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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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17
Task/Stern-Brocot-sequence/PicoLisp/stern-brocot-sequence.l Normal file
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(de nmbr (N)
(let (A 1 B 0)
(while (gt0 N)
(if (bit? 1 N)
(inc 'B A)
(inc 'A B) )
(setq N (>> 1 N)) )
B ) )
(let Lst (mapcar nmbr (range 1 2000))
(println 'First-15: (head 15 Lst))
(for N 10
(println 'First N 'found 'at: (index N Lst)) )
(println 'First 100 'found 'at: (index 100 Lst))
(for (L Lst (cdr L) (cddr L))
(test 1 (gcd (car L) (cadr L))) )
(prinl "All consecutive pairs are relative prime!") )

51
Task/Stern-Brocot-sequence/REXX/stern-brocot-sequence.rexx
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/*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= 15 /* N not defined? Then use default.*/
if idx=='' | idx=="," then idx= 10 /*IDX " " " " " */
if fix=='' | fix=="," then fix= 100 /*FIX " " " " " */
if chk=='' | chk=="," then chk=1000 /*CHK " " " " " */
if N=='' | N=="," then N= 15 /*Not specified? Then use the default.*/
if idx=='' | idx=="," then idx= 10 /* " " " " " " */
if fix=='' | fix=="," then fix= 100 /* " " " " " " */
if chk=='' | chk=="," then chk=1000 /* " " " " " " */
say center('the first' N "numbers in the Stern─Brocot sequence", 70, '═')
say center('the first' N "numbers in the Stern─Brocot sequence", 70, '═')
a=Stern_Brocot(N) /*invoke function to generate sequence.*/
say a /*display the sequence to the terminal.*/
say
say center('the 1-based index for the first' idx "integers", 70, '═')
say center('the 1─based index for the first' idx "integers", 70, '═')
a=Stern_Brocot(-idx) /*invoke function to generate sequence.*/
do i=1 for idx
say 'for ' right(i,length(idx))", the index is: " wordpos(i,a)
w=length(idx); do i=1 for idx
say 'for ' right(i, w)", the index is: " wordpos(i, a)
end /*i*/
say
say center('the 1-based index for' fix, 70, "═")
say center('the 1─based index for' fix, 70, "═")
a=Stern_Brocot(-fix) /*invoke function to generate sequence.*/
say 'for ' fix", the index is: " wordpos(fix, a)
say
say center('checking if all two consecutive members have a GCD=1', 70, '═')
a=Stern_Brocot(chk) /*invoke function to generate sequence.*/
do c=1 for chk-1; if gcd(subword(a,c,2))==1 then iterate
say 'GCD check failed at member' c"."; exit 13
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 '───── All ' chk " two consecutive members have a GCD of unity."
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gcd: procedure; $=; do i=1 for arg(); $=$ arg(i); end /*i*/ /*arg list. */
parse var $ x z .; if x=0 then x=z; x=abs(x) /*zero case?*/
do j=2 to words($); y=abs(word($,j)); if y=0 then iterate /*ignore 0's*/
do until y==0; parse value x//y y with y x; end /*heavy work*/
end /*j*/
return x /*return GCD*/
gcd: procedure; $=; do i=1 for arg(); $=$ arg(i) /*get arg list. */
end /*i*/
parse var $ x z .; if x=0 then x=z /*is zero case? */
x=abs(x) /*use absolute x*/
do j=2 to words($); y=abs( word($, j) )
if y=0 then iterate /*ignore zeros. */
do until y==0; parse value x//y y with y x /* ◄──heavy work*/
end /*until*/
end /*j*/
return x /*return the GCD*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
Stern_Brocot: parse arg h 1 f; $=1 1; if h<0 then h=1e9
else f=0; f=abs(f)
do k=2 until words($)>=h | wordpos(f,$)\==0
_=word($,k); $=$ (_+word($,k-1)) _; if f==0 then iterate
end /*until*/
if f==0 then return subword($,1,h)
Stern_Brocot: parse arg h 1 f; $=1 1; if h<0 then h=1e9
else f=0
f=abs(f)
do k=2 until words($)>=h | wordpos(f, $)\==0; _=word($, k)
$=$ (_ + word($, k-1) ) _
end /*k*/
if f==0 then return subword($, 1, h)
return $

56
Task/Stern-Brocot-sequence/Ring/stern-brocot-sequence.ring Normal file
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# Project : Stern-Brocot sequence
# Date : 2018/02/01
# Author : Gal Zsolt [~ CalmoSoft ~]
# Email : <calmosoft@gmail.com>
limit = 1200
item = list(limit+1)
item[1] = 1
item[2] = 1
nr = 2
gcd = 1
gcdall = 1
for num = 3 to limit
item[num] = item[nr] + item[nr-1]
item[num+1] = item[nr]
nr = nr + 1
num = num + 1
next
showarray(item,15)
for x = 1 to 100
if x < 11 or x = 100
totalitem(x)
ok
next
for n = 1 to len(item) - 1
if gcd(item[n],item[n+1]) != 1
gcdall = gcd
ok
next
if gcdall = 1
see "Correct: The first 999 consecutive pairs are relative prime!" + nl
ok
func totalitem(p)
pos = find(item, p)
see string(x) + " at Stern #" + pos + "." + nl
func showarray(vect,ln)
svect = ""
for n = 1 to ln
svect = svect + vect[n] + ", "
next
svect = left(svect, len(svect) - 2)
see svect
see nl
func gcd(gcd,b)
while b
c = gcd
gcd = b
b = c % b
end
return gcd

2
Task/Stern-Brocot-sequence/Sidef/stern-brocot-sequence.sidef
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@ -1,7 +1,7 @@
# Declare a function to generate the Stern-Brocot sequence
func stern_brocot {
var list = [1, 1]
func {
{
list.append(list[0]+list[1], list[1])
list.shift
}