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angelikatyborska's solution

to Alphametics in the Ruby Track

Published at Jul 13 2018 · 1 comment
Instructions
Test suite
Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Write a function to solve alphametics puzzles.

Alphametics is a puzzle where letters in words are replaced with numbers.

For example SEND + MORE = MONEY:

  S E N D
  M O R E +
-----------
M O N E Y

Replacing these with valid numbers gives:

  9 5 6 7
  1 0 8 5 +
-----------
1 0 6 5 2

This is correct because every letter is replaced by a different number and the words, translated into numbers, then make a valid sum.

Each letter must represent a different digit, and the leading digit of a multi-digit number must not be zero.

Write a function to solve alphametics puzzles.


For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby alphametics_test.rb

To include color from the command line:

ruby -r minitest/pride alphametics_test.rb

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

alphametics_test.rb

require 'minitest/autorun'
require_relative 'alphametics'

# Common test data version: 1.0.0 b9bada8
class AlphameticsTest < Minitest::Test

  def test_puzzle_with_three_letters
    # skip
    input = 'I + BB == ILL'
    expected = { 'B' => 9, 'I' => 1, 'L' => 0 }
    assert_equal expected, Alphametics.solve(input)
  end

  def test_solution_must_have_unique_value_for_each_letter
    skip
    input = 'A == B'
    expected = {}
    assert_equal expected, Alphametics.solve(input)
  end

  def test_leading_zero_solution_is_invalid
    skip
    input = 'ACA + DD == BD'
    expected = {}
    assert_equal expected, Alphametics.solve(input)
  end

  def test_puzzle_with_four_letters
    skip
    input = 'AS + A == MOM'
    expected = { 'A' => 9, 'M' => 1, 'O' => 0, 'S' => 2 }
    assert_equal expected, Alphametics.solve(input)
  end

  def test_puzzle_with_six_letters
    skip
    input = 'NO + NO + TOO == LATE'
    expected = { 'A' => 0, 'E' => 2, 'L' => 1, 'N' => 7,
                 'O' => 4, 'T' => 9 }
    assert_equal expected, Alphametics.solve(input)
  end

  def test_puzzle_with_seven_letters
    skip
    input = 'HE + SEES + THE == LIGHT'
    expected = { 'E' => 4, 'G' => 2, 'H' => 5, 'I' => 0,
                 'L' => 1, 'S' => 9, 'T' => 7 }
    assert_equal expected, Alphametics.solve(input)
  end

  # The obvious algorithm can take a long time to solve this puzzle,
  # but an optimised solution can solve it fairly quickly.
  # (It's OK to submit your solution without getting this test to pass.)
  def test_puzzle_with_eight_letters
    skip
    input = 'SEND + MORE == MONEY'
    expected = { 'D' => 7, 'E' => 5, 'M' => 1, 'N' => 6,
                 'O' => 0, 'R' => 8, 'S' => 9, 'Y' => 2 }
    assert_equal expected, Alphametics.solve(input)
  end

  # The obvious algorithm can take a long time to solve this puzzle,
  # but an optimised solution can solve it fairly quickly.
  # (It's OK to submit your solution without getting this test to pass.)
  def test_puzzle_with_ten_letters
    skip
    input = 'AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE'
    expected = { 'A' => 5, 'D' => 3, 'E' => 4, 'F' => 7,
                 'G' => 8, 'N' => 0, 'O' => 2, 'R' => 1,
                 'S' => 6, 'T' => 9 }
    assert_equal expected, Alphametics.solve(input)
  end

  # Problems in exercism evolve over time, as we find better ways to ask
  # questions.
  # The version number refers to the version of the problem you solved,
  # not your solution.
  #
  # Define a constant named VERSION inside of the top level BookKeeping
  # module, which may be placed near the end of your file.
  #
  # In your file, it will look like this:
  #
  # module BookKeeping
  #   VERSION = 1 # Where the version number matches the one in the test.
  # end
  #
  # If you are curious, read more about constants on RubyDoc:
  # http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html

  def test_bookkeeping
    skip
    assert_equal 4, BookKeeping::VERSION
  end
end
module BookKeeping
  VERSION = 4
end

class Alphametics
  class << self
    def solve(expression)
      letters, constitutents, sum = parse(expression)
      permutations = (0..9).to_a.permutation(letters.length)

      # a solution is a zip of letters and a permutation
      # letters = [97, 99, 103]
      # permutation = [4, 6, 9]
      # solution = {97 => 4, 99 => 6, 103 => 9}

      correct_permutation = permutations.find do |permutation|
        check_permutation(constitutents, sum, letters, permutation)
      end

      format_solution(letters, correct_permutation) || {}
    end

    private

    def parse(expression)
      constitutents, sum = expression.split(/\s?==\s?/)
      sum = sum.codepoints
      constitutents = constitutents.split(/\s?\+\s?/).map(&:codepoints)
      letters = [sum, constitutents].flatten.uniq.sort
      [letters, constitutents, sum]
    end

    def check_permutation(constitutents, sum, letters, permutation)
      first = ->(string) { string[0] }
      first_letters = [
        *constitutents.map(&first),
        first.call(sum)
      ]

      (0...sum.length).all? do |i|
        if first_letters.all? { |letter| letter_to_digit(letters, permutation, letter) != 0 }
          sum_of_constitutents = sum_column(constitutents, letters, permutation, i)
          sum_of_constitutents % 10 == letter_to_digit(letters, permutation, sum[-1 - i])
        else
          false
        end
      end
    end

    def sum_column(constitutents, letters, permutation, index)
      numbers = constitutents.map do |c|
        if index < c.length
          letter_to_digit(letters, permutation, c[-1 - index])
        else
          0
        end
      end

      carry_over = index == 0 ? 0 : sum_column(constitutents, letters, permutation, index - 1) / 10
      carry_over + numbers.reduce(&:+)
    end

    def format_solution(letters, permutation)
      return unless permutation
      solution = letters.zip(permutation.slice(0, letters.length))
      solution&.map {|k_and_v| [k_and_v[0].chr, k_and_v[1]]}.to_h
    end

    def letter_to_digit(letters, permutation, letter)
      permutation[letters.index(letter)]
    end
  end
end

Community comments

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Avatar of angelikatyborska

This only fixes the comment, no actual code change from iteration 4 to iteration 5 happened.

What can you learn from this solution?

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

  • What compromises have been made?
  • Are there new concepts here that you could read more about to improve your understanding?