# miscellaneous stuff

require "big"

module Euler
  alias NumType = Int32 | Int64 | UInt32 | UInt64 | BigInt

  def self.trial_division(n : NumType)
    factors = [] of NumType
    check = ->(p: NumType) {
      q, r = n.divmod(p)
      while r.zero?
        factors << p
        n = q
        q, r = n.divmod(p)
      end
    }

    check.call(2)
    check.call(3)
    p = 5
    while p * p <= n
      check.call(p)
      p += 2
      check.call(p)
      p += 4
    end
    factors << n if n > 1
    factors
  end

  def self.prime_factorization(n : NumType)
    result = {} of NumType => NumType
    factors = self.trial_division(n)

    factors.each do |f|
      result[f] = 0
      num = n
      while num % f == 0
        result[f] += 1
        num /= f
      end
    end

    result
  end

  def self.palindrome?(x)
    x.to_s.reverse == x.to_s
  end

  def self.to_digit_list(n : NumType)
    n.to_s.chars.map { |d| d.to_i }
  end

  def self.to_big_ints(num_list : Array(NumType))
    num_list.map { |n| BigInt.new(n) }
  end
end