Add dominoes exercise (#61)

Author: keiravillekode

config.json

@@ -433,6 +433,14 @@
         "prerequisites": [],
         "difficulty": 7
       },
+      {
+        "slug": "dominoes",
+        "name": "Dominoes",
+        "uuid": "4415c54b-162c-47df-a8c7-c47ff0effdb7",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 8
+      },
       {
         "slug": "zebra-puzzle",
         "name": "Zebra Puzzle",

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

@@ -0,0 +1,15 @@
+# Instructions
+
+Make a chain of dominoes.
+
+Compute a way to order a given set of domino stones so that they form a correct domino chain.
+In the chain, the dots on one half of a stone must match the dots on the neighboring half of an adjacent stone.
+Additionally, the dots on the halves of the stones without neighbors (the first and last stone) must 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/.docs/introduction.md

@@ -0,0 +1,13 @@
+# Introduction
+
+In Toyland, the trains are always busy delivering treasures across the city, from shiny marbles to rare building blocks.
+The tracks they run on are made of colorful domino-shaped pieces, each marked with two numbers.
+For the trains to move, the dominoes must form a perfect chain where the numbers match.
+
+Today, an urgent delivery of rare toys is on hold.
+You've been handed a set of track pieces to inspect.
+If they can form a continuous chain, the train will be on its way, bringing smiles across Toyland.
+If not, the set will be discarded, and another will be tried.
+
+The toys are counting on you to solve this puzzle.
+Will the dominoes connect the tracks and send the train rolling, or will the set be left behind?

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

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

exercises/practice/dominoes/.meta/example.fut

@@ -0,0 +1,26 @@
+
+def root (parents: []i64) (i: i64): i64 =
+  let i = loop i = i while parents[i] != i do
+    parents[i]
+  in
+    i
+
+def can_chain [n] (dominoes: [n][2]i32): bool =
+  let (tally, parents) = loop (tally, parents) = (replicate 7 0, iota 7) for stone in dominoes do
+    let left = i64.i32 stone[0]
+    let right = i64.i32 stone[1]
+    let tally = tally with [left] = tally[left] + 1
+    let tally = tally with [right] = tally[right] + 1
+    let left = root parents left
+    let right = root parents right
+    let parents = parents with [right] = left
+    in
+      (tally, parents)
+  in
+    let count = loop count = 0 for i < 7 do
+      if tally[i] % 2 != 0 then 7 else
+      if tally[i] == 0 then count else
+      if parents[i] != i then count else
+      count + 1
+    in
+      count < 2

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.fut

@@ -0,0 +1 @@
+def can_chain [n] (dominoes: [n][2]i32): bool = ???

exercises/practice/dominoes/test.fut

@@ -0,0 +1,69 @@
+import "dominoes"
+
+-- empty input = empty output
+-- ==
+-- input  { empty([0][2]i32) }
+-- output { true }
+
+-- singleton input = singleton output
+-- ==
+-- input  { [[1, 1]] }
+-- output { true }
+
+-- singleton that can't be chained
+-- ==
+-- input  { [[1, 2]] }
+-- output { false }
+
+-- three elements
+-- ==
+-- input  { [[1, 2], [3, 1], [2, 3]] }
+-- output { true }
+
+-- can reverse dominoes
+-- ==
+-- input  { [[1, 2], [1, 3], [2, 3]] }
+-- output { true }
+
+-- can't be chained
+-- ==
+-- input  { [[1, 2], [4, 1], [2, 3]] }
+-- output { false }
+
+-- disconnected - simple
+-- ==
+-- input  { [[1, 1], [2, 2]] }
+-- output { false }
+
+-- disconnected - double loop
+-- ==
+-- input  { [[1, 2], [2, 1], [3, 4], [4, 3]] }
+-- output { false }
+
+-- disconnected - single isolated
+-- ==
+-- input  { [[1, 2], [2, 3], [3, 1], [4, 4]] }
+-- output { false }
+
+-- need backtrack
+-- ==
+-- input  { [[1, 2], [2, 3], [3, 1], [2, 4], [2, 4]] }
+-- output { true }
+
+-- separate loops
+-- ==
+-- input  { [[1, 2], [2, 3], [3, 1], [1, 1], [2, 2], [3, 3]] }
+-- output { true }
+
+-- nine elements
+-- ==
+-- input  { [[1, 2], [5, 3], [3, 1], [1, 2], [2, 4], [1, 6], [2, 3], [3, 4], [5, 6]] }
+-- output { true }
+
+-- separate three-domino loops
+-- ==
+-- input  { [[1, 2], [2, 3], [3, 1], [4, 5], [5, 6], [6, 4]] }
+-- output { false }
+
+let main [n] (dominoes: [n][2]i32): bool =
+  can_chain dominoes