Taxicab numbers

# title: Taxicab numbers
# source: https://rosettacode.org/wiki/Taxicab_numbers
# category: Rosetta Code
# difficulty: Medium
# summary: Search a small cube-sum table for numbers that can be written as two sums of two cubes.
# tags: popular, math, search, cubes
# vibe: 0.4

def sum_key(left, right)
  "#{left ** 3 + right ** 3}"
end

def taxicab_numbers(limit)
  groups = {}
  order = []
  left = 1

  while left <= limit
    right = left
    while right <= limit
      key = sum_key(left, right)
      if groups[key] == nil
        groups[key] = []
        order << key
      end
      groups[key] << [left, right]
      right = right + 1
    end
    left = left + 1
  end

  rows = []
  order.each do |key|
    if groups[key].length > 1
      rows << { value: key, decompositions: groups[key] }
    end
  end

  rows
end

def run
  taxicab_numbers(12).first(2)
end