Step by Step solution about How to resolve the algorithm Continued fraction/Arithmetic/G(matrix ng, continued fraction n) step by step in the Ruby programming language

The provided Ruby code defines a baby NG (number generator) algorithm and uses it to generate rational numbers from a given string representation. Here's a breakdown:

Class Definition (NG):

• It defines a class NG that implements the baby NG algorithm.
• The constructor initialize takes four arguments: a1, a, b1, and b. These are initial values for the algorithm.

Instance Methods of NG:

• ingress(n): Updates the internal state of the NG algorithm by performing the ingress operation. It takes an input number n.
• needterm?: Checks if the NG algorithm needs to terminate (i.e., if the fraction has terminated).
• egress: Performs the egress operation and calculates the next rational number.
• egress_done: Calls egress and sets a and b to a1 and b1 if termination is required.
• done?: Checks if the NG algorithm is finished (i.e., if both a and b are zero).

Usage of the NG Algorithm:

• The code includes a list of string representations of rational numbers (data) and their corresponding initial values for the NG algorithm (ng).
• It iterates through the data list and for each entry:
  • Creates an NG object using the provided initial values.
  • Calls r2cf(*r) to generate a series of numbers from the string representation of the rational number.
  • For each number n, it calls egress on the NG object and prints the result.
  • Calls egress_done to handle any necessary termination steps.

Utility function r2cf(x, y):

• This function generates a series of numbers from a string representation of a rational number.
• It takes two numbers, x and y, and yields each number in the sequence.

Example:

For the string "[3;7] + 1/2", the code will generate the following sequence of rational numbers:

2 5/7 22/7

Overall:

The code uses the NG class to generate rational numbers from string representations. It iterates through a list of test cases, demonstrates the ingress/egress operations, and handles termination gracefully. This code can be useful for generating continued fraction representations of rational numbers and solving simple fraction arithmetic problems.

# I define a class to implement baby NG
class NG
  def initialize(a1, a, b1, b)
    @a1, @a, @b1, @b = a1, a, b1, b
  end
  def ingress(n)
    @a, @a1 = @a1, @a + @a1 * n
    @b, @b1 = @b1, @b + @b1 * n
  end
  def needterm?
    return true if @b == 0 or @b1 == 0
    return true unless @a/@b == @a1/@b1
    false
  end
  def egress
    n = @a / @b
    @a,  @b  = @b,  @a  - @b  * n
    @a1, @b1 = @b1, @a1 - @b1 * n
    n
  end
  def egress_done
    @a, @b = @a1, @b1 if needterm?
    egress
  end
  def done?
    @b == 0 and @b1 == 0
  end
end


data = [["[1;5,2] + 1/2",      [2,1,0,2], [13,11]],
        ["[3;7] + 1/2",        [2,1,0,2], [22, 7]],
        ["[3;7] divided by 4", [1,0,0,4], [22, 7]]]

data.each do |str, ng, r|
  printf "%-20s->", str
  op = NG.new(*ng)
  r2cf(*r) do |n|
    print " #{op.egress}" unless op.needterm?
    op.ingress(n)
  end
  print " #{op.egress_done}" until op.done?
  puts
end