = LT
| a == b = EQ
| otherwise = GT
main = mapM_ print (sortBy cmpThird pythTriangles)
import Control.Monad
pythTriangles :: [(Int,Int,Int)]
pythTriangles = do
a <- [1..20]
b <- [a+1..20]
c <- [1..2*b]
guard (a*a + b*b == c*c)
return (a,b,c)
cmpThird (_,_,a) (_,_,b)
| a < b = LT
| a == b = EQ
| otherwise = GT
main = mapM_ print (sortBy cmpThird pythTriangles)
import Data.Function
import Data.List
pythTriangles =
[(a,b,c) | a <- [1..20], b <- [a+1..20], c <- [1..2*b], a*a + b*b == c*c]
main = mapM_ print $ sortBy (compare `on` third) pythTriangles where
third (_,_,x) = x
import Data.List
pythTriangles =
[(a,b,c) | a <- [1..20], b <- [a+1..20], c <- [1..2*b], a*a + b*b == c*c]
main = mapM_ print $ sortBy (compare `on` third) pythTriangles where
third (_,_,x) = x
Submit a new solution for java, erlang, cpp, fsharp ...
There are 14 other solutions in additional languages (clojure, fantom, groovy, ocaml ...)
