Pythagorean quadruples: Difference between revisions
Added solution for EDSAC
(Scala contribution added.) |
(Added solution for EDSAC) |
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Line 14:
::::: which is:
:::::::: <big><big> 4 + 9 + 36 = 49 </big></big>
Line 21:
For positive integers up '''2,200''' (inclusive), for all values of '''a''',
'''b''', '''c''', and '''d''',
<br>find (and show here) those values of '''d''' that ''<u>can't</u>'' be represented.
Show the values of '''d''' on one line of output (optionally with a title).
Line 29:
* [[Euler's sum of powers conjecture]].
* [[Pythagorean triples]].
;Reference:
:* the Wikipedia article: [https://en.wikipedia.org/wiki/Pythagorean_quadruple Pythagorean quadruple].
<br><br>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">F quad(top = 2200)
V r = [0B] * top
V ab = [0B] * (top * 2)^2
L(a) 1 .< top
L(b) a .< top
ab[a * a + b * b] = 1B
V s = 3
L(c) 1 .< top
(V s1, s, V s2) = (s, s + 2, s + 2)
L(d) c + 1 .< top
I ab[s1]
r[d] = 1B
s1 += s2
s2 += 2
R enumerate(r).filter((i, val) -> !val & i).map((i, val) -> i)
print(quad())</syntaxhighlight>
{{out}}
<pre>
[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]
</pre>
=={{header|ALGOL 68}}==
As with the optimised REXX solution, we find the values of d for which there are no a^2 + b^2 = d^2 - c^2.
<
# find values of d where d^2 =/= a^2 + b^2 + c^2 for any integers a, b, c #
# where d in [1..2200], a, b, c =/= 0 #
Line 66 ⟶ 96:
OD;
print( ( newline ) )
END</
{{out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
=={{header|Amazing Hopper}}==
{{trans|C}}
The process runs in 2.9 secs. on an Intel Core 2 Duo at 2.53 or 2.66 GHz. It's SLOW, but believe me, when it comes to Hopper, it's quite a feat! :D
<syntaxhighlight lang="text">
#include <flow.h>
DEF-MAIN(argv, argc)
SET(N, 2200)
DIM( MUL(MUL(N,N),2) ) AS-ZEROS( temp )
DIM( N ) AS-ZEROS( found )
MSET( a,T1,T2 )
TIC(T1)
SEQ-SPC(1,N,N,a), LET( a := MUL(a,a) )
SET(i,1), SET(r,0)
PERF-UP(i,N,1)
LET( r := ADD( [i] GET( a ), [i:end] CGET(a) ) )
SET-RANGE( r ), SET(temp, 1), CLR-RANGE
NEXT
SET(c,1), SET(s,3), MSET(s1,s2,d)
PERF-UP(c, N, 1)
LET( s1 := s )
s += 2
LET( s2 := s )
LET( d := ADD(c,1) )
PERF-UP(d, N, 1)
COND ( [s1] GET(temp) )
[d] {1} PUT(found)
CEND
s1 += s2
s2 += 2
NEXT
NEXT
TOC(T1, T2), PRNL("Time = ", T2 )
PRN( "Imprimiendo resultados:\n" )
CART( IS-ZERO?( found ) ) MOVE-TO( r )
PRNL( r )
MCLEAR(temp, found, a, r)
END
</syntaxhighlight>
{{out}}
<pre>
Time = 2.88824
Imprimiendo resultados:
1,2,4,5,8,10,16,20,32,40,64,80,128,160,256,320,512,640,1024,1280,2048
</pre>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">-- double :: Num -> Num
on double(x)
x + x
end double
-- powersOfTwo :: Generator [Int]
on powersOfTwo()
iterate(double, 1)
end powersOfTwo
on run
-- Two infinite lists, from each of which we can draw an arbitrary number of initial terms
set xs to powersOfTwo() -- {1, 2, 4, 8, 16, 32 ...
set ys to fmapGen(timesFive, powersOfTwo()) -- {5, 10, 20, 40, 80, 160 ...
-- Another infinite list, derived from the first two (sorted in rising value)
set zs to mergeInOrder(xs, ys) -- {1, 2, 4, 5, 8, 10 ...
-- Taking terms from the derived list while their value is below 2200 ...
takeWhileGen(le2200, zs)
--> {1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048}
end run
-- le2200 :: Num -> Bool
on le2200(x)
x ≤ 2200
end le2200
-- timesFive :: Num -> Num
on timesFive(x)
5 * x
end timesFive
-- mergeInOrder :: Generator [Int] -> Generator [Int] -> Generator [Int]
on mergeInOrder(ga, gb)
script
property a : uncons(ga)
property b : uncons(gb)
on |λ|()
if (Nothing of a or Nothing of b) then
missing value
else
set ta to Just of a
set tb to Just of b
if |1| of ta < |1| of tb then
set a to uncons(|2| of ta)
return |1| of ta
else
set b to uncons(|2| of tb)
return |1| of tb
end if
end if
end |λ|
end script
end mergeInOrder
-- GENERIC -----------------------------------------------------------------
-- fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
on fmapGen(f, gen)
script
property g : gen
property mf : mReturn(f)'s |λ|
on |λ|()
set v to g's |λ|()
if v is missing value then
v
else
mf(v)
end if
end |λ|
end script
end fmapGen
-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate
-- Just :: a -> Maybe a
on Just(x)
{type:"Maybe", Nothing:false, Just:x}
end Just
-- length :: [a] -> Int
on |length|(xs)
set c to class of xs
if list is c or string is c then
length of xs
else
(2 ^ 29 - 1) -- (maxInt - simple proxy for non-finite)
end if
end |length|
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- Nothing :: Maybe a
on Nothing()
{type:"Maybe", Nothing:true}
end Nothing
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to xs's |λ|()
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take
-- takeWhileGen :: (a -> Bool) -> Gen [a] -> [a]
on takeWhileGen(p, xs)
set ys to {}
set v to |λ|() of xs
tell mReturn(p)
repeat while (|λ|(v))
set end of ys to v
set v to xs's |λ|()
end repeat
end tell
return ys
end takeWhileGen
-- Tuple (,) :: a -> b -> (a, b)
on Tuple(a, b)
{type:"Tuple", |1|:a, |2|:b, length:2}
end Tuple
-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
set lng to |length|(xs)
if 0 = lng then
Nothing()
else
if (2 ^ 29 - 1) as integer > lng then
if class of xs is string then
set cs to text items of xs
Just(Tuple(item 1 of cs, rest of cs))
else
Just(Tuple(item 1 of xs, rest of xs))
end if
else
Just(Tuple(item 1 of take(1, xs), xs))
end if
end if
end uncons</syntaxhighlight>
{{Out}}
<pre>{1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048}</pre>
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f PYTHAGOREAN_QUADRUPLES.AWK
# converted from Go
BEGIN {
n = 2200
s = 3
for (a=1; a<=n; a++) {
a2 = a * a
for (b=a; b<=n; b++) {
ab[a2 + b * b] = 1
}
}
for (c=1; c<=n; c++) {
s1 = s
s += 2
s2 = s
for (d=c+1; d<=n; d++) {
if (ab[s1]) {
r[d] = 1
}
s1 += s2
s2 += 2
}
}
for (d=1; d<=n; d++) {
if (!r[d]) {
printf("%d ",d)
}
}
printf("\n")
exit(0)
}
</syntaxhighlight>
{{out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
Line 75 ⟶ 398:
===Version 1===
Five seconds on my Intel Linux box.
<
#include <math.h>
#include <string.h>
Line 100 ⟶ 423:
if(!r[a]) printf("%d ",a); // print non solution
printf("\n");
}</
{{out}}
<pre>
Line 109 ⟶ 432:
===Version 2 (much faster)===
Translation of second version of FreeBASIC entry. Runs in about 0.15 seconds.
<
#include <stdio.h>
#include <string.h>
Line 144 ⟶ 467:
free(ab);
return 0;
}</
{{out}}
<pre>
Same as first version.
</pre>
=={{header|C sharp|C#}}==
{{trans|Java}}
<syntaxhighlight lang="csharp">using System;
namespace PythagoreanQuadruples {
class Program {
const int MAX = 2200;
const int MAX2 = MAX * MAX * 2;
static void Main(string[] args) {
bool[] found = new bool[MAX + 1]; // all false by default
bool[] a2b2 = new bool[MAX2 + 1]; // ditto
int s = 3;
for(int a = 1; a <= MAX; a++) {
int a2 = a * a;
for (int b=a; b<=MAX; b++) {
a2b2[a2 + b * b] = true;
}
}
for (int c = 1; c <= MAX; c++) {
int s1 = s;
s += 2;
int s2 = s;
for (int d = c + 1; d <= MAX; d++) {
if (a2b2[s1]) found[d] = true;
s1 += s2;
s2 += 2;
}
}
Console.WriteLine("The values of d <= {0} which can't be represented:", MAX);
for (int d = 1; d < MAX; d++) {
if (!found[d]) Console.Write("{0} ", d);
}
Console.WriteLine();
}
}
}</syntaxhighlight>
{{out}}
<pre>The values of d <= 2200 which can't be represented:
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|C++}}==
{{trans|D}}
<syntaxhighlight lang="cpp">#include <iostream>
#include <vector>
constexpr int N = 2200;
constexpr int N2 = 2 * N * N;
int main() {
using namespace std;
vector<bool> found(N + 1);
vector<bool> aabb(N2 + 1);
int s = 3;
for (int a = 1; a < N; ++a) {
int aa = a * a;
for (int b = 1; b < N; ++b) {
aabb[aa + b * b] = true;
}
}
for (int c = 1; c <= N; ++c) {
int s1 = s;
s += 2;
int s2 = s;
for (int d = c + 1; d <= N; ++d) {
if (aabb[s1]) {
found[d] = true;
}
s1 += s2;
s2 += 2;
}
}
cout << "The values of d <= " << N << " which can't be represented:" << endl;
for (int d = 1; d <= N; ++d) {
if (!found[d]) {
cout << d << " ";
}
}
cout << endl;
return 0;
}</syntaxhighlight>
{{out}}
<pre>The values of d <= 2200 which can't be represented:
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|Crystal}}==
{{trans|Ruby}}
<syntaxhighlight lang="ruby">n = 2200
l_add, l = Hash(Int32, Bool).new(false), Hash(Int32, Bool).new(false)
(1..n).each do |x|
x2 = x * x
(x..n).each { |y| l_add[x2 + y * y] = true }
end
s = 3
(1..n).each do |x|
s1 = s
s += 2
s2 = s
((x+1)..n).each do |y|
l[y] = true if l_add[s1]
s1 += s2
s2 += 2
end
end
puts (1..n).reject{ |x| l[x] }.join(" ")</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
Translation of faster Ruby version using Enumerators.
<syntaxhighlight lang="ruby">squares = (0..).each.map { |n| 2_u64**n }
squares5 = (0..).each.map { |n| 2_u64**n * 5 }
n = squares.next.as(Int)
m = squares5.next.as(Int)
pyth_quad = Iterator.of do
if n < m
value = n
n = squares.next.as(Int)
else
value = m
m = squares5.next.as(Int)
end
value
end
puts pyth_quad.take_while { |n| n <= 1000000000 }.join(" ")</syntaxhighlight>
{{Out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 2560 4096 5120 8192 10240 16384 20480 32768 40960 65536 81920 131072 163840 262144 327680 524288 655360 1048576 1310720 2097152 2621440 4194304 5242880 8388608 10485760 16777216 20971520 33554432 41943040 67108864 83886080 134217728 167772160 268435456 335544320 536870912 671088640
</pre>
=={{header|D}}==
{{trans|C}}
<
import std.stdio;
Line 194 ⟶ 660:
}
writeln;
}</
{{out}}
<pre>The values of d <= 2200 which can't be represented:
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|EDSAC order code}}==
A solution from first principles would probably take a long time on EDSAC, so we use the theoretical results [https://mathoverflow.net/questions/90914/sums-of-three-non-zero-squares quoted in MathOverflow]. From these it follows easily that if d is a power of 2, or 5 times a power of 2, then d^2 is not the sum of three non-zero squares. The converse does not follow, but if d is a counterexample then d^2 exceeds 5*(10^10), and therefore d exceeds the limit in the task description. The EDSAC output thus consists of two interleaved arrays, as in the AppleScript solution.
<syntaxhighlight lang="edsac">
[Pythagorean quadruples - Rosetta Code
EDSAC program, Initial Orders 2]
[Arrange the storage]
T46K P56F [N parameter: modified library s/r P7 to print integer]
T47K P106F [M parameter: main routine]
[Library subroutine M3, prints header at load time.
Here, header leaves teleprinter in figures mode.]
PFGKIFAFRDLFUFOFE@A6FG@E8FEZPF
*NUMBERS!WHOSE!SQUARES!ARE!NOT!THE!SUM!
OF!THREE!NONZERO!SQUARES@&MAXIMUM#!V!
..PK [after header, blank tape and PK (WWG, 1951, page 91)]
[------------------------------------------------------------------------------]
[Main routine]
E25K TM GK [load at address specified by M parameter]
[Constants]
[0] P1100F [limit, right-justified, e.g. P1100F for 2200]
[1] !F [teleprinter space]
[2] @F [carriage return]
[3] &F [line feed]
[4] K4096F [teleprinter null]
[5] PD [17-bit constant 1]
[6] P2D [17-bit constant 5]
[Variables]
[7] PF [2^m, where m = 0, 1, 2, ...]
[8] PF [5*2^n, where n = 0, 1, 2, ...]
[Enter here, with acc = 0]
[Complete header by printing limit]
[9] A4@ T1F [print leading zeros as nulls]
A@ TF [pass limit to print subroutine in 0F]
[13] A13@ GN [call print subroutine; leaves acc clear]
O2@ O3@ [print new line]
[Initialize variables]
A5@ T7@ [2^m := 1]
A6@ T8@ [5*2^n := 5]
[Loop back to here after printing number]
[Print 2^m or 5*2^n, whichever is smaller]
[21] A7@ S8@ [compare values]
E28@ [jump if 5*2^n is smaller]
A8@ [else restore 2^m in acc]
LD U7@ [double value in memory]
E32@ [jump to common code]
[28] T4F [clear acc]
A8@ [acc := 5*2^n]
LD U8@ [double value in memory]
[32] RD [common code: undo doubling in acc]
TF [pass number to print subroutine in 0F]
A@ SF [test for number > limit]
G42@ [jump to exit if so]
O1@ [print space before number]
T4F [clear acc]
[39] A39@ GN [call print subroutine; leaves acc clear]
E21@ [loop back for next number]
[Here when done]
[42] O2@ O3@ [print new line]
O4@ [print null to flush teleprinter buffer]
ZF [halt the machine]
[------------------------------------------------------------]
[Subroutine to print 17-bit non-negative integer
Parameters: 0F = integer to be printed (not preserved)
1F = character for leading zero
(preserved; typically null, space or zero)
Workspace: 4F, 5F
Even address; 39 locations]
E25K TN [load at address specified by N parameter]
GKA3FT34@A1FT35@S37@T36@T4DAFT4FH38@V4FRDA4D
R1024FH30@E23@O35@A2FT36@T5FV4DYFL8FT4DA5F
L1024FUFA36@G16@OFTFT35@A36@G17@ZFPFPFP4FZ219D
E25K TM GK [M parameter again]
E9Z [define entry point]
PF [acc = 0 on entry]
</syntaxhighlight>
{{out}}
<pre>
NUMBERS WHOSE SQUARES ARE NOT THE SUM OF THREE NONZERO SQUARES
MAXIMUM = 2200
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
=={{header|FreeBASIC}}==
===From the Wikipedia page===
[https://en.wikipedia.org/wiki/Pythagorean_quadruple Alternate parametrization, second version both A and B even.]Time just less then 0.7 second on a AMD Athlon II X4 645 3.34GHz win7 64bit. Program uses one core. When the limit is set to 576 (abs. minimum for 2200), the time is about 0.85 sec.
<
' compile with: fbc -s console
Line 254 ⟶ 807:
Print : Print "hit any key to end program"
Sleep
End</
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
===Brute force===
Based on the second REXX version: A^2 + B^2 = D^2 - C^2. Faster then the first version, about 0.2 second
<
' compile with: fbc -s console
Line 294 ⟶ 847:
Print : Print "hit any key to end program"
Sleep
End</
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
_limit = 2200
long x, x2, y, s = 3, s1, s2, counter
long l( _limit )
long ladd( _limit * _limit * 2 )
for x = 1 to _limit
x2 = x * x
for y = x to _limit
ladd( x2 + y * y ) = 1
next
next
for x = 1 to _limit
s1 = s
s = s + 2
s2 = s
for y = x + 1 to _limit
if ladd(s1) == 1 then l(y) = 1
s1 = s1 + s2
s2 = s2 + 2
next
next
counter = 1
for x = 1 to _limit
if ( l(x) == 0 )
if ( counter mod 7 == 0 )
printf @"%6ld", x : counter == 1 : continue
else
printf @"%6ld\b", x
counter++
end if
end if
next
print
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
1 2 4 5 8 10 16
20 32 40 64 80 128 160
256 320 512 640 1024 1280 2048
</pre>
=={{header|Go}}==
{{trans|FreeBASIC}}
<
import "fmt"
Line 341 ⟶ 944:
}
fmt.Println()
}</
{{out}}
Line 349 ⟶ 952:
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">powersOfTwo :: [Int]
powersOfTwo = iterate (2 *) 1
unrepresentable :: [Int]
unrepresentable = merge powersOfTwo ((5 *) <$> powersOfTwo)
merge :: [Int] -> [Int] -> [Int]
merge xxs@(x:xs) yys@(y:ys)
main :: IO ()
main = do
putStrLn "The values of d <= 2200 which can't be represented."
print $ takeWhile (<= 2200) unrepresentable</syntaxhighlight>
{{out}}
<pre>The values of d <= 2200 which can't be represented.
[1,2,4,5,8,10,16,20,32,40,64,80,128,160,256,320,512,640,1024,1280,2048]</pre>
=={{header|J}}==
Approach: generate the set of all triple sums of squares, then select the legs for which there aren't any squared "d"s. The solution is straightforward interactive play.
<syntaxhighlight lang="j">
Filter =: (#~`)(`:6)
B =: *: A =: i. >: i. 2200
S1 =: , B +/ B NB. S1 is a raveled table of the sums of squares
S1 =: <:&({:B)Filter S1 NB. remove sums of squares exceeding bound
S1 =: ~. S1 NB. remove duplicate entries
S2 =: , B +/ S1
S2 =: <:&({:B)Filter S2
S2 =: ~. S2
RESULT =: (B -.@:e. S2) # A
RESULT
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</syntaxhighlight>
=={{header|Java}}==
Replace translation with Java coded implementation.
Compute sequence directly.
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.List;
public class PythagoreanQuadruples {
public static void main(String[] args) {
long d = 2200;
System.out.printf("Values of d < %d where a, b, and c are non-zero and a^2 + b^2 + c^2 = d^2 has no solutions:%n%s%n", d, getPythagoreanQuadruples(d));
}
// See: https://oeis.org/A094958
private static List<Long> getPythagoreanQuadruples(long max) {
List<Long> list = new ArrayList<>();
long n = -1;
long m = -1;
while ( true ) {
long nTest = (long) Math.pow(2, n+1);
long mTest = (long) (5L * Math.pow(2, m+1));
long test = 0;
if ( nTest > mTest ) {
test = mTest;
m++;
}
else {
test = nTest;
n++;
}
if ( test < max ) {
list.add(test);
}
else {
break;
}
}
return list;
}
}
</syntaxhighlight>
{{out}}
<pre>
Values of d < 2200 where a, b, and c are non-zero and a^2 + b^2 + c^2 = d^2 has no solutions:
[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]
</pre>
=={{header|
{{
<syntaxhighlight lang="javascript">(() => {
'use strict';
const xs = takeWhileGen(
x => 2200 >= x,
mergeInOrder(
powersOfTwo(),
fmapGen(x => 5 * x, powersOfTwo())
)
);
return (
console.log(JSON.stringify(xs)),
}
// powersOfTwo :: Gen [Int]
const powersOfTwo =
// mergeInOrder :: Gen
const mergeInOrder = (ga,
function* go(ma, mb)
while (!a.Nothing && !b.Nothing)
ta = a.Just,
tb = b.Just;
if (fst(ta) < fst(tb)) {
yield(fst(ta));
a = uncons(snd(ta))
} else {
yield(fst(tb));
b = uncons(snd(tb))
}
}
}
return go(uncons(ga), uncons(gb))
};
// GENERIC FUNCTIONS ----------------------------
// fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
function* fmapGen(f, gen) {
const g = gen;
let v = take(1, g);
while (0 < v.length) {
yield(f(v))
v = take(1, g)
}
}
// fst :: (a, b) -> a
const fst = tpl => tpl[0];
// iterate :: (a -> a) -> a -> Generator [a]
function* iterate(f, x) {
let v = x;
while (true) {
yield(v);
v = f(v);
}
}
// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});
// Returns Infinity over objects without finite length
// this enables zip and zipWith to choose the shorter
// argument when one is non-finite, like cycle, repeat etc
// length :: [a] -> Int
const length = xs => xs.length || Infinity;
// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});
// snd :: (a, b) -> b
const snd = tpl => tpl[1];
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
xs.constructor.constructor.name !== 'GeneratorFunction' ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// takeWhileGen :: (a -> Bool) -> Generator [a] -> [a]
const takeWhileGen = (p, xs) => {
const ys = [];
let
nxt = xs.next(),
v = nxt.value;
while (!nxt.done && p(v)) {
ys.push(v);
nxt = xs.next();
v = nxt.value
}
return ys;
};
// Tuple (,) :: a -> b -> (a, b)
const Tuple = (a, b) => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// uncons :: [a] -> Maybe (a, [a])
const uncons = xs => {
const lng = length(xs);
return (0 < lng) ? (
lng < Infinity ? (
Just(Tuple(xs[0], xs.slice(1))) // Finite list
) : (() => {
const nxt = take(1, xs);
return 0 < nxt.length ? (
Just(Tuple(nxt[0], xs))
) : Nothing();
})() // Lazy generator
) : Nothing();
};
// MAIN ---
return main();
})();</syntaxhighlight>
{{Out}}
<pre>[1,2,4,5,8,10,16,20,32,40,64,80,128,160,256,320,512,640,1024,1280,2048]</pre>
=={{header|jq}}==
Line 417 ⟶ 1,200:
be accomplished in jq without `foreach`. Notice also how
`first/1` is used in `is_pythagorean_quad/0` to avoid unnecessary computation.
<
def is_pythagorean_quad:
. as $d
Line 432 ⟶ 1,215:
# The specific task:
[range(1; 2201) | select( is_pythagorean_quad | not )] | join(" ")</
'''Invocation and Output'''
Line 440 ⟶ 1,223:
=={{header|Julia}}==
{{trans|C}}
<
r = falses(N)
ab = falses(2N ^ 2)
Line 461 ⟶ 1,243:
end
return
end
println("Pythagorean quadruples up to 2200: ", join(quadruples(), ", "))</
{{out}}
Line 472 ⟶ 1,254:
===Version 1 ===
This uses a similar approach to the REXX optimized version. It also takes advantage of a hint in the C entry that there is no solution if both a and b are odd (confirmed by Wikipedia article). Runs in about 7 seconds on my modest laptop which is more than 4 times faster than the brute force version would have been:
<
const val MAX = 2200
Line 506 ⟶ 1,288:
for (i in 1..MAX) if (!found[i]) print("$i ")
println()
}</
{{out}}
Line 517 ⟶ 1,299:
One thing I've noticed about the resulting sequence is that it appears to be an interleaving of the two series 2 ^ n and 5 * (2 ^ n) for n >= 0 though whether it's possible to prove this mathematically I don't know.
<
const val MAX = 2200
Line 546 ⟶ 1,328:
for (d in 1..MAX) if (!found[d]) print("$d ")
println()
}</
{{out}}
Line 553 ⟶ 1,335:
</pre>
=={{header|
<syntaxhighlight lang="lua">-- initialize
local N = 2200
local ar = {}
for i=1,N do
ar[i] = false
end
-- process
for a=1,N do
for b=a,N do
if (a % 2 ~= 1) or (b % 2 ~= 1) then
local aabb = a * a + b * b
for c=b,N do
local aabbcc = aabb + c * c
local d = math.floor(math.sqrt(aabbcc))
if (aabbcc == d * d) and (d <= N) then
ar[d] = true
end
end
end
end
-- print('done with a='..a)
end
-- print
for i=1,N do
if not ar[i] then
io.write(i.." ")
end
end
print()</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">max = 2200;
maxsq = max^2;
d = Range[max]^2;
Dynamic[{a, b, Length[d]}]
Do[
Do[
c = Range[1, Floor[(maxsq - a^2 - b^2)^(1/2)]];
dposs = a^2 + b^2 + c^2;
d = Complement[d, dposs]
,
{b, Floor[(maxsq - a^2)^(1/2)]}
]
,
{a, Floor[maxsq^(1/2)]}
]
Sqrt[d]</syntaxhighlight>
{{out}}
<pre>{1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048}</pre>
=={{header|Modula-2}}==
{{trans|C}}
<syntaxhighlight lang="modula2">MODULE PythagoreanQuadruples;
FROM FormatString IMPORT FormatString;
FROM RealMath IMPORT sqrt;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE WriteInteger(i : INTEGER);
VAR buffer : ARRAY[0..16] OF CHAR;
BEGIN
FormatString("%i", buffer, i);
WriteString(buffer)
END WriteInteger;
(* Main *)
CONST N = 2200;
VAR
r : ARRAY[0..N] OF BOOLEAN;
a,b,c,d : INTEGER;
aabb,aabbcc : INTEGER;
BEGIN
(* Initialize *)
FOR a:=0 TO HIGH(r) DO
r[a] := FALSE
END;
(* Process *)
FOR a:=1 TO N DO
FOR b:=a TO N DO
IF (a MOD 2 = 1) AND (b MOD 2 = 1) THEN
(* For positive odd a and b, no solution *)
CONTINUE
END;
aabb := a*a + b*b;
FOR c:=b TO N DO
aabbcc := aabb + c*c;
d := INT(sqrt(FLOAT(aabbcc)));
IF (aabbcc = d*d) AND (d <= N) THEN
(* solution *)
r[d] := TRUE
END
END
END
END;
FOR a:=1 TO N DO
IF NOT r[a] THEN
(* pritn non-solution *)
WriteInteger(a);
WriteString(" ")
END
END;
WriteLn;
ReadChar
END PythagoreanQuadruples.</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 </pre>
=={{header|Nim}}==
{{trans|FreeBasic}}
===Version 1===
<syntaxhighlight lang="text">import math
const N = 2_200
template isOdd(n: int): bool = (n and 1) != 0
var r = newSeq[bool](N + 1)
for a in 1..N:
for b in a..N:
if a.isOdd and b.isOdd: continue
let aabb = a * a + b * b
for c in b..N:
let aabbcc = aabb + c * c
d = sqrt(aabbcc.float).int
if aabbcc == d * d and d <= N: r[d] = true
for i in 1..N:
if not r[I]: stdout.write i, " "
echo()</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
===Version 2===
<syntaxhighlight lang="text">const N = 2_200
const N2 = N * N * 2
var r = newSeq[bool](N + 1)
var ab = newSeq[bool](N2 + 1)
for a in 1..N:
let a2 = a * a
for b in a..N:
ab[a2 + b * b] = true
var s = 3
for c in 1..N:
var s1 = s
s += 2
var s2 = s
for d in (c+1)..N:
if ab[s1]: r[d] = true
s1 += s2
s2 += 2
for d in 1..N:
if not r[d]: stdout.write d, " "</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 </pre>
=={{header|Pascal}}==
{{works with|Free Pascal}} compiled with fpc 3.2.0 ( 2019.01.10 ) -O4 -Xs
===version 1===
Brute froce, but not as brute as [http://rosettacode.org/mw/index.php?title=Pythagorean_quadruples#Ring Ring].Did it ever run?<BR>
Stopping search if limit is reached<BR>
<syntaxhighlight lang="pascal">program pythQuad;
//find phythagorean Quadrupel up to a,b,c,d <= 2200
//a^2 + b^2 +c^2 = d^2
//find all values of d which are not possible
//brute force
//split in two procedure to reduce register pressure for CPU32
const
MaxFactor =2200;
limit = MaxFactor*MaxFactor;
type
tIdx = NativeUint;
tSum = NativeUint;
var
check : array[0..MaxFactor] of boolean;
checkCnt : LongWord;
procedure Find2(s:tSum;idx:tSum);
//second sum (a*a+b*b) +c*c =?= d*d
var
s1 : tSum;
d : tSum;
begin
d := trunc(sqrt(s+idx*idx));// calculate first sqrt
For idx := idx to MaxFactor do
Begin
s1 := s+idx*idx;
If s1 <= limit then
Begin
while s1 > d*d do //adjust sqrt
inc(d);
inc(checkCnt);
IF s1=d*d then
check[d] := true;
end
else
Break;
end;
end;
procedure Find1;
//first sum a*a+b*b
var
a,b : tIdx;
s : tSum;
begin
For a := 1 to MaxFactor do
For b := a to MaxFactor do
Begin
s := a*a+b*b;
if s < limit then
Find1(s,b)
else
break;
end;
end;
var
i : NativeUint;
begin
Find1;
For i := 1 to MaxFactor do
If Not(Check[i]) then
write(i,' ');
writeln;
writeln(CheckCnt,' checks were done');
end.
</syntaxhighlight>
{{out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
929605937 checks were done
real 0m2.323s -> 9 cpu-cycles per check on Ryzen 5 1600 3,7 Ghz ( Turbo )
</pre>
===version 2===
Using a variant of [http://rosettacode.org/wiki/Pythagorean_quadruples#optimized REXX optimized] optimized<BR>
As I now see the same as [http://rosettacode.org/wiki/Pythagorean_quadruples#ALGOL_68 Algol68]<BR>
a^2 + b^2 is like moving/jumping a rake with tines at a^2 from tine(1) to tine(MaxFactor) and mark their positions<BR>
Quite fast.
<syntaxhighlight lang="pascal">program pythQuad_2;
//find phythagorean Quadrupel up to a,b,c,d <= 2200
//a^2 + b^2 +c^2 = d^2
//a^2 + b^2 = d^2-c^2
{$IFDEF FPC}
{$R+,O+} //debug purposes, not slower
{$OPTIMIZATION ON,ALL}
{$CODEALIGN proc=16}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
uses
sysutils;
const
MaxFactor = 2200;//22000;//40960;
limit = MaxFactor*MaxFactor;
type
tIdx = NativeUint;
tSum = NativeUint;
var
// global variables are initiated with 0 at startUp
sumA2B2 :array[0..limit] of byte;
check : array[0..MaxFactor] of byte;
procedure BuildSumA2B2;
var
a,b,a2,Uplmt: tIdx;
begin
//Uplimt = a*a+b*b < Maxfactor | max(a,b) = Uplmt
Uplmt := Trunc(MaxFactor*sqrt(0.5));
For a := 1 to Uplmt do
Begin
a2:= a*a;
For b := a downto 1 do
sumA2B2[b*b+a2] := 1
end;
end;
procedure CheckDifD2C2;
var
d,d2,c : tIdx;
begin
For d := 1 to MaxFactor do
Begin
//c < d => (d*d-c*c) > 0
d2 := d*d;
For c := d-1 downto 1 do
Begin
// d*d-c*c == (d+c)*(d-c) nonsense
if sumA2B2[d2-c*c] <> 0 then
Begin
Check[d] := 1;
//first for d found is enough
BREAK;
end;
end;
end;
end;
var
i : NativeUint;
begin
BuildSumA2B2;
CheckDifD2C2;
//FindHoles
For i := 1 to MaxFactor do
If Check[i] = 0 then
write(i,' ');
writeln;
end.
</syntaxhighlight>
{{Out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
real 0m0,002s ( Ryzen 2200G 3.7 Ghz )
MaxFactor = 22000
.. 2048 2560 4096 5120 8192 10240 16384 20480
real 0m0,746s
MaxFactor = 40960
.. 2048 2560 4096 5120 8192 10240 16384 20480 32768 40960
real 0m3,222s
</pre>
=={{header|Perl}}==
{{trans|Raku}}
<syntaxhighlight lang="perl">my $N = 2200;
push @sq, $_**2 for 0 .. $N;
my @not = (0) x $N;
@not[0] = 1;
for my $d (1 ..
my $last = 0;
for my $
for my $b (1 .. ceiling($a/2)
last if
my $x =
if ($x == int $x) {
$not[$d] = 1;
$last = 1;
last
Line 576 ⟶ 1,699:
}
sub ceiling { int $_[0] + 1 - 1e-15 }
for (0 .. $#not) {
$result .= "$_ " unless $not[$_]
}
print "$result\n"</syntaxhighlight>
{{out}}
<pre>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">N</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2200</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">N2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">N</span><span style="color: #0000FF;">*</span><span style="color: #000000;">N</span><span style="color: #0000FF;">*</span><span style="color: #000000;">2</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">found</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">squares</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">N2</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- first mark all numbers that can be the sum of two squares</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">a2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">*</span><span style="color: #000000;">a</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">a</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">a2</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">*</span><span style="color: #000000;">b</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000080;font-style:italic;">-- now find all d such that d^2 - c^2 is in squares</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">d2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">*</span><span style="color: #000000;">d</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">squares</span><span style="color: #0000FF;">[</span><span style="color: #000000;">d2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">found</span><span style="color: #0000FF;">[</span><span style="color: #000000;">d</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">N</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #000000;">found</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">i</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
{1,2,4,5,8,10,16,20,32,40,64,80,128,160,256,320,512,640,1024,1280,2048}
</pre>
=={{header|PicoLisp}}==
{{trans|C}}
<
(let (AB NIL S 3 R)
(for A N
Line 602 ⟶ 1,766:
(or (idx 'R A) (link A)) ) ) ) )
(println (quadruples 2200))</
{{out}}
<pre>(1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048)</pre>
=={{header|PureBasic}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="purebasic">OpenConsole()
limite.i = 2200
s.i = 3
Dim l.i(limite)
Dim ladd.i(limite * limite * 2)
For x.i = 1 To limite
x2.i = x * x
For y = x To limite
ladd(x2 + y * y) = 1
Next y
Next x
For x.i = 1 To limite
s1.i = s
s.i + 2
s2.i = s
For y = x +1 To limite
If ladd(s1) = 1
l(y) = 1
EndIf
s1 + s2
s2 + 2
Next y
Next x
For x.i = 1 To limite
If l(x) = 0
Print(Str(x) + " ")
EndIf
Next x
Input()
CloseConsole()</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|Python}}==
===Search===
{{trans|Julia}}
<
r = [False] * top
ab = [False] * (top * 2)**2
Line 627 ⟶ 1,830:
if __name__ == '__main__':
n = 2200
print(f"Those values of d in 1..{n} that can't be represented: {quad(n)}")</
{{out}}
<pre>Those values of d in 1..2200 that can't be represented: [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]</pre>
===Composition of simpler generators===
Or, as an alternative to search – a generative solution (defining the generator we need as a composition of simpler generators):
{{Trans|Haskell}}
{{Trans|JavaScript}}
{{Trans|AppleScript}}
<syntaxhighlight lang="python">'''Pythagorean Quadruples'''
from itertools import islice, takewhile
# unrepresentables :: () -> [Int]
def unrepresentables():
'''A non-finite stream of powers of two which can
not be represented as a Pythagorean quadruple.
'''
return merge(
powersOfTwo()
)(
5 * x for x in powersOfTwo()
)
# powersOfTwo :: Gen [Int]
def powersOfTwo():
'''A non-finite stream of successive powers of two.
'''
def double(x):
return 2 * x
return iterate(double)(1)
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''For positive integers up to 2,200 (inclusive)
'''
def p(x):
return 2200 >= x
print(
list(
takewhile(p, unrepresentables())
)
)
# ----------------------- GENERIC ------------------------
# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return go
# merge :: Gen [Int] -> Gen [Int] -> Gen [Int]
def merge(ga):
'''An ordered stream of values drawn from two
other ordered streams.
'''
def go(gb):
def f(ma, mb):
a, b = ma, mb
while a and b:
ta, tb = a, b
if ta[0] < tb[0]:
yield ta[0]
a = uncons(ta[1])
else:
yield tb[0]
b = uncons(tb[1])
return f(uncons(ga), uncons(gb))
return go
# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
def go(xs):
return (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)
return go
# uncons :: [a] -> Maybe (a, [a])
def uncons(xs):
'''The deconstruction of a non-empty list
(or generator stream) into two parts:
a head value, and the remaining values.
'''
if isinstance(xs, list):
return (xs[0], xs[1:]) if xs else None
else:
nxt = take(1)(xs)
return (nxt[0], xs) if nxt else None
# MAIN ---
if __name__ == '__main__':
main()</syntaxhighlight>
{{Out}}
<pre>[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]</pre>
=={{header|R}}==
The best solution to this problem - using lots of for loops - is practically language agnostic. The R way of doing this is far less efficient, taking about 10 minutes on my machine, but it's the obvious way to do this in R.
<syntaxhighlight lang="rsplus">squares <- d <- seq_len(2200)^2
aAndb <- outer(squares, squares, '+')
aAndb <- aAndb[upper.tri(aAndb, diag = TRUE)]
sapply(squares, function(c) d <<- setdiff(d, aAndb + c))
print(sqrt(d))</syntaxhighlight>
{{out}}
<pre>[1] 1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|Racket}}==
Line 636 ⟶ 1,965:
{{trans|Python}}
<
(require data/bit-vector)
Line 661 ⟶ 1,990:
(printf "Those values of d in 1..~a that can't be represented: ~a~%" n (quadruples n)))
(report 2200)</
{{out}}
<pre>Those values of d in 1..2200 that can't be represented: (1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048)</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2018.09}}
<syntaxhighlight lang="raku" line>my \N = 2200;
my @sq = (0 .. N)»²;
my @not = False xx N;
@not[0] = True;
(1 .. N).race.map: -> $d {
my $last = 0;
for $d ... ($d/3).ceiling -> $a {
for 1 .. ($a/2).ceiling -> $b {
last if (my $ab = @sq[$a] + @sq[$b]) > @sq[$d];
if (@sq[$d] - $ab).sqrt.narrow ~~ Int {
@not[$d] = True;
$last = 1;
last
}
}
last if $last;
}
}
say @not.grep( *.not, :k );</syntaxhighlight>
{{out}}
<pre>(1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048)</pre>
=={{header|REXX}}==
Line 671 ⟶ 2,028:
This version is a brute force algorithm, with some optimization (to save compute time)
<br>which pre-computes some of the squares of the positive integers used in the search.
<syntaxhighlight lang="rexx">/*REXX pgm computes/shows (integers), D that aren't possible for: a² + b² + c² = d² */
parse arg hi . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi=2200; high=
@.=. /*array of integers to be squared. */
!.=. /* " " " squared. */
do j=1 for high /*precompute possible squares (to max).*/
end /*j*/
d.=. /*array of possible solutions (D) */
do a=1 for hi-2; aodd=
do b=a to hi-1;
if aodd then if b//2 then iterate /*Are A and B both odd? Then skip.*/
ab = @.a + @.b /*calculate sum of 2 (A,B) squares.*/
do c=b to hi; abc= ab + @.c /* " " " 3 (A,B,C) " */
s=!.abc; d.s= /*define this D solution as being found*/
end /*c*/
Line 703 ⟶ 2,053:
do p=1 for hi; if d.p==. then $=$ p /*Not possible? Then add it to the list*/
end /*p*/ /* [↓] display list of not-possibles. */
say substr($, 2) /*stick a fork in it, we're all done. */</
{{out|output|text= when using the default input:}}
<pre>
Line 714 ⟶ 2,064:
This REXX version is an optimized version, it solves the formula:
:::::::: <big><big> a<sup>2</sup> + b<sup>2</sup> = d<sup>2</sup> - c<sup>2</sup>
</big></big>
This REXX version is
Programming note: testing for '''a''' and '''b''' both being <big>odd</big> (lines '''15''' and '''16''' that each contain a '''do''' loop) as
<br>being a case that won't produce any solutions actually slows up the calculations and makes the program execute slower.
<syntaxhighlight lang="rexx">/*REXX pgm computes/shows (integers), D that aren't possible for: a² + b² + c² = d² */
parse arg hi . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi=2200 /*Not specified? Then use the default.*/
high= hi * 3
@.=
do s=1 for high; _= s*s; r._= s; @.s=_ /*precompute squares and square roots. */
end /*s*/
!.= /*array of differences between squares.*/
do c=1 for high; cc = @.c
do d=c+1 to high; dif= @.d - cc
end /*d*/
end /*c*/
d.=. /*array of the possible solutions
do a=1 for hi-2 /*go hunting for solutions to equation.*/
do b=a to hi-1;
if
do n=1 for words(
d._= /*mark the D integer as being found. */
end /*n*/
Line 748 ⟶ 2,099:
say
$= /* [↓] find all the "not possibles". */
do p=1 for hi; if d.p==. then $= $ p
end /*p*/ /* [↓] display list of not-possibles. */
say substr($, 2) /*stick a fork in it, we're all done. */</
{{out|output|text= is the same as the 1<sup>st</sup> REXX version.}} <br><br>
=={{header|Ring}}==
<
limit = 2200
Line 779 ⟶ 2,127:
next
see pqstr + nl
</syntaxhighlight>
{{Out}}
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
=={{header|Ruby}}==
{{trans|VBA}}
<syntaxhighlight lang="ruby">n = 2200
l_add, l = {}, {}
1.step(n) do |x|
x2 = x*x
x.step(n) {|y| l_add[x2 + y*y] = true}
end
s = 3
1.step(n) do |x|
s1 = s
s += 2
s2 = s
(x+1).step(n) do |y|
l[y] = true if l_add[s1]
s1 += s2
s2 += 2
end
end
puts (1..n).reject{|x| l[x]}.join(" ")
</syntaxhighlight>
{{Out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
Considering the observations in the Rust and Sidef sections and toying with Enumerators :
<syntaxhighlight lang="ruby">squares = Enumerator.new{|y| (0..).each{|n| y << 2**n} }
squares5 = Enumerator.new{|y| (0..).each{|n| y << 2**n*5} }
pyth_quad = Enumerator.new do |y|
n = squares.next
m = squares5.next
loop do
if n < m
y << n
n = squares.next
else
y << m
m = squares5.next
end
end
end
# this takes less than a millisecond
puts pyth_quad.take_while{|n| n <= 1000000000}.join(" ")</syntaxhighlight>
{{Out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 2560 4096 5120 8192 10240 16384 20480 32768 40960 65536 81920 131072 163840 262144 327680 524288 655360 1048576 1310720 2097152 2621440 4194304 5242880 8388608 10485760 16777216 20971520 33554432 41943040 67108864 83886080 134217728 167772160 268435456 335544320 536870912 671088640
</pre>
=={{header|Rust}}==
{{output?}}
This is equivalent to https://oeis.org/A094958
which simply contains positive integers of the form 2^n or 5*2^n. Multiple implementations are provided.
<syntaxhighlight lang="rust">
use std::collections::BinaryHeap;
fn a094958_iter() -> Vec<u16> {
(0..12)
.map(|n| vec![1 << n, 5 * (1 << n)])
.flatten()
.filter(|x| x < &2200)
.collect::<BinaryHeap<u16>>()
.into_sorted_vec()
}
fn a094958_filter() -> Vec<u16> {
(1..2200) // ported from Sidef
.filter(|n| ((n & (n - 1) == 0) || (n % 5 == 0 && ((n / 5) & (n / 5 - 1) == 0))))
.collect()
}
fn a094958_loop() -> Vec<u16> {
let mut v = vec![];
for n in 0..12 {
v.push(1 << n);
if 5 * (1 << n) < 2200 {
v.push(5 * (1 << n));
}
}
v.sort();
return v;
}
fn main() {
println!("{:?}", a094958_iter());
println!("{:?}", a094958_loop());
println!("{:?}", a094958_filter());
}
#[cfg(test)]
mod tests {
use super::*;
static HAPPY: &str = "[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]";
#[test]
fn test_a094958_iter() {
assert!(format!("{:?}", a094958_iter()) == HAPPY);
}
#[test]
fn test_a094958_loop() {
assert!(format!("{:?}", a094958_loop()) == HAPPY);
}
#[test]
fn test_a094958_filter() {
assert!(format!("{:?}", a094958_filter()) == HAPPY);
}
}
</syntaxhighlight>
=={{header|Scala}}==
{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/drfij1d/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/6AHn7YXSRbKHzmOY5rWAwg Scastie (remote JVM)].
<
val MAX = 2200
val MAX2: Int = MAX * MAX * 2
Line 811 ⟶ 2,272:
println(notRepresented.mkString(" "))
}</
=={{header|Sidef}}==
<syntaxhighlight lang="ruby"># Finds all solutions (a,b) such that: a^2 + b^2 = n^2
func sum_of_two_squares(n) is cached {
Line 855 ⟶ 2,314:
for p,e in (prime_powers) {
var pp = p**e
var r =
take([[r, pp], [pp - r, pp]])
}
Line 910 ⟶ 2,369:
sum_of_three_squares(n) || take(n)
}
}</
{{out}}
<pre>
Line 917 ⟶ 2,376:
Numbers d that cannot be expressed as a^2 + b^2 + c^2 = d^2, are numbers of the form 2^n or 5*2^n:
<
for n in (1..2200) {
if ((n & (n-1) == 0) || (n%%5 && ((n/5) & (n/5 - 1) == 0))) {
Line 923 ⟶ 2,382:
}
}
}</
{{out}}
<pre>
[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]
</pre>
=={{header|Swift}}==
{{trans|C}}
<syntaxhighlight lang="swift">func missingD(upTo n: Int) -> [Int] {
var a2 = 0, s = 3, s1 = 0, s2 = 0
var res = [Int](repeating: 0, count: n + 1)
var ab = [Int](repeating: 0, count: n * n * 2 + 1)
for a in 1...n {
a2 = a * a
for b in a...n {
ab[a2 + b * b] = 1
}
}
for c in 1..<n {
s1 = s
s += 2
s2 = s
for d in c+1...n {
if ab[s1] != 0 {
res[d] = 1
}
s1 += s2
s2 += 2
}
}
return (1...n).filter({ res[$0] == 0 })
}
print(missingD(upTo: 2200))</syntaxhighlight>
{{out}}
<pre>[1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048]</pre>
=={{header|VBA}}==
{{trans|FreeBasic}}
<syntaxhighlight lang="vb">Const n = 2200
Public Sub pq()
Dim s As Long, s1 As Long, s2 As Long, x As Long, x2 As Long, y As Long: s = 3
Dim l(n) As Boolean, l_add(9680000) As Boolean '9680000=n * n * 2
For x = 1 To n
x2 = x * x
For y = x To n
l_add(x2 + y * y) = True
Next y
Next x
For x = 1 To n
s1 = s
s = s + 2
s2 = s
For y = x + 1 To n
If l_add(s1) Then l(y) = True
s1 = s1 + s2
s2 = s2 + 2
Next
Next
For x = 1 To n
If Not l(x) Then Debug.Print x;
Next
Debug.Print
End Sub</syntaxhighlight>{{out}}
<pre> 1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 </pre>
=={{header|Wren}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="wren">var N = 2200
var N2 = N * N * 2
var s = 3
var s1 = 0
var s2 = 0
var r = List.filled(N + 1, false)
var ab = List.filled(N2 + 1, false)
for (a in 1..N) {
var a2 = a * a
for (b in a..N) ab[a2 + b*b] = true
}
for (c in 1..N) {
s1 = s
s = s + 2
s2 = s
var d = c + 1
while (d <= N) {
if (ab[s1]) r[d] = true
s1 = s1 + s2
s2 = s2 + 2
d = d + 1
}
}
for (d in 1..N) {
if (!r[d]) System.write("%(d) ")
}
System.print()</syntaxhighlight>
{{out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
=={{header|XPL0}}==
{{trans|C}}
Twenty-seven seconds on my (cheap) Raspberry Pi 4.
<syntaxhighlight lang "XPL0">def N = 2200;
int A, B, C, D, AABB, AABBCC;
char R(N+1);
[FillMem(R, 0, N+1); \zero solution array
for A:= 1 to N do
[for B:= A to N do
[if (A&1 and B&1) = 0 then \for positive odd A and B, no solution
[AABB:= A*A + B*B;
for C:= B to N do
[AABBCC:= AABB + C*C;
D:= sqrt(AABBCC);
if AABBCC = D*D and D <= N then R(D):= 1; \solution
];
];
];
];
for A:= 1 to N do
if R(A) = 0 then
[IntOut(0, A); ChOut(0, ^ )]; \print non-solutions
CrLf(0);
]</syntaxhighlight>
{{out}}
<pre>
1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048
</pre>
=={{header|Yabasic}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="freebasic">limite = 2200
s = 3
dim l(limite)
dim ladd(limite * limite * 2)
for x = 1 to limite
x2 = x * x
for y = x to limite
ladd(x2 + y * y) = 1
next y
next x
for x = 1 to limite
s1 = s
s = s + 2
s2 = s
for y = x +1 to limite
if ladd(s1) = 1 l(y) = 1
s1 = s1 + s2
s2 = s2 + 2
next y
next x
for x = 1 to limite
if l(x) = 0 print str$(x), " ";
next x
print
end</syntaxhighlight>
{{out}}
<pre>1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048</pre>
=={{header|zkl}}==
{{trans|ALGOL 68}}
<
# where d in [1..2200], a, b, c =/= 0 #
# max number to check #
Line 958 ⟶ 2,585:
if(not solution[ d ]) print(d, " ");
}
println();</
{{out}}
<pre>
| |||