Heronian triangles: Difference between revisions
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7 65 68 _ 210 140
3 148 149 _ 210 300</lang>
=={{header|jq}}==
{{works with|jq|1.4}}
<lang jq># input should be an array of the lengths of the sides
def hero:
(add/2) as $s
| ($s*($s - .[0])*($s - .[1])*($s - .[2])) as $a2
| if $a2 > 0 then ($a2 | sqrt) else 0 end;
def is_heronian:
hero as $h
| $h > 0 and ($h|floor) == $h;
def gcd3(x; y; z):
# subfunction expects [a,b] as input
def rgcd:
if .[1] == 0 then .[0]
else [.[1], .[0] % .[1]] | rgcd
end;
[ ([x,y] | rgcd), z ] | rgcd;
def task(maxside):
def rjust(width): tostring | " " * (width - length) + .;
[ range(1; maxside+1) as $c
| range(1; $c+1) as $b
| range(1; $b+1) as $a
| if ($a + $b) > $c and gcd3($a; $b; $c) == 1
then [$a,$b,$c] | if is_heronian then . else empty end
else empty
end ]
# sort by increasing area, perimeter, then sides
| sort_by( [ hero, add, .[2] ] )
| "The number of primitive Heronian triangles with sides up to \(maxside): \(length)",
"The first ten when ordered by increasing area, then perimeter, then maximum sides:",
" perimeter area",
(.[0:10][] | "\(rjust(11)) \(add | rjust(3)) \(hero | rjust(4))" ),
"All those with area 210, ordered as previously:",
" perimeter area",
( .[] | select( hero == 210 ) | "\(rjust(11)) \(add|rjust(3)) \(hero|rjust(4))" ) ;
task(200)</lang>
{{out}}
<lang sh>$ time jq -n -r -f heronian.jq
The number of primitive Heronian triangles with sides up to 200: 517
The first ten when ordered by increasing area, then perimeter, then maximum sides:
perimeter area
[3,4,5] 12 6
[5,5,6] 16 12
[5,5,8] 18 12
[4,13,15] 32 24
[5,12,13] 30 30
[9,10,17] 36 36
[3,25,26] 54 36
[7,15,20] 42 42
[10,13,13] 36 60
[8,15,17] 40 60
All those with area 210, ordered as previously:
perimeter area
[17,25,28] 70 210
[20,21,29] 70 210
[12,35,37] 84 210
[17,28,39] 84 210
[7,65,68] 140 210
[3,148,149] 300 210</lang>
=={{header|Perl}}==
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