[New Exercise]: Dominoes (#275)

I leave the difficulty at 5 atm

config.json

@@ -737,6 +737,14 @@
         "prerequisites": [],
         "difficulty": 5
       },
+      {
+        "slug": "dominoes",
+        "name": "Dominoes",
+        "uuid": "c3ba77dc-ca14-4d76-b449-f9cabad16d00",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 5
+      },
       {
         "slug": "binary-search-tree",
         "name": "Binary Search Tree",

exercises/practice/dominoes/.docs/instructions.md

@@ -0,0 +1,13 @@
+# Instructions
+
+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 neighboring half of an adjacent stone) and that dots on the halves of the stones which don't have a neighbor (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.

exercises/practice/dominoes/.meta/Dominoes.example.ps1

@@ -0,0 +1,60 @@
+Function Test-DominoesChain() {
+    <#
+    .SYNOPSIS
+    Implement a function to test if a dominoes chain can be made.
+
+    .DESCRIPTION
+    Given a list of dominoes, check to see if they can form a chain.
+    A correct chain mean the dots on one half of a stone match the dots on the neighboring half of an adjacent stone,
+    and that dots on the halves of the stones which don't have a neighbor (the first and last stone) match each other.
+
+    .PARAMETER Dominoes
+    A list of 2-elements arrays, each array represent a domino.
+
+    .EXAMPLE
+    Test-DominoesChain -Dominoes @( @(1, 5), @(5, 6), @(6, 1))
+    Return: true
+    #>
+    [CmdletBinding()]
+    Param(
+        [Collections.Generic.List[int[]]]$Dominoes
+    )
+    if ($Dominoes.Count -eq 0) {
+        return $true
+    }
+
+    $len = $Dominoes.Count
+    [Collections.Generic.List[Int[]]]$chain = $Dominoes[0]
+    $Dominoes.RemoveAt(0)
+
+    Backtrack $Dominoes $chain $len
+}
+
+
+Function Backtrack($dominoes, $chain, $len) {
+    <#
+    .DESCRIPTION
+    Helper function to backtrack solutions
+    #>
+    if ($chain.Count -eq $len) {
+        return $chain[0][0] -eq $chain[-1][1]
+    }
+
+    $tail = $chain[-1][1]
+
+    for ($i = 0; $i -lt $dominoes.Count; $i++) {
+        $left_pip, $right_pip = $dominoes[$i]
+        if ($tail -in $dominoes[$i]) {
+            $domino = $right_pip -eq $tail ? @($right_pip, $left_pip) : $dominoes[$i]
+            $chain.Add($domino)
+            $dominoes.RemoveAt($i)
+            if (Backtrack $dominoes $chain $len) {
+                return $true
+            }else {
+                $chain.RemoveAt($chain.Count -1)
+                $dominoes.Insert($i, $domino)
+            }
+        }
+    }
+    return $false
+}

exercises/practice/dominoes/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "glaxxie"
+  ],
+  "files": {
+    "solution": [
+      "Dominoes.ps1"
+    ],
+    "test": [
+      "Dominoes.tests.ps1"
+    ],
+    "example": [
+      ".meta/Dominoes.example.ps1"
+    ]
+  },
+  "blurb": "Make a chain of dominoes."
+}

exercises/practice/dominoes/.meta/tests.toml

@@ -0,0 +1,49 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[31a673f2-5e54-49fe-bd79-1c1dae476c9c]
+description = "empty input = empty output"
+
+[4f99b933-367b-404b-8c6d-36d5923ee476]
+description = "singleton input = singleton output"
+
+[91122d10-5ec7-47cb-b759-033756375869]
+description = "singleton that can't be chained"
+
+[be8bc26b-fd3d-440b-8e9f-d698a0623be3]
+description = "three elements"
+
+[99e615c6-c059-401c-9e87-ad7af11fea5c]
+description = "can reverse dominoes"
+
+[51f0c291-5d43-40c5-b316-0429069528c9]
+description = "can't be chained"
+
+[9a75e078-a025-4c23-8c3a-238553657f39]
+description = "disconnected - simple"
+
+[0da0c7fe-d492-445d-b9ef-1f111f07a301]
+description = "disconnected - double loop"
+
+[b6087ff0-f555-4ea0-a71c-f9d707c5994a]
+description = "disconnected - single isolated"
+
+[2174fbdc-8b48-4bac-9914-8090d06ef978]
+description = "need backtrack"
+
+[167bb480-dfd1-4318-a20d-4f90adb4a09f]
+description = "separate loops"
+
+[cd061538-6046-45a7-ace9-6708fe8f6504]
+description = "nine elements"
+
+[44704c7c-3adb-4d98-bd30-f45527cf8b49]
+description = "separate three-domino loops"

exercises/practice/dominoes/Dominoes.ps1

@@ -0,0 +1,22 @@
+Function Test-DominoesChain() {
+    <#
+    .SYNOPSIS
+    Implement a function to test if a dominoes chain can be made.
+
+    .DESCRIPTION
+    Given a list of dominoes, check to see if they can form a chain.
+    A correct chain mean the dots on one half of a stone match the dots on the neighboring half of an adjacent stone,
+    and that dots on the halves of the stones which don't have a neighbor (the first and last stone) match each other.
+
+    .PARAMETER Dominoes
+    A list of 2-elements arrays, each array represent a domino.
+
+    .EXAMPLE
+    Test-DominoesChain -Dominoes @( @(1, 5), @(5, 6), @(6, 1))
+    Return: true
+    #>
+    [CmdletBinding()]
+    Param(
+        [Collections.Generic.List[int[]]]$Dominoes
+    )
+}

exercises/practice/dominoes/Dominoes.tests.ps1

@@ -0,0 +1,83 @@
+BeforeAll {
+    . "./Dominoes.ps1"
+}
+
+Describe "Dominoes test cases" {
+    It "empty input = empty output" {
+        $got = Test-DominoesChain -Dominoes @( )
+
+        $got | Should -BeTrue
+    }
+
+    It "singleton input = singleton output" {
+        $got = Test-DominoesChain -Dominoes @( ,@(1, 1) )
+
+        $got | Should -BeTrue
+    }
+
+    It "singleton that can't be chained" {
+        $got = Test-DominoesChain -Dominoes @( ,@(1, 2) )
+
+        $got | Should -BeFalse
+    }
+
+    It "three elements" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(3, 1), @(2, 3) )
+
+        $got | Should -BeTrue
+    }
+
+    It "can reverse dominoes" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(1, 3), @(2, 3) )
+
+        $got | Should -BeTrue
+    }
+
+    It "can't be chained" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(4, 1), @(2, 3) )
+
+        $got | Should -BeFalse
+    }
+
+    It "disconnected - simple" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 1), @(2, 2) )
+
+        $got | Should -BeFalse
+    }
+
+    It "disconnected - double loop" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(2, 1), @(3, 4), @(4, 3) )
+
+        $got | Should -BeFalse
+    }
+
+    It "disconnected - single isolated" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(2, 3), @(3, 1), @(4, 4) )
+
+        $got | Should -BeFalse
+    }
+
+    It "need backtrack" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(2, 3), @(3, 1), @(2, 4), @(2, 4) )
+
+        $got | Should -BeTrue
+    }
+
+    It "separate loops" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(2, 3), @(3, 1), @(1, 1), @(2, 2), @(3, 3) )
+
+        $got | Should -BeTrue
+    }
+
+    It "nine elements" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(5, 3), @(3, 1), @(1, 2), @(2, 4), @(1, 6), @(2,3), @(3, 4), @(5, 6) )
+
+        $got | Should -BeTrue
+    }
+
+    It "separate three-domino loops" {
+        $got = Test-DominoesChain -Dominoes @( @(1, 2), @(2, 3), @(3, 1), @(4, 5), @(5, 6), @(6, 4) )
+
+        $got | Should -BeFalse
+    }
+}