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Pythagorean triples: Difference between revisions
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return 0;
}</lang>output:<lang>Up to 100, there are 17 triples, of which 7 are primitive</lang>
=={{header|Icon}} and {{header|Unicon}}==
This uses the elegant formula (#IV) from [[wp:Formulas_for_generating_Pythagorean_triples|Formulas for generating Pythagorean triples]]
<lang Icon>
link math
link printf
procedure main(A) # P-triples
plimit := (0 < integer(\A[1])) | 100 # get perimiter limit
nonprimitiveS := set() # record unique non-primitives triples
primitiveS := set() # record unique primitive triples
u := 0
while (g := (u +:= 1)^2) + 3 * u + 2 < plimit / 2 do {
every v := seq(1) do {
a := g + (i := 2*u*v)
b := (h := 2*v^2) + i
c := g + h + i
if (p := a + b + c) > plimit then break
insert( (gcd(u,v)=1 & u%2=1, primitiveS) | nonprimitiveS, memo(a,b,c))
every k := seq(2) do { # k is for larger non-primitives
if k*p > plimit then break
insert(nonprimitiveS,memo(a*k,b*k,c*k) )
}
}
}
printf("Under perimiter=%d: Pythagorean Triples=%d including primitives=%d\n",
plimit,*nonprimitiveS+*primitiveS,*primitiveS)
every put(gcol := [] , &collections)
printf("Time=%d, Collections: total=%d string=%d block=%d",&time,gcol[1],gcol[3],gcol[4])
end
procedure memo(x[]) #: return a csv string of arguments in sorted order
every (s := "") ||:= !sort(x) do s ||:= ","
return s[1:-1]
end</lang>
{{libheader|Icon Programming Library}}
[http://www.cs.arizona.edu/icon/library/src/procs/math.icn math.icn provides gcd]
[http://www.cs.arizona.edu/icon/library/src/procs/printf.icn printf.icn provides printf]
The output from some sample runs with BLKSIZE=500000000 and STRSIZE=50000000 is below. It starts getting very slow after 10M at about 9 minutes.
Output:<pre>
Under perimiter=10: Pythagorean Triples=0 including primitives=0
Time=3, Collections: total=0 string=0 block=0
Under perimiter=100: Pythagorean Triples=17 including primitives=7
Time=3, Collections: total=0 string=0 block=0
Under perimiter=1000: Pythagorean Triples=325 including primitives=70
Time=6, Collections: total=0 string=0 block=0
Under perimiter=10000: Pythagorean Triples=4858 including primitives=703
Time=57, Collections: total=0 string=0 block=0
Under perimiter=100000: Pythagorean Triples=64741 including primitives=7026
Time=738, Collections: total=0 string=0 block=0
Under perimiter=1000000: Pythagorean Triples=808950 including primitives=70229
Time=12454, Collections: total=0 string=0 block=0
Under perimiter=10000000: Pythagorean Triples=9706567 including primitives=702309
Time=560625, Collections: total=16 string=8 block=8</pre>
=={{header|J}}==
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