Golfing the Farey Sequence

Ruby
1

A Farey Sequence is all the fractions between 0 and 1 (inclusive) with
a denominator no bigger than N, arranged in increasing order of
magnitude.

For example, the Farey Sequence of order 3 is:
0/1, 1/3, 1/2, 2/3, 1/1

and the Farey Sequence of order 7 is:
0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3, 5/7,
3/4, 4/5, 5/6, 6/7, 1/1

My challenge - come up with the least-bytes Ruby code that, given a
constant N set to the order, can print out the sequence (one value per
line).

Here’s starting code, based on the algorithm included in the Wikipedia
article for the Farey Sequence:[1]

N = 7

a,b,c,d=0,1,1,N
puts “#{a}/#{b}”
while c<N
k = (N+b)/d
e = kc-a
f=kd-b
a,b,c,d=c,d,e,f
puts “#{a}/#{b}”
end

[1] Farey sequence - Wikipedia

2

On Sun, 18 Mar 2007, Phrogz wrote:

Here’s a cheap shot :stuck_out_tongue:

Here’s starting code, based on the algorithm included in the Wikipedia
article for the Farey Sequence:[1]

  • N = 7

  • N = 8

    a,b,c,d=0,1,1,N

  • puts “#{a}/#{b}”
    while c<N
  • puts “#{a}/#{b}”
    k = (N+b)/d
    e = kc-a
    f=k    d-b
    a,b,c,d=c,d,e,f
  • puts “#{a}/#{b}”
    end

[1] Farey sequence - Wikipedia

John C. Phone : (64)(3) 358 6639
Tait Electronics Fax : (64)(3) 359 4632
PO Box 1645 Christchurch Email : [email protected]
New Zealand

3

On Mar 19, 4:12 pm, John C. [email protected] wrote:

a,b,c,d=0,1,1,N

  • puts “#{a}/#{b}”
    while c<N
  • puts “#{a}/#{b}”
    k = (N+b)/d
    e = kc-a
    f=k    d-b
    a,b,c,d=c,d,e,f
  • puts “#{a}/#{b}”
    end

I don’t think there are any cheap shots in golf…except those that
change the output. You’ve left off the final “1/1” for the sequence
this way.

4

On Tue, 20 Mar 2007, Phrogz wrote:

You’ve left off the final “1/1” for the sequence
this way.
Drat! You’re right. I didn’t notice N went into the front of the
sequence.
Ah well, I’m obliged to hunt an expensive shot then.

Ooh. Wait, there is a very very cheap shot available…
a,b,c,d=0,1,1,7
puts “#{a}/#{b}”
while c<7
k = (N+b)/d
e = kc-a
f=kd-b
a,b,c,d=c,d,e,f
puts “#{a}/#{b}”
end

Now that’s really low!

Another less silly is…

a,b,c,d=0,1,1,7
puts “#{a}/#{b}”
while c<7
k = (N+b)/d
e = kc-a
a,b,c,d=c,d,e,kd-b
puts “#{a}/#{b}”
end

But not much better.

I suspect the next level up will be to trade storage space for lines
of code.

John C. Phone : (64)(3) 358 6639
Tait Electronics Fax : (64)(3) 359 4632
PO Box 1645 Christchurch Email : [email protected]
New Zealand

5

A little shorter:

N=7
a={}
0.upto(N) { |i|
1.upto(N) { |j|
a[(i+0.0)/j] ||= “#{i}/#{j}”
}}
a.sort.each{|k,v|puts v if k<=1}

-rr-

6

Phrogz wrote:

puts “#{a}/#{b}”
while c<N
k = (N+b)/d
e = kc-a
f=kd-b
a,b,c,d=c,d,e,f
puts “#{a}/#{b}”
end

[1] Farey sequence - Wikipedia

Longer, but builds numerator/denominator arrays based on direct
definition of Farey sequence.

n=[0,1]
d=[1,1]

(N-1).times {
i=0
while (i<d.length-1)
if d[i]+d[i+1]<=N
d[i,1]=[d[i],d[i]+d[i+1]]
n[i,1]=[n[i],n[i]+n[i+1]]
i+=2
else
i+=1
end
end
}

d.each_index{ |i| print(n[i],“/”, d[i],", ") }

7

On Tue, 20 Mar 2007, John C. wrote:

Now that’s really low!

Low as in the ethical sense, not the byte count.

Way lower in the ethical sense and pretty nifty in the byte count is…
puts "0/1
1/7
1/6
1/5
1/4
2/7
1/3
2/5
3/7
1/2
4/7
3/5
2/3
5/7
3/4
4/5
5/6
6/7
1/1
"

John C. Phone : (64)(3) 358 6639
Tait Electronics Fax : (64)(3) 359 4632
PO Box 1645 Christchurch Email : [email protected]
New Zealand

8

0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3,
5/7, 3/4, 4/5, 5/6, 6/7, 1/1

My challenge - come up with the least-bytes Ruby code that, given a
constant N set to the order, can print out the sequence (one value
per line).

Here’s a minor improvement on size (Still keeping N as parameter).

N=7
a,b,c,d=0,1,1,N
puts “#{a}/#{b}”
while c<N
a,b,c,d=c,d,(N+b)/d*c-a,N-(N+b)%d
puts “#{a}/#{b}”
end

Longer, but builds numerator/denominator arrays based on direct
definition of Farey sequence.

Still working on this approach too, but original post should have
included:

N=7