Step by Step solution about How to resolve the algorithm Lychrel numbers step by step in the Ruby programming language

The provided Ruby code explores the concept of Lychrel numbers and their related numbers. Here's a detailed explanation:

1. add_reverse(num, max_iter):

   • Adds the reverse of a given integer num to itself and repeats this process until a palindrome is reached or a maximum number of iterations (max_iter) is exceeded.
   • The function returns a set containing all the intermediate numbers generated during this process.

2. palindrome?(num):

   • Checks if a given integer num is a palindrome, meaning it reads the same forwards and backward.

3. reverse_int(num):

   • Reverses the digits of a given integer num and returns the reversed integer.

4. split_roots_from_relateds(roots_and_relateds):

   • Takes a list of sets of integers and splits them into two groups:
     • Roots: A unique subset of numbers that are not part of any other set.
     • Related: The remaining numbers that are related to one or more roots.

5. find_lychrel(maxn, max_reversions):

   • Computes Lychrel numbers and their related numbers for integers in the range 1 to maxn.
   • For each number, it limits the reverse-digits-and-adds process to a maximum of max_reversions*2 iterations.
   • Returns two lists:
     • A list of roots that do not become palindromes within the iteration limit.
     • A list of numbers related to the roots.

6. Lychrel Calculations:

   • The code sets maxn to 10,000 and reversion_limit to 500.
   • It calculates Lychrel numbers and their related numbers for each integer in the range 1 to 10,000, limiting the number of reversals to 2 * 500 = 1000.

7. Output:

   • Prints out the number of Lychrel numbers found, along with a list of these numbers.
   • Prints out the number of Lychrel related numbers, along with a list of these numbers.
   • Identifies and prints out Lychrel palindromes (Lychrel numbers that are also palindromes) and their count.

Overall, this code is designed to explore and identify Lychrel numbers and related concepts, providing a detailed analysis of their properties and characteristics.

require 'set'

def add_reverse(num, max_iter=1000)
  (1..max_iter).each_with_object(Set.new([num])) do |_,nums|
    num += reverse_int(num)
    nums << num
    return nums if palindrome?(num)
  end
end

def palindrome?(num)
  num == reverse_int(num)
end

def reverse_int(num)
  num.to_s.reverse.to_i
end

def split_roots_from_relateds(roots_and_relateds)
  roots = roots_and_relateds.dup
  i = 1
  while i < roots.length
    this = roots[i]
    if roots[0...i].any?{|prev| this.intersect?(prev)}
      roots.delete_at(i)
    else
      i += 1
    end
  end
  root = roots.map{|each_set| each_set.min}
  related = roots_and_relateds.map{|each_set| each_set.min}
  related = related.reject{|n| root.include?(n)}
  return root, related
end

def find_lychrel(maxn, max_reversions)
  series = (1..maxn).map{|n| add_reverse(n, max_reversions*2)}
  roots_and_relateds = series.select{|s| s.length > max_reversions}
  split_roots_from_relateds(roots_and_relateds)
end

maxn, reversion_limit = 10000, 500
puts "Calculations using n = 1..#{maxn} and limiting each search to 2*#{reversion_limit} reverse-digits-and-adds"
lychrel, l_related = find_lychrel(maxn, reversion_limit)
puts "  Number of Lychrel numbers: #{lychrel.length}"
puts "    Lychrel numbers: #{lychrel}"
puts "  Number of Lychrel related: #{l_related.length}"
pals = (lychrel + l_related).select{|x| palindrome?(x)}.sort
puts "  Number of Lychrel palindromes: #{pals.length}"
puts "    Lychrel palindromes: #{pals}"