How to resolve the algorithm Farey sequence step by step in the Ring programming language

Published on 12 May 2024 09:40 PM
#Ring

How to resolve the algorithm Farey sequence step by step in the Ring programming language

Table of Contents

Problem Statement

The   Farey sequence   Fn   of order   n   is the sequence of completely reduced fractions between   0   and   1   which, when in lowest terms, have denominators less than or equal to   n,   arranged in order of increasing size. The   Farey sequence   is sometimes incorrectly called a   Farey series.

Each Farey sequence:

The Farey sequences of orders   1   to   5   are:

The length   (the number of fractions)   of a Farey sequence asymptotically approaches:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Farey sequence step by step in the Ring programming language

Source code in the ring programming language

# Project : Farey sequence

for i = 1 to 11
     count = 0 
     see "F" + string(i) + " = " 
     farey(i, false)
next
see nl
for x = 100 to 1000 step 100
      count = 0 
      see "F" + string(x) + " = "
      see farey(x, false)
      see nl
next

func farey(n, descending)
        a = 0
        b = 1
        c = 1
        d = n 
        if descending = true
           a = 1
           c = n -1
        ok 
        count = count + 1
        if n < 12
           see string(a) + "/" + string(b) + " " 
        ok
        while ((c <= n) and not descending) or ((a > 0) and descending)
                  aa = a
                  bb = b
                  cc = c
                  dd = d
                  k = floor((n + b) / d)
                  a = cc 
                  b = dd
                  c = k * cc - aa 
                  d = k * dd - bb
                  count = count + 1
                  if n < 12
                     see string(a) + "/" + string(b) + " "
                  ok
        end 
        if n < 12
           see nl
        ok
        return count

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