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.
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>
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>
Iterator
<lang csharp>using System; using System.Collections.Generic;
static class Program {
static IEnumerable<Tuple<int, int, int>> GetPythTriples(int upperBound) { for (int a = 1; a <= upperBound; a++) for (int b = a + 1; b <= upperBound; b++) for (int c = b + 1; c <= upperBound; c++) if (a * a + b * b == c * c) yield return new Tuple<int, int, int>(a, b, c); }
static void Main() { foreach (var triple in GetPythTriples(20)) Console.WriteLine(triple); }
}</lang>
C++
There is no equivalent construct in C++. The code below uses three 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
Clojure
<lang lisp>(for [x (range 1 21) y (range x 21) z (range y 21) :when (= (+ (* x x) (* y y)) (* z z))] [x y z])</lang>
Common Lisp
Common Lisp doesn't have list comprehensions built in, but 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. The following is mostly a toy.
<lang d>import std.string: writeln; import std.algorithm: iota; import std.array, std.typetuple;
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;
// save original iteration variables 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()); } } }
// restore original iteration variables 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^^2 + y^^2 == z^^2); writeln(r);
}</lang>
It computes the result: 5 13 10 17 15 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>
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>
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' triples=: 1 + 3&comb isPyth=: 2&{"1 = 1&{"1 +&.:*: 0&{"1 pythTr=: (#~ isPyth)@triples</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>
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>
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 or coroutine.
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)
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>
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
A couple of ways, neither feel particularly elegant. Ruby's OO style really enforces writing left-to-right.
a=[]; (1..n).each {|x| (1..n).each {|y| (1..n).each {|z| a << [x,y,z] if x**2 + y**2 == z**2}}}; a
- no temp array, but a lot of housework to flatten and remove nils
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))
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>
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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