 # vgrigoriu's solution

## to Dominoes in the C# Track

Published at Sep 29 2019 · 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.

## Running the tests

To run the tests, run the command `dotnet test` from within the exercise directory.

Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time. Once you get the first test passing, remove the `Skip` property from the next test and work on getting that test passing. Once none of the tests are skipped and they are all passing, you can submit your solution using `exercism submit Dominoes.cs`

## Further information

For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.

### DominoesTest.cs

``````// This file was auto-generated based on version 2.1.0 of the canonical data.

using System;
using Xunit;

public class DominoesTest
{
[Fact]
public void Empty_input_empty_output()
{
var dominoes = Array.Empty<(int, int)>();
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Singleton_input_singleton_output()
{
var dominoes = new[] { (1, 1) };
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Singleton_that_cant_be_chained()
{
var dominoes = new[] { (1, 2) };
Assert.False(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Three_elements()
{
var dominoes = new[] { (1, 2), (3, 1), (2, 3) };
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Can_reverse_dominoes()
{
var dominoes = new[] { (1, 2), (1, 3), (2, 3) };
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Cant_be_chained()
{
var dominoes = new[] { (1, 2), (4, 1), (2, 3) };
Assert.False(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Disconnected_simple()
{
var dominoes = new[] { (1, 1), (2, 2) };
Assert.False(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Disconnected_double_loop()
{
var dominoes = new[] { (1, 2), (2, 1), (3, 4), (4, 3) };
Assert.False(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Disconnected_single_isolated()
{
var dominoes = new[] { (1, 2), (2, 3), (3, 1), (4, 4) };
Assert.False(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Need_backtrack()
{
var dominoes = new[] { (1, 2), (2, 3), (3, 1), (2, 4), (2, 4) };
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Separate_loops()
{
var dominoes = new[] { (1, 2), (2, 3), (3, 1), (1, 1), (2, 2), (3, 3) };
Assert.True(Dominoes.CanChain(dominoes));
}

[Fact(Skip = "Remove to run test")]
public void Nine_elements()
{
var dominoes = new[] { (1, 2), (5, 3), (3, 1), (1, 2), (2, 4), (1, 6), (2, 3), (3, 4), (5, 6) };
Assert.True(Dominoes.CanChain(dominoes));
}
}``````
``````﻿using System;
using System.Collections.Generic;
using System.Linq;

public static class Dominoes
{
public static bool CanChain(IEnumerable<(int, int)> dominoes)
{
if (dominoes.Count() == 0)
{
Console.WriteLine("No dominoes");
return true;
}

var firstDomino = dominoes.First();
var (found, chain) = FindChainStartingWith(firstDomino, dominoes.Skip(1));

return found && IsValidChain(chain);
}

private static (bool, IEnumerable<(int, int)>) FindChainStartingWith((int, int) start, IEnumerable<(int,int)> candidates)
{
if (candidates.Count() == 0)
{
return (true, new List<(int,int)> {start});
}

var candidatesArray = candidates.ToArray();
for (var i = 0; i < candidatesArray.Length; i++)
{
var domino = candidatesArray[i];
var remainingCandidates = GetRemainingCandidates(candidatesArray, domino);
bool found = false;
IEnumerable<(int, int)> chain = Enumerable.Empty<(int, int)>();
if (domino.Item1 == start.Item2)
{
(found, chain) = FindChainStartingWith(domino, remainingCandidates);
}
else if (domino.Item2 == start.Item2)
{
(found, chain) = FindChainStartingWith((domino.Item2, domino.Item1), remainingCandidates);
}

if (found)
{
return (true, new List<(int,int)> {start}.Concat(chain));
}
}

return (false, null);
}

private static IEnumerable<(int,int)> GetRemainingCandidates((int, int)[] dominoes, (int, int) except)
{
var eliminated = false;
foreach (var domino in dominoes)
{
if (domino.Item1 == except.Item1 && domino.Item2 == except.Item2 && !eliminated)
{
eliminated = true;
continue;
}

yield return domino;
}
}

private static bool IsValidChain(IEnumerable<(int, int)> dominoes)
{
var dominoesArray = dominoes.ToArray();
for (int i = 0; i < dominoesArray.Length; i++)
{
var currDomino = dominoesArray[i];
var nextDomino = dominoesArray[(i+1) % dominoesArray.Length];
if (currDomino.Item2 != nextDomino.Item1)
{
return false;
}
}

return true;
}
}``````