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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]
haskell
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
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)
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).
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.
haskell
8 `gcd` 12
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
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).
