List comprehensions
You are encouraged to solve this task according to the task description, using any language you may know.
A list comprehension is a special syntax in some programming languages to describe lists. It is similar to the way mathematicians describe sets, with a set comprehension, hence the name.
Some attributes of a list comprehension are that:
- They should be distinct from (nested) for loops within the syntax of the language.
- They should return either a list or an iterator (something that returns successive members of a collection, in order).
- The syntax has parts corresponding to that of set-builder notation.
Write a list comprehension that builds the list of all Pythagorean triples with elements between 1 and n. If the language has multiple ways for expressing such a construct (for example, direct list comprehensions and generators), write one example for each.
Ada
There is no equivalent construct in Ada. In Ada05, the predefined library Ada.Containers implements 3 types of Doubly_Linked_Lists : Basic; Indefinite; Restricted. <lang Ada>with Ada.Text_IO; use Ada.Text_IO; with Ada.Containers.Doubly_Linked_Lists;
procedure Pythagore_Set is
type Triangles is array (1 .. 3) of Positive;
package Triangle_Lists is new Ada.Containers.Doubly_Linked_Lists (
Triangles);
use Triangle_Lists;
function Find_List (Upper_Bound : Positive) return List is
L : List := Empty_List;
begin
for A in 1 .. Upper_Bound loop
for B in A + 1 .. Upper_Bound loop
for C in B + 1 .. Upper_Bound loop
if ((A * A + B * B) = C * C) then
Append (L, (A, B, C));
end if;
end loop;
end loop;
end loop;
return L;
end Find_List;
Triangle_List : List; C : Cursor; T : Triangles;
begin
Triangle_List := Find_List (Upper_Bound => 20);
C := First (Triangle_List);
while Has_Element (C) loop
T := Element (C);
Put
("(" &
Integer'Image (T (1)) &
Integer'Image (T (2)) &
Integer'Image (T (3)) &
") ");
Next (C);
end loop;
end Pythagore_Set; </lang>
program output:
( 3 4 5) ( 5 12 13) ( 6 8 10) ( 8 15 17) ( 9 12 15) ( 12 16 20)
ALGOL 68
ALGOL 68 does not have list comprehension, however it is sometimes reasonably generous about where a flex array is declared. And with the addition of an append operator "+:=" for lists they can be similarly manipulated.
<lang algol68>MODE XYZ = STRUCT(INT x,y,z);
OP +:= = (REF FLEX[]XYZ lhs, XYZ rhs)FLEX[]XYZ: (
[UPB lhs+1]XYZ out; out[:UPB lhs] := lhs; out[UPB out] := rhs; lhs := out
);
INT n = 20; print (([]XYZ(
FLEX[0]XYZ xyz; FOR x TO n DO FOR y FROM x+1 TO n DO FOR z FROM y+1 TO n DO IF x*x + y*y = z*z THEN xyz +:= XYZ(x,y,z) FI OD OD OD; xyz), new line
))</lang> Output:
+3 +4 +5 +5 +12 +13 +6 +8 +10 +8 +15 +17 +9 +12 +15 +12 +16 +20
AutoHotkey
List Comprehension is not built in. <lang AutoHotkey> comprehend("show", range(1, 20), "triples") return
comprehend(doToVariable, inSet, satisfying) {
set := %satisfying%(inSet.begin, inSet.end)
index := 1
While % set[index, 1]
{
item := set[index, 1] . ", " . set[index, 2] . ", " . set[index, 3]
%doToVariable%(item)
index += 1
}
return
}
show(var)
{
msgbox % var
}
range(begin, end)
{
set := object()
set.begin := begin
set.end := end
return set
}
!r::reload !q::exitapp
triples(begin, end) {
set := object()
index := 1
range := end - begin
loop, % range
{
x := begin + A_Index
loop, % range
{
y := A_Index + x
if y > 20
break loop, % range {
z := A_Index + y
if z > 20
break
isTriple := ((x ** 2 + y ** 2) == z ** 2)
if isTriple
{
set[index, 1] := x
set[index, 2] := y
set[index, 3] := z
index += 1
; msgbox % "triple: " x . y . z
}
} } } return set } </lang>
Bracmat
Bracmat does not have built-in list comprehension, but nevertheless there is a solution for fixed n that does not employ explicit loop syntax. By their positions in the pattern and the monotonically increasing values in the subject, it is guaranteed that x always is smaller than y and that y always is smaller than z. The combination of flags %@ ensures that x, y and z pick minimally one (%) and at most one (@) element from the subject list.
<lang bracmat>
:?py { Initialize the accumulating result list. }
& ( 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 { This is the subject }
: ? { Here starts the pattern }
%@?x
?
%@?y
?
%@?z
( ?
& -1*!z^2+!x^2+!y^2:0
& (!x,!y,!z) !py:?py
& ~ { This 'failure' expression forces backtracking }
) { Here ends the pattern }
| out$!py { You get here when backtracking has
exhausted all combinations of x, y and z }
);</lang>
Output:
(12,16,20) (9,12,15) (8,15,17) (6,8,10) (5,12,13) (3,4,5)
C#
LINQ
<lang csharp>using System.Linq;
static class Program {
static void Main()
{
var ts =
from a in Enumerable.Range(1, 20)
from b in Enumerable.Range(a, 21 - a)
from c in Enumerable.Range(b, 21 - b)
where a * a + b * b == c * c
select new { a, b, c };
foreach (var t in ts)
System.Console.WriteLine("{0}, {1}, {2}", t.a, t.b, t.c);
}
} </lang>
C++
There is no equivalent construct in C++. The code below uses two nested loops and an if statement:
<lang cpp>#include <vector>
- include <cmath>
- include <iostream>
- include <algorithm>
- include <iterator>
void list_comprehension( std::vector<int> & , int ) ;
int main( ) {
std::vector<int> triangles ; list_comprehension( triangles , 20 ) ; std::copy( triangles.begin( ) , triangles.end( ) ,
std::ostream_iterator<int>( std::cout , " " ) ) ;
std::cout << std::endl ; return 0 ;
}
void list_comprehension( std::vector<int> & numbers , int upper_border ) {
for ( int a = 1 ; a < upper_border ; a++ ) {
for ( int b = a + 1 ; b < upper_border ; b++ ) {
double c = pow( a * a + b * b , 0.5 ) ; //remembering Mr. Pythagoras if ( ( c * c ) < pow( upper_border , 2 ) + 1 ) { if ( c == floor( c ) ) { numbers.push_back( a ) ; numbers.push_back( b ) ; numbers.push_back( static_cast<int>( c ) ) ; } }
} }
} </lang>
This produces the following output:
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15 12 16 20
<lang cpp>#include <functional>
- include <iostream>
void PythagoreanTriples(int limit, std::function<void(int,int,int)> yield) {
for (int a = 1; a < limit; ++a) {
for (int b = a+1; b < limit; ++b) {
for (int c = b+1; c <= limit; ++c) {
if (a*a + b*b == c*c) {
yield(a, b, c);
}
}
}
}
}
int main() {
PythagoreanTriples(20, [](int x, int y, int z)
{
std::cout << x << "," << y << "," << z << "\n";
});
return 0;
}</lang>
Output:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
Clojure
<lang lisp>(defn pythagorean-triples [n]
(for [x (range 1 (inc n))
y (range x (inc n)) z (range y (inc n)) :when (= (+ (* x x) (* y y)) (* z z))]
[x y z]))</lang>
CoffeeScript
<lang coffeescript>flatten = (arr) -> arr.reduce ((memo, b) -> memo.concat b), []
pyth = (n) ->
flatten (for x in [1..n]
flatten (for y in [x..n]
for z in [y..n] when x*x + y*y is z*z
[x, y, z]
))
console.dir pyth 20</lang>
pyth can also be written more concisely as
<lang coffeescript>pyth = (n) -> flatten (flatten ([x, y, z] for z in [y..n] when x*x + y*y is z*z for y in [x..n]) for x in [1..n])</lang>
Common Lisp
Common Lisp's loop macro has all of the features of list comprehension, except for nested iteration. (loop for x from 1 to 3 for y from x to 3 collect (list x y)) only returns ((1 1) (2 2) (3 3)). You can nest your macro calls, so (loop for x from 1 to 3 append (loop for y from x to 3 collect (list x y))) returns ((1 1) (1 2) (1 3) (2 2) (2 3) (3 3)).
Here are the Pythagorean triples:
<lang lisp>(defun pythagorean-triples (n)
(loop for x from 1 to n
append (loop for y from x to n
append (loop for z from y to n
when (= (+ (* x x) (* y y)) (* z z))
collect (list x y z)))))</lang>
We can also define a new macro for list comprehensions. We can implement them easily with the help of the iterate package.
<lang lisp>(defun nest (l)
(if (cdr l) `(,@(car l) ,(nest (cdr l))) (car l)))
(defun desugar-listc-form (form)
(if (string= (car form) 'for) `(iter ,form) form))
(defmacro listc (expr &body (form . forms) &aux (outer (gensym)))
(nest
`((iter ,outer ,form)
,@(mapcar #'desugar-listc-form forms)
(in ,outer (collect ,expr)))))</lang>
We can then define a function to compute Pythagorean triples as follows:
<lang lisp>(defun pythagorean-triples (n)
(listc (list x y z) (for x from 1 to n) (for y from x to n) (for z from y to n) (when (= (+ (expt x 2) (expt y 2)) (expt z 2)))))</lang>
D
D doesn't have list comprehensions. One implementation: <lang d>import std.stdio, std.typetuple, std.range;
TA[] select(TA, TI1, TC1, TI2, TC2, TI3, TC3, TP)
(lazy TA mapper,
ref TI1 iter1, TC1 items1,
ref TI2 iter2, lazy TC2 items2,
ref TI3 iter3, lazy TC3 items3,
lazy TP where) {
Appender!(TA[]) result;
auto iters = TypeTuple!(iter1, iter2, iter3);
foreach (el1; items1) {
iter1 = el1;
foreach (el2; items2) {
iter2 = el2;
foreach (el3; items3) {
iter3 = el3;
if (where())
result.put(mapper());
}
}
}
TypeTuple!(iter1, iter2, iter3) = iters; return result.data;
}
void main() {
enum int n = 21; int x, y, z; auto r = select([x,y,z], x, iota(1,n+1), y, iota(x,n+1), z, iota(y,n+1), x*x + y*y == z*z); writeln(r);
}</lang> Output:
[[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
E
<lang e>pragma.enable("accumulator") # considered experimental
accum [] for x in 1..n { for y in x..n { for z in y..n { if (x**2 + y**2 <=> z**2) { _.with([x,y,z]) } } } }</lang>
Efene
<lang efene>pythag = fn (N) {
[(A, B, C) for A in lists.seq(1, N) \
for B in lists.seq(A, N) \
for C in lists.seq(B, N) \
if A + B + C <= N and A * A + B * B == C * C]
}
@public run = fn () {
io.format("~p~n", [pythag(20)])
} </lang>
Ela
<lang ela>let pyth n = [(x,y,z) \\ x <- [1..n], y <- [x..n], z <- [y..n] | x**2 + y**2 == z**2]</lang>
Erlang
<lang erlang>pythag(N) ->
[ {A,B,C} || A <- lists:seq(1,N),
B <- lists:seq(A,N),
C <- lists:seq(B,N),
A+B+C =< N,
A*A+B*B == C*C ].</lang>
F#
<lang fsharp>let pyth n = [ for a in [1..n] do
for b in [a..n] do
for c in [b..n] do
if (a*a+b*b = c*c) then yield (a,b,c)]</lang>
GAP
<lang gap># We keep only primitive pythagorean triples pyth := n ->
Filtered(Cartesian([1 .. n], [1 .. n], [1 .. n]), u -> u[3]^2 = u[1]^2 + u[2]^2 and u[1] < u[2] and GcdInt(u[1], u[2]) = 1);
pyth(100);
- [ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 7, 24, 25 ], [ 8, 15, 17 ], [ 9, 40, 41 ], [ 11, 60, 61 ], [ 12, 35, 37 ],
- [ 13, 84, 85 ], [ 16, 63, 65 ], [ 20, 21, 29 ], [ 28, 45, 53 ], [ 33, 56, 65 ], [ 36, 77, 85 ], [ 39, 80, 89 ],
- [ 48, 55, 73 ], [ 65, 72, 97 ] ]</lang>
Haskell
<lang haskell>pyth n = [(x,y,z) | x <- [1..n], y <- [x..n], z <- [y..n], x^2 + y^2 == z^2]</lang>
Since lists are monads, one can alternatively also use the do-notation (which is practical if the comprehension is large):
<lang haskell>import Control.Monad
pyth n = do
x <- [1..n] y <- [x..n] z <- [y..n] guard $ x^2 + y^2 == z^2 return (x,y,z)</lang>
Ioke
<lang ioke>for(
x <- 1..20, y <- x..20, z <- y..20, x * x + y * y == z * z, [x, y, z]
)</lang>
J
<lang J>require'stats' buildSet=:conjunction def '(#~ v) u y' triples=: 1 + 3&comb isPyth=: 2&{"1 = 1&{"1 +&.:*: 0&{"1 pythTr=: triples buildSet isPyth</lang>
The idiom here has two major elements:
First, you need a statement indicating the values of interest. In this case, (1+3&comb) which when used as a function of n specifies a list of triples each in the range 1..n.
Second, you need a statement of the form (#~ B) where B returns true for the desired members, and false for the undesired members.
In the above example, the word isPyth is our predicate (represented as B in the preceding paragraph). This corresponds to the constraint clause in set builder notation.
In the above example the word triples represents the universe of potential solutions (some of which will be valid, some not). This corresponds to the generator part of set builder notation.
The argument to isPyth will be the candidate solutions (the result of triples). The argument to triples will be the largest element desired in a triple.
Example use:
<lang J> pythTr 20
3 4 5 5 12 13 6 8 10 8 15 17 9 12 15
12 16 20</lang>
JavaScript
See here for more details
<lang javascript>function range(begin, end) {
for (let i = begin; i < end; ++i)
yield i;
}
function triples(n) {
return [[x,y,z] for each (x in range(1,n+1))
for each (y in range(x,n+1))
for each (z in range(y,n+1))
if (x*x + y*y == z*z) ]
}
for each (var triple in triples(20))
print(triple);</lang>
outputs:
3,4,5 5,12,13 6,8,10 8,15,17 9,12,15 12,16,20
Lua
Lua doesn't have list comprehensions built in, but they can be constructed from chained coroutines:
<lang lua> LC={} LC.__index = LC
function LC:new(o)
o = o or {}
setmetatable(o, self)
return o
end
function LC:add_iter(func)
local prev_iter = self.iter
self.iter = coroutine.wrap(
(prev_iter == nil) and (function() func{} end)
or (function() for arg in prev_iter do func(arg) end end))
return self
end
function maybe_call(maybe_func, arg)
if type(maybe_func) == "function" then return maybe_func(arg) end return maybe_func
end
function LC:range(key, first, last)
return self:add_iter(function(arg)
for value=maybe_call(first, arg), maybe_call(last, arg) do
arg[key] = value
coroutine.yield(arg)
end
end)
end
function LC:where(pred)
return self:add_iter(function(arg) if pred(arg) then coroutine.yield(arg) end end)
end </lang>
We can then define a function to compute Pythagorean triples as follows:
<lang lua> function get(key)
return (function(arg) return arg[key] end)
end
function is_pythagorean(arg)
return (arg.x^2 + arg.y^2 == arg.z^2)
end
function list_pythagorean_triples(n)
return LC:new():range("x",1,n):range("y",1,get("x")):range("z", get("y"), n):where(is_pythagorean).iter
end
for arg in list_pythagorean_triples(100) do
print(arg.x, arg.y, arg.z)
end </lang>
Mathematica
<lang mathematica>Select[Tuples[Range[n], 3], #11^2 + #12^2 == #13^2 &]</lang>
MATLAB / Octave
In Matlab/Octave, one does not think much about lists rather than vectors and matrices. Probably, the find() operation comes closes to the task <lang Matlab> N = 100;
[a,b] = mesgrid(1:N, 1:N); c = sqrt(a.^2 + b.^2); [x,y] = find( c==fix(c) );</lang>
Nemerle
Demonstrating a list comprehension and an iterator. List comprehension adapted from Haskell example, iterator adapted from C# example. <lang Nemerle>using System; using System.Console; using System.Collections.Generic;
module Program {
PythTriples(n : int) : list[int * int * int]
{
$[ (x, y, z) | x in [1..n], y in [x..n], z in [y..n], ((x**2) + (y**2)) == (z**2) ]
}
GetPythTriples(n : int) : IEnumerable[int * int * int]
{
foreach (x in [1..n])
{
foreach (y in [x..n])
{
foreach (z in [y..n])
{
when (((x**2) + (y**2)) == (z**2))
{
yield (x, y, z)
}
}
}
}
}
Main() : void
{
WriteLine("Pythagorean triples up to x = 20: {0}", PythTriples(20));
foreach (triple in GetPythTriples(20))
{
Write(triple)
}
}
}</lang>
OCaml
OCaml Batteries Included has uniform comprehension syntax for lists, arrays, enumerations (like streams), lazy lists (like lists but evaluated on-demand), sets, hashtables, etc.
Comprehension are of the form
[? expression | x <- enumeration ; condition; condition ; ...]
For instance, <lang ocaml># [? 2 * x | x <- 0 -- max_int ; x * x > 3];; - : int Enum.t = <abstr></lang> or, to compute a list, <lang ocaml># [? List: 2 * x | x <- 0 -- 100 ; x * x > 3];; - : int list = [2; 4; 6; 8; 10]</lang> or, to compute a set, <lang ocaml># [? PSet: 2 * x | x <- 0 -- 100 ; x * x > 3];; - : int PSet.t = <abstr></lang>
etc..
Oz
Oz does not have list comprehension.
However, there is a list comprehension package available here. It uses the unofficial and deprecated macro system. Usage example:
<lang oz>functor import
LazyList Application System
define
fun {Pyth N}
<<list [X Y Z] with
X <- {List.number 1 N 1} Y <- {List.number X N 1} Z <- {List.number Y N 1} where X*X + Y*Y == Z*Z
>> end
{ForAll {Pyth 20} System.show}
{Application.exit 0}
end</lang>
PARI/GP
GP 2.6.0 added support for a new comprehension syntax: <lang parigp>f(n)=[v|v<-vector(n^3,i,vector(3,j,i\n^(j-1)%n)),norml2(v)==2*v[3]^2]</lang>
Older versions of GP can emulate this through select:
<lang parigp>f(n)=select(v->norml2(v)==2*v[3]^2,vector(n^3,i,vector(3,j,i\n^(j-1)%n)))</lang>
Version 2.4.2 (obsolete, but widespread on Windows systems) requires inversion: <lang parigp>f(n)=select(vector(n^3,i,vector(3,j,i\n^(j-1)%n)),v->norml2(v)==2*v[3]^2)</lang>
Perl
Perl 5 does not have built-in list comprehension syntax. The closest approach are the list map and grep (elsewhere often known as filter) operators:
<lang perl>sub triples ($) {
my ($n) = @_;
map { my $x = $_; map { my $y = $_; map { [$x, $y, $_] } grep { $x**2 + $y**2 == $_**2 } 1..$n } 1..$n } 1..$n;
}</lang>
map binds $_ to each element of the input list and collects the results from the block. grep returns every element of the input list for which the block returns true. The .. operator generates a list of numbers in a specific range.
<lang perl>for my $t (triples(10)) {
print "@$t\n";
}</lang>
Perl 6
Perl 6 has single-dimensional list comprehensions that fall out naturally from nested modifiers; multidimensional comprehensions are also supported via the cross operator; however, Perl 6 does not (yet) support multi-dimensional list comprehensions with dependencies between the lists, so the most straightforward way is currently: <lang perl6>my $n = 20; gather for 1..$n -> $x {
for $x..$n -> $y {
for $y..$n -> $z {
take $x,$y,$z if $x*$x + $y*$y == $z*$z;
}
}
}</lang>
Note that gather/take is the primitive in Perl 6 corresponding to generators or coroutines in other languages. It is not, however, tied to function call syntax in Perl 6. We can get away with that because lists are lazy, and the demand for more of the list is implicit; it does not need to be driven by function calls.
PicoLisp
PicoLisp doesn't have list comprehensions. We might use a generator function, pipe, coroutine or pilog predicate.
Using a generator function
<lang PicoLisp>(de pythag (N)
(job '((X . 1) (Y . 1) (Z . 0))
(loop
(when (> (inc 'Z) N)
(when (> (inc 'Y) N)
(setq Y (inc 'X)) )
(setq Z Y) )
(T (> X N))
(T (= (+ (* X X) (* Y Y)) (* Z Z))
(list X Y Z) ) ) ) )
(while (pythag 20)
(println @) )</lang>
Using a pipe
<lang PicoLisp>(pipe
(for X 20
(for Y (range X 20)
(for Z (range Y 20)
(when (= (+ (* X X) (* Y Y)) (* Z Z))
(pr (list X Y Z)) ) ) ) )
(while (rd)
(println @) ) )</lang>
Using a coroutine
Coroutines are available only in the 64-bit version. <lang PicoLisp>(de pythag (N)
(co 'pythag
(for X N
(for Y (range X N)
(for Z (range Y N)
(when (= (+ (* X X) (* Y Y)) (* Z Z))
(yield (list X Y Z)) ) ) ) ) ) )
(while (pythag 20)
(println @) )</lang>
Output in all three cases:
(3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20)
Using Pilog
<lang PicoLisp>(be pythag (@N @X @Y @Z)
(for @X @N)
(for @Y @X @N)
(for @Z @Y @N)
(@ let (X (-> @X) Y (-> @Y) Z (-> @Z))
(= (+ (* X X) (* Y Y)) (* Z Z)) ) )</lang>
Test: <lang PicoLisp>: (? (pythag 20 @X @Y @Z))
@X=3 @Y=4 @Z=5 @X=5 @Y=12 @Z=13 @X=6 @Y=8 @Z=10 @X=8 @Y=15 @Z=17 @X=9 @Y=12 @Z=15 @X=12 @Y=16 @Z=20
-> NIL</lang>
Prolog
SWI-Prolog does not have list comprehension, however we can simulate it.
<lang Prolog>% We need operators
- - op(700, xfx, <-).
- - op(450, xfx, ..).
- - op(1100, yfx, &).
% we need to define the intervals of numbers Vs <- M..N :-
integer(M),
integer(N), M =< N, between(M, N, Vs).
% finally we define list comprehension
% prototype is Vs <- {Var, Dec, Pred} where
% Var is the list of variables to output
% Dec is the list of intervals of the variables
% Pred is the list of predicates
Vs <- {Var & Dec & Pred} :-
findall(Var, maplist(call, [Dec, Pred]), Vs).
</lang>
Examples of use :
List of Pythagorean triples :
?- V <- {X, Y, Z & X <- 1..20, Y <- X..20, Z <- Y..20 & X*X+Y*Y =:= Z*Z}.
V = [ (3,4,5), (5,12,13), (6,8,10), (8,15,17), (9,12,15), (12,16,20)] ;
false.
List of double of x, where x^2 is greater than 50 :
?- V <- {Y & X <- 1..20 & X*X > 50, Y is 2 * X}.
V = [16,18,20,22,24,26,28,30,32,34,36,38,40] ;
false.
Python
List comprehension:
<lang python>[(x,y,z) for x in xrange(1,n+1) for y in xrange(x,n+1) for z in xrange(y,n+1) if x**2 + y**2 == z**2]</lang>
A Python generator comprehension (note the outer round brackets), returns an iterator over the same result rather than an explicit list:
<lang python>((x,y,z) for x in xrange(1,n+1) for y in xrange(x,n+1) for z in xrange(y,n+1) if x**2 + y**2 == z**2)</lang>
R
R have inherent list comprehension: <lang R> x = (0:10) > x^2
[1] 0 1 4 9 16 25 36 49 64 81 100
> Reduce(function(y,z){return (y+z)},x) [1] 55 > x[x[(0:length(x))] %% 2==0] [1] 0 2 4 6 8 10 </lang>
R's "data frame" functions can be used to achieve the same code clarity (at the cost of expanding the entire grid into memory before the filtering step)
<lang R> subset(expand.grid(x=1:n, y=1:n, z=1:n), x^2 + y^2 == z^2) </lang>
Racket
<lang scheme>#lang racket (for*/list ([x (in-range 1 21)]
[y (in-range x 21)]
[z (in-range y 21)]
#:when (= (+ (* x x) (* y y)) (* z z)))
(list x y z))
</lang>
Rascal
<lang Rascal> public list[tuple[int, int, int]] PythTriples(int n) = [<a, b, c> | a <- [1..n], b <- [1..n], c <- [1 .. n], a*a + b*b == c*c]; </lang>
REXX
There is no native comprehensive supoort for lists per se, except that
normal lists can be processed quite easily and without much effort.
<lang rexx>/*REXX program to list Pythagorean triples up to a specified number. */
parse arg n . /*get the argument (possibly). */
if n== then n=100 /*Not specified? Then assume 100*/
call gen_triples n /*generate Pythagorean triples. */ call showhdr /*show a nice header. */ call showlist triples /*show the Pythagorean triples. */ exit /*─────────────────────────────────────GEN_TRIPLES subroutine───────────*/ gen_triples: parse arg lim /*generate Pythorgorean triples. */ triples=
do a=1 for lim-2; aa=a*a /*a*a is faster than a**2 */
do b=a+1 to lim-1; aabb=aa+b*b
do c=b+1 to lim; if aabb==c*c then triples=triples '['a"-"||b'-'c"]"
end /*a*/
end /*b*/
end /*c*/
triples=strip(triples) return words(triples) /*─────────────────────────────────────SHOWHDR subroutine───────────────*/ showHdr: say if 'f0'x==0 then do; super2='b2'x; le='8c'x; end /*EBCDIC: super2, LE */
else do; super2='fd'x; le='f3'x; end /* ASCII: " " */
note='(a'super2 "+ b"super2 '= c'super2", c "le n')' /*prettify equat.*/ say 'Pythagorean triples' note":" return /*─────────────────────────────────────SHOWLIST subroutine──────────────*/ showlist: procedure; parse arg L /*get the list (L). */ w=words(L) /*number of members in the list. */ say; do j=1 for w /*display the members of the list*/
say word(L,j)
end
say; say w 'members listed.' return</lang> output
Pythagorean triples (a² + b² = c², c ≤ 100): [3-4-5] [5-12-13] [6-8-10] [7-24-25] [8-15-17] [9-12-15] [9-40-41] [10-24-26] [11-60-61] [12-16-20] [12-35-37] [13-84-85] [14-48-50] [15-20-25] [15-36-39] [16-30-34] [16-63-65] [18-24-30] [18-80-82] [20-21-29] [20-48-52] [21-28-35] [21-72-75] [24-32-40] [24-45-51] [24-70-74] [25-60-65] [27-36-45] [28-45-53] [28-96-100] [30-40-50] [30-72-78] [32-60-68] [33-44-55] [33-56-65] [35-84-91] [36-48-60] [36-77-85] [39-52-65] [39-80-89] [40-42-58] [40-75-85] [42-56-70] [45-60-75] [48-55-73] [48-64-80] [51-68-85] [54-72-90] [57-76-95] [60-63-87] [60-80-100] [65-72-97] 52 members listed.
Ruby
Ruby has no special syntax for list comprehensions.
Enumerable#select comprises a list from one variable, like Perl grep() or Python filter(). Some lists need Array#map! to transform the variable.
- (1..100).select { |x| x % 3 == 0 } is the list of all x from 1 to 100 such that x is a multiple of 3.
- methods.select { |name| name.length <= 5 } is the list of all methods from self with names not longer than 5 characters.
- Dir["/bin/*"].select { |p| File.setuid? p }.map! { |p| File.basename p } is the list of all files in /bin with a setuid bit.
Ruby's object-oriented style enforces writing 1..100 before x. Think not of x in 1..100. Think of 1..100 giving x.
There is no elegant way to comprise a list from multiple variables. Pythagorean triplets need three variables, with 1..n giving x, then x..n giving y, then y..n giving z. A less than elegant way is to nest three blocks.
Ruby 1.9.2
<lang ruby>n = 20
- select Pythagorean triplets
r = ((1..n).flat_map { |x|
(x..n).flat_map { |y|
(y..n).flat_map { |z|
x, y, z.keep_if { x * x + y * y == z * z }}}})
p r # print the array _r_</lang>
Output: [[3, 4, 5], [5, 12, 13], [6, 8, 10], [8, 15, 17], [9, 12, 15], [12, 16, 20]]
Ruby 1.9.2 introduces two new methods: Enumerable#flat_map joins all the arrays from the block. Array#keep_if is an alternative to Enumerable#select that modifies the original array. (We avoid Array#select! because it might not return the array.)
- The [[x, y, z]].keep_if { ... } returns either an array of one Pythagorean triplet, or an empty array.
- The inner (y..n).flat_map { ... } concatenates those arrays for all z given some x, y.
- The middle (x..n).flat_map { ... } concatenates the inner arrays for all y given some x.
- The outer (1..n).flat_map { ... } concatenates the middle arrays for all x.
Ruby 1.8.6
<lang ruby>n = 20
unless Enumerable.method_defined? :flat_map
module Enumerable
def flat_map
inject([]) { |a, x| a.concat yield(x) }
end
end
end
unless Array.method_defined? :keep_if
class Array
def keep_if
delete_if { |x| not yield(x) }
end
end
end
- select Pythagorean triplets
r = ((1..n).flat_map { |x|
(x..n).flat_map { |y|
(y..n).flat_map { |z|
x, y, z.keep_if { x * x + y * y == z * z }}}})
p r # print the array _r_</lang>
This is the exact same code, except that it now defines Enumerable#flat_map and Array#keep_if when those methods are missing. It now works with older versions of Ruby, like 1.8.6.
Run BASIC
<lang runbasic>for x = 1 to 20
for y = x to 20 for z = y to 20 if x^2 + y^2 = z^2 then print "[";x;",";y;",";z;"]" next z next y
next x</lang>Output:
[3,4,5] [5,12,13] [6,8,10] [8,15,17] [9,12,15] [12,16,20]
Scala
<lang scala>def pythagoranTriangles(n: Int) = for {
x <- 1 to 21 y <- x to 21 z <- y to 21 if x * x + y * y == z * z
} yield (x, y, z)</lang>
which is a syntactic sugar for:
<lang scala> def pythagoranTriangles(n: Int) = (1 to n) flatMap (x =>
(x to n) flatMap (y =>
(y to n) filter (z => x * x + y * y == z * z) map (z =>
(x, y, z))))</lang>
Alas, the type of collection returned depends on the type of the collection
being comprehended. In the example above, we are comprehending a Range.
Since a Range of triangles doesn't make sense, it returns the
closest (supertype) collection for which it does, an IndexedSeq.
To get a List out of it, just pass a List to it:
<lang scala>def pythagoranTriangles(n: Int) = for {
x <- List.range(1, n + 1) y <- x to 21 z <- y to 21 if x * x + y * y == z * z
} yield (x, y, z)</lang>
Sample:
scala> pythagoranTriangles(21) res36: List[(Int, Int, Int)] = List((3,4,5), (5,12,13), (6,8,10), (8,15,17), (9,12,15), (12,16,20))
Scheme
Scheme has no native list comprehensions, but SRFI-42 [1] provides them:
<lang scheme> (list-ec (:range x 1 21)
(:range y x 21)
(:range z y 21)
(if (= (* z z) (+ (* x x) (* y y))))
(list x y z))
</lang>
((3 4 5) (5 12 13) (6 8 10) (8 15 17) (9 12 15) (12 16 20))
Smalltalk
<lang smalltalk> | test |
test := [ :a :b :c | a*a+(b*b)=(c*c) ].
(1 to: 20)
combinations: 3 atATimeDo: [ :x |
(test valueWithArguments: x)
ifTrue: [ ':-)' logCr: x ] ].
"output on Transcript:
- (3 4 5)
- (5 12 13)
- (6 8 10)
- (8 15 17)
- (9 12 15)
- (12 16 20)"
</lang>
SuperCollider
<lang supercollider>var pyth = {
arg n = 10; // default
all {: [x,y,z],
x <- (1..n),
y <- (x..n),
z <- (y..n),
(x**2) + (y**2) == (z**2)
};
};
pyth.value(20); // example call</lang> returns <lang supercollider>[ [ 3, 4, 5 ], [ 5, 12, 13 ], [ 6, 8, 10 ], [ 8, 15, 17 ], [ 9, 12, 15 ], [ 12, 16, 20 ] ]</lang>
Tcl
Tcl does not have list comprehensions built-in to the language, but they can be constructed. <lang tcl>package require Tcl 8.5
proc lcomp {expression args} {
# Check the number of arguments.
if {[llength $args] < 2} {
error "wrong # args: should be \"lcomp expression var1 list1\
?... varN listN? ?condition?\""
}
# Extract condition from $args, or use default.
if {[llength $args] % 2 == 1} {
set condition [lindex $args end]
set args [lrange $args 0 end-1]
} else {
set condition 1
}
# Collect all var/list pairs and store in reverse order.
set varlst [list]
foreach {var lst} $args {
set varlst [concat [list $var] [list $lst] $varlst]
}
# Actual command to be executed, repeatedly.
set script {lappend result [subst $expression]}
# If necessary, make $script conditional.
if {$condition ne "1"} {
set script [list if $condition $script]
}
# Apply layers of foreach constructs around $script.
foreach {var lst} $varlst {
set script [list foreach $var $lst $script]
}
# Do it!
set result [list]
{*}$script ;# Change to "eval $script" if using Tcl 8.4 or older.
return $result
}
set range {1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20} puts [lcomp {$x $y $z} x $range y $range z $range {$x < $y && $x**2 + $y**2 == $z**2}]</lang>
{3 4 5} {5 12 13} {6 8 10} {8 15 17} {9 12 15} {12 16 20}
TI-89 BASIC
TI-89 BASIC does not have a true list comprehension, but it has the seq() operator which can be used for some similar purposes.
<lang ti89b>{1, 2, 3, 4} → a seq(a[i]^2, i, 1, dim(a))</lang>
produces {1, 4, 9, 16}. When the input is simply a numeric range, an input list is not needed; this produces the same result:
<lang ti89b>seq(x^2, x, 1, 4)</lang>
Visual Basic .NET
<lang vbnet>Module ListComp
Sub Main()
Dim ts = From a In Enumerable.Range(1, 20) _
From b In Enumerable.Range(a, 21 - a) _
From c In Enumerable.Range(b, 21 - b) _
Where a * a + b * b = c * c _
Select New With { a, b, c }
For Each t In ts
System.Console.WriteLine("{0}, {1}, {2}", t.a, t.b, t.c)
Next
End Sub
End Module</lang>
Output:
3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17 9, 12, 15 12, 16, 20
Wrapl
<lang wrapl>ALL WITH x <- 1:to(n), y <- x:to(n), z <- y:to(n) DO (x^2 + y^2 = z^2) & [x, y, z];</lang>
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