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# artkirienko's solution

## to Dominoes in the Ruby Track

Published at Jul 12 2020 · 0 comments
Instructions
Test suite
Solution

Make a chain of dominoes.

Compute a way to order a given set of dominoes in such a way that they form a correct domino chain (the dots on one half of a stone match the dots on the neighbouring half of an adjacent stone) and that dots on the halves of the stones which don't have a neighbour (the first and last stone) match each other.

For example given the stones `[2|1]`, `[2|3]` and `[1|3]` you should compute something like `[1|2] [2|3] [3|1]` or `[3|2] [2|1] [1|3]` or `[1|3] [3|2] [2|1]` etc, where the first and last numbers are the same.

For stones `[1|2]`, `[4|1]` and `[2|3]` the resulting chain is not valid: `[4|1] [1|2] [2|3]`'s first and last numbers are not the same. 4 != 3

Some test cases may use duplicate stones in a chain solution, assume that multiple Domino sets are being used.

For installation and learning resources, refer to the Ruby resources 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 dominoes_test.rb
``````

To include color from the command line:

``````ruby -r minitest/pride dominoes_test.rb
``````

## Submitting Incomplete Solutions

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

### dominoes_test.rb

``````require 'minitest/autorun'
require_relative 'dominoes'

# Common test data version: 2.1.0 b5bc74d
class DominoesTest < Minitest::Test
def test_empty_input_empty_output
# skip
dominoes = []
assert Dominoes.chain?(dominoes)
end

def test_singleton_input_singleton_output
skip
dominoes = [[1, 1]]
assert Dominoes.chain?(dominoes)
end

def test_singleton_that_can_not_be_chained
skip
dominoes = [[1, 2]]
refute Dominoes.chain?(dominoes)
end

def test_three_elements
skip
dominoes = [[1, 2], [3, 1], [2, 3]]
assert Dominoes.chain?(dominoes)
end

def test_can_reverse_dominoes
skip
dominoes = [[1, 2], [1, 3], [2, 3]]
assert Dominoes.chain?(dominoes)
end

def test_can_not_be_chained
skip
dominoes = [[1, 2], [4, 1], [2, 3]]
refute Dominoes.chain?(dominoes)
end

def test_disconnected_simple
skip
dominoes = [[1, 1], [2, 2]]
refute Dominoes.chain?(dominoes)
end

def test_disconnected_double_loop
skip
dominoes = [[1, 2], [2, 1], [3, 4], [4, 3]]
refute Dominoes.chain?(dominoes)
end

def test_disconnected_single_isolated
skip
dominoes = [[1, 2], [2, 3], [3, 1], [4, 4]]
refute Dominoes.chain?(dominoes)
end

def test_need_backtrack
skip
dominoes = [[1, 2], [2, 3], [3, 1], [2, 4], [2, 4]]
assert Dominoes.chain?(dominoes)
end

def test_separate_loops
skip
dominoes = [[1, 2], [2, 3], [3, 1], [1, 1], [2, 2], [3, 3]]
assert Dominoes.chain?(dominoes)
end

def test_nine_elements
skip
dominoes = [[1, 2], [5, 3], [3, 1], [1, 2], [2, 4], [1, 6], [2, 3], [3, 4], [5, 6]]
assert Dominoes.chain?(dominoes)
end
end``````
``````# frozen_string_literal: true

class Dominoes
class << self
# @param dominoes [Array<Array<Integer>>] set of dominoes
# @return [Boolean] if there is a way to order a given set of dominoes
#  in such a way that they form a correct domino chain (the dots on one
#  half of a stone match the dots on the neighbouring half of an adjacent
#  stone) and that dots on the halves of the stones which don't have
#  a neighbour (the first and last stone) match each other
def chain?(dominoes)
return true if dominoes.empty?

new(dominoes).chain?
end
end

# @param dominoes [Array<Array<Integer>>] set of dominoes
# @return [Dominoes]
def initialize(dominoes)
@dominoes = dominoes
end

# @return [Boolean] if there is a way to order a given set of dominoes in
#  such a way that they form a correct domino chain (the dots on one half of
#  a stone match the dots on the neighbouring half of an adjacent stone) and
#  that dots on the halves of the stones which don't have a neighbour
#  (the first and last stone) match each other
def chain?
backtrack([], nil, nil)
end

private

# @param res [Array<Integer>] indices of dominoies used in chain
# @param first [Integer] dots on the first stone in chain
# @param last [Integer] dots on the last stone in chain
# @return [Boolean] if the chain is found
def backtrack(res, first, last)
return true if dominoes.size == res.size && first == last

if res.empty?
dominoes.each.with_index.any? do |dominoe, i|
backtrack([i], dominoe.first, dominoe.last) ||
backtrack([i], dominoe.last, dominoe.first)
end
else
dominoes.each.with_index.any? do |dominoe, i|
unless res.include?(i)
last == dominoe.first && backtrack(res + [i], first, dominoe.last) ||
last == dominoe.last && backtrack(res + [i], first, dominoe.first)
end
end
end
end
end``````