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]
python
from math import sqrt
a = 1
ret = []
while a <= 20:
b = 1
while b <= 20:
c = sqrt((a**2)+(b**2))
if int(c) == c and sorted([a,b,int(c)]) not in ret:
ret.append(sorted([a,b,int(c)]))
b +=1
a +=1
print ret
or if you wanna get snarky..
print sorted(set([tuple(sorted((a,b,int(sqrt((a**2)+(b**2)))))) for a in xrange(1,21) for \
b in xrange(1,21) if int(sqrt((a**2)+(b**2))) == sqrt((a**2)+(b**2))]))
a = 1
ret = []
while a <= 20:
b = 1
while b <= 20:
c = sqrt((a**2)+(b**2))
if int(c) == c and sorted([a,b,int(c)]) not in ret:
ret.append(sorted([a,b,int(c)]))
b +=1
a +=1
print ret
or if you wanna get snarky..
print sorted(set([tuple(sorted((a,b,int(sqrt((a**2)+(b**2)))))) for a in xrange(1,21) for \
b in xrange(1,21) if int(sqrt((a**2)+(b**2))) == sqrt((a**2)+(b**2))]))
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))
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')
java
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 }));
}
}
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).
perl
#!/usr/bin/perl
my @results;
for my $x (1..20) {
for my $y ($x..20) {
my $z = sqrt($x**2+$y**2);
push @results, [$x,$y,$z] if $z == int($z);
}
}
for my $triangle ( sort { $a->[2] <=> $b->[2] } @results) {
print "[".join(',',@$triangle)."]\n";
}
my @results;
for my $x (1..20) {
for my $y ($x..20) {
my $z = sqrt($x**2+$y**2);
push @results, [$x,$y,$z] if $z == int($z);
}
}
for my $triangle ( sort { $a->[2] <=> $b->[2] } @results) {
print "[".join(',',@$triangle)."]\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.
python
def gcd_recursive(i, j):
if min(i, j) == 0:
return max(i, j)
else:
return gcd_recursive(min(i, j), abs(i - j))
def gcd_iterative(i, j):
while min(i, j) != 0:
i, j = min(i, j), abs(i - j)
return max(i, j)
if __name__ == "__main__":
print gcd_recursive(8, 12)
print gcd_iterative(8, 12)
if min(i, j) == 0:
return max(i, j)
else:
return gcd_recursive(min(i, j), abs(i - j))
def gcd_iterative(i, j):
while min(i, j) != 0:
i, j = min(i, j), abs(i - j)
return max(i, j)
if __name__ == "__main__":
print gcd_recursive(8, 12)
print gcd_iterative(8, 12)
from fractions import gcd
print gcd(8, 12)
print gcd(8, 12)
clojure
(defn gcd [a b]
(if (zero? b)
a
(recur b (mod b a))))
(if (zero? b)
a
(recur b (mod b a))))
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))
}
java
static int gcd(int a, int b) {
if (Math.min(a, b) == 0)
return Math.max(a, b);
else
return gcd(Math.min(a, b), Math.abs(a - b));
}
if (Math.min(a, b) == 0)
return Math.max(a, b);
else
return gcd(Math.min(a, b), Math.abs(a - b));
}
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).
perl
sub gcd {
my ($a, $b) = @_;
($a,$b) = ($b,$a) if $a > $b;
while ($a) { ($a, $b) = ($b % $a, $a) }
return $b;
}
print gcd( 8, 12 );
my ($a, $b) = @_;
($a,$b) = ($b,$a) if $a > $b;
while ($a) { ($a, $b) = ($b % $a, $a) }
return $b;
}
print gcd( 8, 12 );
my $g = gcd (8, 12);
print $g;
sub gcd {
# Euclid's Algorithm - recursive
my ($c, $d) = @_;
return $c unless $d;
return gcd ($d, $c % $d);
}
print $g;
sub gcd {
# Euclid's Algorithm - recursive
my ($c, $d) = @_;
return $c unless $d;
return gcd ($d, $c % $d);
}
my $g = gcd2 (8, 12);
print $g;
sub gcd2 {
# Dijkstra's Algorithm - recursive
my ($c, $d) = @_;
return $c if $c == $d;
return $c > $d? gcd2 ($c - $d, $d) : gcd2 ($c, $d - $c);
}
print $g;
sub gcd2 {
# Dijkstra's Algorithm - recursive
my ($c, $d) = @_;
return $c if $c == $d;
return $c > $d? gcd2 ($c - $d, $d) : gcd2 ($c, $d - $c);
}
