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Proper divisors: Difference between revisions
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→{{header|REXX}}: added/changed comments and whitespace, used a template for the OUTPUTs, simplified the code, used better idiomatic code for handling C.L. input, cre-worked the integer square root code.
m (→{{header|REXX}}: added/changed comments and whitespace, used a template for the OUTPUTs, simplified the code, used better idiomatic code for handling C.L. input, cre-worked the integer square root code.) |
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With the (subroutine) optimization, it's over twenty times faster.
<lang rexx>/*REXX program finds proper divisors (and count) of integer ranges; finds the max count.*/
parse arg bot top inc range xtra
if
if range=='' | range=="," then range=20000 /* " " " " " " */
w=1+max(length(top), length(bot), length(range)) /*determine the biggest number of these*/
numeric digits max(9, w) /*have enough digits for // operator.*/
say right(n,max(20,digits())) 'has' center(#,4) "proper divisors: " q▼
@.= 'and'
if q=='∞' then #=q /*adjust number of Pdivisors for zero. */
end /*r*/ /* [↑] process 2nd range of integers.*/▼
end /*n*/
__= 'is the highest number of proper divisors in range 1──►'range▼
say /* [↑] process 1st range of integers.*/
say m __", and it's for: " subword(@.m,3)▼
m=0 /*M ≡ maximum number of Pdivs (so far).*/
do r=1 for range /*process the second range specified. */
q=Pdivs(r); #=words(q) /*get proper divs; get number of Pdivs.*/
if #<m then iterate /*Less then max? Then ignore this #. */
@.#=@.# @. r; m=# /*add this Pdiv to max list; set new M.*/
say /* [↓] handle any given extra numbers.*/
do i=1 for words(xtra); n=word(xtra, i) /*obtain an extra number from XTRA
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Pdivs: procedure; parse arg x,b; x=abs(x); if x==1 then return '' /*unity?*/
odd=x // 2;
r=0 /* [↓] ══integer square root══ ___ */
q=1; do while q<=z; q=q*4; end /*R: an integer which will be √ X */
do while q>1; q=q%4; _=z-r-q; r=r%2; if _>=0 then do; z=_; r=r+q; end
end /*while q>1*/ /* [↑] compute the integer sqrt of X.*/
a=1 /* [↓] use all, or only odd #s. ___*/
do j=2 +odd by 1 +odd to
if x//j==0 then do; a=a j; b=x%j b /*if ÷, add both divisors to α & ß. */
end
Line 3,328 ⟶ 3,343:
if j*j==x then return a j b /*Was X a square? If so, add √ X */
return a b /*return the divisors (both lists). */</lang>
<pre>
0 has ∞ proper divisors: ∞
Line 3,355 ⟶ 3,370:
It accomplishes a faster speed by incorporating the calculation of an ''integer square root'' of an integer (without using any floating point arithmetic).
<lang rexx>/*REXX program finds proper divisors (and count) of integer ranges; finds the max count.*/
parse arg bot top inc range xtra
if
if range=='' | range=="," then range=20000 /* " " " " " " */
w=1+max(length(top), length(bot), length(range)) /*determine the biggest number of these*/
numeric digits max(9, w) /*have enough digits for // operator.*/
▲ say right(n,max(20,digits())) 'has' center(#,4) "proper divisors: " q
@.= 'and'
if q=='∞' then #=q /*adjust number of Pdivisors for zero. */
say right(n, max(20, w) ) 'has' center(#, 4) "proper divisors: " q
▲ end /*r*/ /* [↑] process 2nd range of integers.*/
end /*n*/
__= 'is the highest number of proper divisors in range 1──►'range▼
say /* [↑] process 1st range of integers.*/
say m __", and it's for: " subword(@.m,3)▼
m=0 /*M ≡ maximum number of Pdivs (so far).*/
do r=1 for range /*process the second range specified. */
q=Pdivs(r); #=words(q) /*get proper divs; get number of Pdivs.*/
if #<m then iterate /*Less then max? Then ignore this #. */
@.#=@.# @. r; m=# /*add this Pdiv to max list; set new M.*/
end /*r*/ /* [↑] process 2nd range of integers.*/
say /* [↓] handle any given extra numbers.*/
do i=1 for words(xtra); n=word(xtra, i) /*obtain an extra number from XTRA
say right(n, max(20, w) ) 'has' center(#, 4) "proper divisors."
end /*i*/ /* [↑] support extra specified integers*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Pdivs: procedure; parse arg x,b; x=abs(x); if x==1 then return '' /*unity?*/
do while q>1; q=q%4; _=z-r-q; r=r%2; if _>=0 then do; z=_; r=r+q; end
end /*while q>1*/ /* [↑] compute the integer sqrt of X.*/
a=1 /* [↓] use all, or only odd #s. ___*/
do j=
if x//j==0 then do; a=a j; b=x%j b /*if ÷, add both divisors to α & ß. */
end
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if j*j==x then return a j b /*Was X a square? If so, add √ X */
return a b /*return the divisors (both lists). */</lang>
=={{header|Ring}}==
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