### Numerical ID Encoding and Sorting

Source: https://github.com/sudhirj/shortuuid.rb/blob/master/README.md

Illustrates encoding numerical IDs (like timestamps) into shorter strings using the default alphabet. It also demonstrates that the default alphabet maintains lexicographical order for same-length encoded strings, and how to use `rjust` for proper comparison.

```ruby
require 'shortuuid'

t1 = Time.now.to_i
puts "Timestamp 1: #{t1}"
encoded_t1 = ShortUUID.encode(t1)
puts "Encoded Timestamp 1: #{encoded_t1}"

t2 = Time.now.to_i
puts "Timestamp 2: #{t2}"
encoded_t2 = ShortUUID.encode(t2)
puts "Encoded Timestamp 2: #{encoded_t2}"

puts "Timestamp 1 < Timestamp 2: #{t1 < t2}"
puts "Encoded Timestamp 1 < Encoded Timestamp 2: #{encoded_t1 < encoded_t2}"

a = 42
b = rand(9999999999999999)

puts "Number a: #{a}"
puts "Number b: #{b}"

puts "a < b: #{a < b}"
puts "Encoded a < Encoded b: #{ShortUUID.encode(a) < ShortUUID.encode(b)}"

puts "Encoded a (padded) < Encoded b (padded): #{ShortUUID.encode(a).rjust(10, '0') < ShortUUID.encode(b).rjust(10, '0')}"

puts "Encoded numbers: #{[a, b].map { |x| ShortUUID.encode(x) }}"
puts "Encoded numbers (padded): #{[a, b].map { |x| ShortUUID.encode(x).rjust(10, '0') }}"
```

--------------------------------

### UUID Shortening and Expansion

Source: https://github.com/sudhirj/shortuuid.rb/blob/master/README.md

Demonstrates how to shorten a standard UUID into a shorter string using the default base62 alphabet and then expand it back to the original UUID. It also shows how to use a custom alphabet for shortening and expansion.

```ruby
require 'securerandom'
require 'shortuuid'

id = SecureRandom.uuid
puts "Original UUID: #{id}"

short_id = ShortUUID.shorten id
puts "Shortened ID: #{short_id}"

expanded_id = ShortUUID.expand short_id
puts "Expanded ID: #{expanded_id}"

vowel_id = ShortUUID.shorten id, "AEIOU".chars
puts "Shortened ID with Vowel Alphabet: #{vowel_id}"

expanded_vowel_id = ShortUUID.expand vowel_id, "AEIOU".chars
puts "Expanded ID from Vowel Alphabet: #{expanded_vowel_id}"
```

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