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Farey sequence: Difference between revisions

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Farey sequence (view source)

Revision as of 15:54, 16 January 2022

6,189 bytes added ,  2 years ago
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→‎{{header|Phix}}: added syntax colouring, marked p2js compatible
m (Updated description and link for Fōrmulæ solution)
m (→‎{{header|Phix}}: added syntax colouring, marked p2js compatible)
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=={{header|Phix}}==
{{trans|AWK}}
<!--<lang Phix>function farey(integer nphixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
integer a=0, b=1, c=1, d=n
<span style="color: #008080;">function</span> <span style="color: #000000;">farey</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
integer items=1
<span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">items</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span>
if n<=11 then
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">11</span> <span style="color: #008080;">then</span>
printf(1,"%d: %d/%d",{n,a,b})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %d/%d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">})</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
while c<=n do
<span style="color: #008080;">while</span> <span style="color: #000000;">c</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
integer k = floor((n+b)/d)
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
{a,b,c,d} = {c,d,k*c-a,k*d-b}
<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">c</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">c</span><span style="color: #0000FF;">-</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">*</span><span style="color: #000000;">d</span><span style="color: #0000FF;">-</span><span style="color: #000000;">b</span><span style="color: #0000FF;">}</span>
items += 1
<span style="color: #000000;">items</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
if n<=11 then
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">11</span> <span style="color: #008080;">then</span>
printf(1," %d/%d",{a,b})
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" %d/%d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">})</span>
end if
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
end while
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
return items
<span style="color: #008080;">return</span> <span style="color: #000000;">items</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
 
printf(1,"Farey sequence for order 1 through 11:\n")
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Farey sequence for order 1 through 11:\n"</span><span style="color: #0000FF;">)</span>
for i=1 to 11 do
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">11</span> <span style="color: #008080;">do</span>
{} = farey(i)
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">farey</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
printf(1,"\n")
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
printf(1,"Farey sequence fractions, 100 to 1000 by hundreds:\n")
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),</span><span style="color: #000000;">farey</span><span style="color: #0000FF;">)</span>
sequence nf = {}
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Farey sequence fractions, 100 to 1000 by hundreds:\n%v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">nf</span><span style="color: #0000FF;">})</span>
for i=100 to 1000 by 100 do
?nf<!--</lang>-->▼
nf = append(nf,farey(i))
end for
▲?nf</lang>
{{out}}
<pre>
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