Just another update
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Ingy döt Net
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6591 changed files with 94363 additions and 23227 deletions
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/*REXX pgm counts number of Pythagorean triples that exist given a max */
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/* perimeter of N, and also counts how many of them are primitives.*/
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trips=0; prims=0
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trips=0; prims=0 /*zero # of triples, primatives. */
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parse arg N .; if N=='' then n=100 /*get "N". If none, then assume.*/
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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. */
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ab=a+b /*compute partial perimeter. */
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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)*/
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do b=a+1 /*triangle can't be isosceles. */
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ab=a+b /*compute partial perimeter. */
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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)*/
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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 primitive? */
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end /*a*/
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end /*b*/
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end /*c*/
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do c=b+1 /*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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cc=c*c /*compute C². */
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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. We found a prim triple*/
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prims=prims+(gcd(a,b)==1) /*is this triple a primitive? */
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end /*a*/
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end /*b*/
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end /*c*/
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say 'max perimeter =' N, /*show a single line of output. */
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left('',7) "Pythagorean triples =" trips, /*left('',0)≡7 blanks.*/
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left('',7) "Pythagorean triples =" trips, /*left('',7)≡7 blanks.*/
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left('',7) 'primitives =' prims
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────GCD subroutine──────────────────────*/
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gcd: procedure; arg x,y; do until _==0; _=x//y; x=y; y=_; end; return x
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gcd: procedure; parse arg x,y
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do until y==0; parse value x//y y with y x; end; return x
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@ -1,35 +1,36 @@
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/*REXX pgm counts number of Pythagorean triples that exist given a max */
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/* perimeter of N, and also counts how many of them are primitives.*/
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@.=0; trips=0; prims=0
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parse arg N .; if N=='' then n=100 /*get "N". If none, then assume.*/
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@.=0; trips=0; prims=0 /*zero some REXX variables. */
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parse arg N .; if N=='' then N=100 /*get "N". If none, then assume.*/
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do a=3 to N%3; aa=a*a /*limit side to 1/3 of perimeter.*/
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aEven= a//2==0
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aEven= a//2==0 /*set var to 1 if A is even.*/
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do b=a+1 by 1+aEven /*triangle can't be isosceles. */
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ab=a+b /*compute partial perimeter. */
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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)*/
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do b=a+1 by 1+aEven /*triangle can't be isosceles. */
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ab=a+b /*compute partial perimeter. */
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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)*/
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do c=b+1; cc=c*c /*3rd side: also compute c² */
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if aEven then if c//2==0 then iterate
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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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if @.a.b.c then iterate
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trips=trips+1 /*eureka. */
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prims=prims+1 /*count this primitive triple. */
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do c=b+1 /*C is the third side of triangle*/
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if aEven then if c//2==0 then iterate
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if ab+c>n then iterate a /*a+b+c > perimeter? Try diff A.*/
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cc=c*c /*compute C². */
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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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if @.a.b.c then iterate /*Is this a duplicate? Try again*/
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trips=trips+1 /*eureka. We found a prim triple*/
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prims=prims+1 /*count this primitive triple. */
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do m=2; !a=a*m; !b=b*m; !c=c*m /*gen non-primitives.*/
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if !a+!b+!c>N then leave /*is this multiple a triple ? */
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trips=trips+1 /*yuppers, then we found another.*/
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if m//2 then @.!a.!b.!c=1 /*don't mark if an even multiple.*/
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end /*m*/
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end /*d*/
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end /*b*/
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do m=2; am=a*m; bm=b*m; cm=c*m /*gen non-primitives.*/
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if am+bm+cm>N then leave /*is this multiple a triple ? */
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trips=trips+1 /*yuppers, then we found another.*/
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if m//2 then @.am.bm.cm=1 /*don't mark if an even multiple.*/
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end /*m*/
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end /*d*/
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end /*b*/
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end /*a*/
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say 'max perimeter =' N, /*show a single line of output. */
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left('',7) "Pythagorean triples =" trips, /*left('',0) = 7 blanks.*/
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say 'max perimeter =' N, /*show a single line of output. */
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left('',7) "Pythagorean triples =" trips, /*left('',7)≡7 blanks.*/
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left('',7) 'primitives =' prims
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/*stick a fork in it, we're done.*/
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