Stern-Brocot sequence: Difference between revisions
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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*/ |
<lang rexx>/*REXX program generates & displays a Stern─Brocot sequence; finds 1─based indices; GCDs*/ |
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parse arg N idx fix chk . /*get optional arguments from the C.L. */ |
parse arg N idx fix chk . /*get optional arguments from the C.L. */ |
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if N=='' | N=="," then N= |
if N=='' | N=="," then N= 15 /*Not specified? Then use the default.*/ |
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if idx=='' | idx=="," then idx= |
if idx=='' | idx=="," then idx= 10 /* " " " " " " */ |
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if fix=='' | fix=="," then fix= |
if fix=='' | fix=="," then fix= 100 /* " " " " " " */ |
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if chk=='' | chk=="," then chk= |
if chk=='' | chk=="," then chk= 1000 /* " " " " " " */ |
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say center('the first' |
if N>0 then say center('the first' N "numbers in the Stern─Brocot sequence", 70, '═') |
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a=Stern_Brocot(N) |
a= Stern_Brocot(N) /*invoke function to generate sequence.*/ |
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say a /*display the sequence to the terminal.*/ |
say a /*display the sequence to the terminal.*/ |
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say |
say |
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say center('the 1─based index for the first' idx "integers", 70, '═') |
say center('the 1─based index for the first' idx "integers", 70, '═') |
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a=Stern_Brocot(-idx) |
a= Stern_Brocot(-idx) /*invoke function to generate sequence.*/ |
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w=length(idx); |
w= length(idx); do i=1 for idx |
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say 'for ' right(i, w)", the index is: " wordpos(i, a) |
say 'for ' right(i, w)", the index is: " wordpos(i, a) |
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end /*i*/ |
end /*i*/ |
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say |
say |
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say center('the 1─based index for' fix, 70, "═") |
say center('the 1─based index for' fix, 70, "═") |
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a=Stern_Brocot(-fix) |
a= Stern_Brocot(-fix) /*invoke function to generate sequence.*/ |
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say 'for ' fix", the index is: " wordpos(fix, a) |
say 'for ' fix", the index is: " wordpos(fix, a) |
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say |
say |
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if chk<2 then exit 0 |
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say center('checking if all two consecutive members have a GCD=1', 70, '═') |
say center('checking if all two consecutive members have a GCD=1', 70, '═') |
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a=Stern_Brocot(chk) |
a= Stern_Brocot(chk) /*invoke function to generate sequence.*/ |
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do c=1 for chk-1; if gcd(subword(a, c, 2))==1 then iterate |
do c=1 for chk-1; if gcd(subword(a, c, 2))==1 then iterate |
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say 'GCD check failed at index' c; exit 13 |
say 'GCD check failed at index' c; exit 13 |
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end /*c*/ |
end /*c*/ |
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say |
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say '───── All ' chk " two consecutive members have a GCD of unity." |
say '───── All ' chk " two consecutive members have a GCD of unity." |
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exit |
exit 0 /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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gcd: procedure; $=; do i=1 for arg(); $=$ arg(i) |
gcd: procedure; $=; do i=1 for arg(); $= $ arg(i) /*get arg list. */ |
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end /*i*/ |
end /*i*/ |
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parse var $ x z .; if x=0 then x= |
parse var $ x z .; if x=0 then x= z /*is zero case? */ |
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x=abs(x) /*use absolute x*/ |
x=abs(x) /*use absolute x*/ |
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do j=2 to words($); y=abs( word($, j) ) |
do j=2 to words($); y=abs( word($, j) ) |
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return x /*return the GCD*/ |
return x /*return the GCD*/ |
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/*──────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────*/ |
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Stern_Brocot: parse arg h 1 f; |
Stern_Brocot: parse arg h 1 f; $= 1 1; if h<0 then h= 1e9 |
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else f= 0 |
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f=abs(f) |
f= abs(f) |
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do k=2 until words($)>=h | wordpos(f, $)\==0 |
do k=2 until words($)>=h | wordpos(f, $)\==0 |
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$=$ (_ + word($, k-1) ) _ |
_= word($, k); $= $ (_ + word($, k-1) ) _ |
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end /*k*/ |
end /*k*/ |
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if f==0 then return subword($, 1, h) |
if f==0 then return subword($, 1, h) |
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