Pythagorean triples: Difference between revisions
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m (→{{header|REXX}}: added more whitespace in output, used different form on "n". -- ~~~~) |
m (→{{header|REXX}}: added another sample output for 1,000. -- ~~~~) |
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prims=0 |
prims=0 |
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do a=3 to N%3; aa=a*a |
do a=3 to N%3; aa=a*a /*limit side to 1/3 of perimeter.*/ |
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do b=a+1 /*triangle can't be isosceles. */ |
do b=a+1 /*triangle can't be isosceles. */ |
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ab=a+b /*compute partial perimeter. */ |
ab=a+b /*compute partial perimeter. */ |
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if ab>=n then iterate a /*a+b>perimeter? Try different A*/ |
if ab>=n then iterate a /*a+b>perimeter? Try different A*/ |
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aabb=aa+b*b /*compute sum of a² + b² (cheat)*/ |
aabb=aa+b*b /*compute sum of a² + b² (cheat)*/ |
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do c=b+1; cc=c*c /*3rd side: also compute c² */ |
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if ab+c>n then iterate a /*a+b+c > perimeter? Try diff A.*/ |
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if cc>aabb then iterate b /*c² > a²+b² ? Try different B.*/ |
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if cc\==aabb then iterate /*c² ¬= a²+b² ? Try different C.*/ |
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trips=trips+1 /*eureka. */ |
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prims=prims+(gcd(a,b)==1) /*is this triple a primative ? */ |
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end /*a*/ |
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end |
end /*b*/ |
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end |
end /*c*/ |
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say 'max perimeter = 'N, /*show a single line of output. */ |
say 'max perimeter = 'N, /*show a single line of output. */ |
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left('', |
left('',7) "Pythagorean triples =" trips, /*left('',0) ≡ 7 blanks.*/ |
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left('', |
left('',7) 'primatives =' prims |
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exit |
exit |
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/*──────────────────────────────────GCD subroutine──────────────────────*/ |
/*──────────────────────────────────GCD subroutine──────────────────────*/ |
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gcd: procedure; arg x,y; do until _==0; _=x//y; x=y; y=_; end; return x</lang> |
gcd: procedure; arg x,y; do until _==0; _=x//y; x=y; y=_; end; return x</lang> |
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'''output''' when using the input of |
'''output''' when using the default input of 100 |
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<pre style="overflow:scroll"> |
<pre style="overflow:scroll"> |
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max perimeter = 100 |
max perimeter = 100 Pythagorean triples = 17 primatives = 7 |
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</pre> |
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'''output''' when using the input of: <tt> 1000 </tt> |
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<pre style="overflow:scroll"> |
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max perimeter = 1000 Pythagorean triples = 325 primatives = 70 |
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</pre> |
</pre> |
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