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Stern-Brocot sequence: Difference between revisions
m
→{{header|REXX}}: added/changed whitespace and comments, added checks to possibly bypass computing some of the tasks.
m (→{{header|AppleScript}}: Tidying) |
m (→{{header|REXX}}: added/changed whitespace and comments, added checks to possibly bypass computing some of the tasks.) |
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<lang rexx>/*REXX program generates & displays a Stern─Brocot sequence; finds 1─based indices; GCDs*/
parse arg N idx fix chk . /*get optional arguments from the C.L. */
if N=='' | N=="," then N=
if idx=='' | idx=="," then idx=
if fix=='' | fix=="," then fix=
if chk=='' | chk=="," then chk=
if N>0 then say center('the first'
a= Stern_Brocot(N)
say a /*display the sequence to the terminal.*/
say
say center('the 1─based index for the first' idx "integers", 70, '═')
a= Stern_Brocot(-idx)
w= length(idx);
say 'for ' right(i, w)", the index is: " wordpos(i, a)
end /*i*/
say
say center('the 1─based index for' fix, 70, "═")
a= Stern_Brocot(-fix)
say 'for ' fix", the index is: " wordpos(fix, a)
say
if chk<2 then exit 0
say center('checking if all two consecutive members have a GCD=1', 70, '═')
a= Stern_Brocot(chk)
do c=1 for chk-1; if gcd(subword(a, c, 2))==1 then iterate
say 'GCD check failed at index' c; exit 13
end /*c*/
say
say '───── All ' chk " two consecutive members have a GCD of unity."
exit
/*──────────────────────────────────────────────────────────────────────────────────────*/
gcd: procedure; $=; do i=1 for arg(); $= $ arg(i)
end /*i*/
parse var $ x z .; if x=0 then x=
x=abs(x) /*use absolute x*/
do j=2 to words($); y=abs( word($, j) )
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return x /*return the GCD*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
Stern_Brocot: parse arg h 1 f;
f= abs(f)
do k=2 until words($)>=h | wordpos(f, $)\==0
_= word($, k); $= $ (_ + word($, k-1) ) _
end /*k*/
if f==0 then return subword($, 1, h)
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