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

Functions:

• colorful?: This function takes an array of digits as input and returns true if the number represented by those digits is "colorful" (i.e., no two products of a subset of the digits are equal).
  • It iterates through all possible chunk sizes (1 to the length of the array) and checks if the product of each chunk is unique.
  • If any duplicate products are found, the function returns false; otherwise, it returns true.

Main Logic:

1. The program first generates a list of colorful numbers less than 100 by applying the colorful? function to each digit sequence of numbers in the range 0..100.
2. It then finds the largest colorful number by iterating down from 98765432 (a known colorful number) until it finds another colorful number.
3. The program then calculates the count of colorful numbers for each digit count (1 to 8) and prints the count for each digit count.
4. Finally, it prints the total count of colorful numbers for all digit counts combined.

Sample Input and Output:

The colorful numbers less than 100 are: 25 37 52 76 89 95, 

Largest colorful number: 9876543210

1 digit colorful numbers count: 10
2 digit colorful numbers count: 51
3 digit colorful numbers count: 158
4 digit colorful numbers count: 428
5 digit colorful numbers count: 1034
6 digit colorful numbers count: 2335
7 digit colorful numbers count: 4963
8 digit colorful numbers count: 9926

Total colorful numbers: 19524

def colorful?(ar)
  products = []
  (1..ar.size).all? do |chunk_size|
    ar.each_cons(chunk_size) do |chunk|
      product = chunk.inject(&:*)
      return false if products.include?(product)
      products << product
    end
  end
end

below100 = (0..100).select{|n| colorful?(n.digits)}
puts "The colorful numbers less than 100 are:", below100.join(" "), ""
puts "Largest colorful number: #{(98765432.downto(1).detect{|n| colorful?(n.digits) })}", ""

total = 0
(1..8).each do |numdigs|
   digits = (numdigs == 1 ? (0..9).to_a : (2..9).to_a)
   count  = digits.permutation(numdigs).count{|perm| colorful?(perm)}
   puts "#{numdigs} digit colorful numbers count: #{count}"
   total += count
end

puts "\nTotal colorful numbers: #{total}"