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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]
php
for ($x = 1; $x <= 20; $x++) {
for ($y = $x; $y <= 20; $y++) {
$z = hypot($x, $y); // or $z = sqrt($x*$x + $y*$y);
if (round($z) == $z) {
$array = array($x, $y, $z);
sort($array, SORT_NUMERIC);
$res[] = $array;
}
}
}
// calculate the total of the sides
foreach ($res as $a) {
$total[] = ($a[0] + $a[1] + $a[2]);
}
array_multisort($total, $res); // and sort them after the total
// result is in $res
for ($y = $x; $y <= 20; $y++) {
$z = hypot($x, $y); // or $z = sqrt($x*$x + $y*$y);
if (round($z) == $z) {
$array = array($x, $y, $z);
sort($array, SORT_NUMERIC);
$res[] = $array;
}
}
}
// calculate the total of the sides
foreach ($res as $a) {
$total[] = ($a[0] + $a[1] + $a[2]);
}
array_multisort($total, $res); // and sort them after the total
// result is in $res
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).
clojure
(defn pythagorean [a b c] (= (+ (* a a) (* b b)) (* c c)))
(defn intsqrt [cc]
(. (. Math sqrt cc) intValue)
)
(defn triples [maxSize]
(filter not-empty
(for [a (range 1 20) b (range a 20)]
(let [c (intsqrt (+ (* a a) (* b b)))]
(if (pythagorean a b c)
[a b c]
()
)))))
(triples 20)
; -> ([3 4 5] [5 12 13] [6 8 10] [8 15 17] [9 12 15] [12 16 20] [15 20 25])
(defn sortByHypotenuse [triples]
(sort-by #(first (rest (rest %))) triples)
)
(sortByHypotenuse (triples 20))
; -> ([3 4 5] [6 8 10] [5 12 13] [9 12 15] [8 15 17] [12 16 20] [15 20 25])
(defn intsqrt [cc]
(. (. Math sqrt cc) intValue)
)
(defn triples [maxSize]
(filter not-empty
(for [a (range 1 20) b (range a 20)]
(let [c (intsqrt (+ (* a a) (* b b)))]
(if (pythagorean a b c)
[a b c]
()
)))))
(triples 20)
; -> ([3 4 5] [5 12 13] [6 8 10] [8 15 17] [9 12 15] [12 16 20] [15 20 25])
(defn sortByHypotenuse [triples]
(sort-by #(first (rest (rest %))) triples)
)
(sortByHypotenuse (triples 20))
; -> ([3 4 5] [6 8 10] [5 12 13] [9 12 15] [8 15 17] [12 16 20] [15 20 25])
(doseq [pt (sort-by #(% 2)
(for [a (range 1 21)
b (range a 21)
:let [aa+bb (+ (* a a) (* b b))
c (Math/round (Math/sqrt aa+bb))]
:when (= aa+bb (* c c))]
[a b c]))]
(println pt))
(for [a (range 1 21)
b (range a 21)
:let [aa+bb (+ (* a a) (* b b))
c (Math/round (Math/sqrt aa+bb))]
:when (= aa+bb (* c c))]
[a b c]))]
(println pt))
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.
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);
}
clojure
(defn gcd [a b]
(if (zero? b)
a
(recur b (mod b a))))
(if (zero? b)
a
(recur b (mod b a))))
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))
}
