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

The provided Ruby code defines two methods, negative_base_encode and negative_base_decode, for converting integers between base 10 and negative bases (between -2 and -62). A brief explanation of the code below:

1. Constants and Variables:

   • DIGITS: A string containing the digits used for negative bases, including decimal digits, uppercase and lowercase English letters.
   • revdigs: An array used to store digits while encoding numbers in negative bases.

2. negative_base_encode Method:

   • This method takes two parameters: n (the integer to encode) and b (the negative base to encode to).
   • It checks if the base b is within the allowed range (-2 to -62) and returns '0' if n is 0.
   • It converts n to the specified negative base by repeatedly dividing it by b and collecting the remainders in revdigs.
   • It calculates the final encoded number by concatenating the digits in revdigs in reverse order.

3. negative_base_decode Method:

   • This method takes two parameters: n (the encoded number in negative base) and b (the negative base to decode from).
   • It checks if the base b is within the allowed range (-2 to -62).
   • It decodes the number by iterating over the digits in n, converting each digit back to its decimal value, and summing them with appropriate negative base powers.

4. Demonstration:

   • The code demonstrates the encoding and decoding process for various integers and negative bases, printing the results as a table showing the original integer, encoded value, and decoded value.

DIGITS = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'

# convert a base 10 integer into a negative base value (as a string)

def negative_base_encode(n, b)
  raise 'base out of range' if (b < -62) || (b > -2)
  return '0' if n == 0
  revdigs = []
  while n != 0 do
    n, r = n.divmod(b)
    if r < 0
      n += 1
      r -= b
    end
    revdigs << r
  end
  return revdigs.reduce('') { |digstr, digit| DIGITS[digit] + digstr }
end

# convert a negative base value (as a string) into a base 10 integer

def negative_base_decode(n, b)
  raise 'base out of range' if (b < -62) || (b > -2)
  value = 0
  n.reverse.each_char.with_index do |ch, inx|
    value += DIGITS.index(ch) * b**inx
  end
  return value
end

# do the task

[ [10, -2], [146, -3], [15, -10], [0, -31], [-6221826, -62] ].each do |pair|
  decimal, base = pair
  encoded = negative_base_encode(decimal, base)
  decoded = negative_base_decode(encoded, base)
  puts("Enc: %8i base %-3i = %5s base %-3i  Dec: %5s base %-3i = %8i base %-3i" %
       [decimal, 10, encoded, base, encoded, base, decoded, 10])
end