Add dominoes exercise (#101)

Author: keiravillekode

config.json

@@ -595,6 +595,14 @@
         "prerequisites": [],
         "difficulty": 8
       },
+      {
+        "slug": "dominoes",
+        "name": "Dominoes",
+        "uuid": "5a28cae2-cd44-4c8c-ac6e-b0ac38e9c2d2",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 8
+      },
       {
         "slug": "grep",
         "name": "Grep",

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/Example.lean

@@ -0,0 +1,36 @@
+namespace Dominoes
+
+def Half := { x : Nat // x ≥ 1 ∧ x ≤ 6 }
+
+def Stone := Half × Half
+
+def findRoot (parents : Array Nat) (entry : Nat) : Nat := Id.run do
+  let mut current := entry
+  while current != parents[current]! do
+    current := parents[current]!
+  return current
+
+def canChain (dominoes : List Stone) : Bool := Id.run do
+  let mut tally := Array.replicate 7 (0 : Nat)
+  for stone in dominoes do
+    let first := stone.1.val
+    let firstCount := tally[first]! + 1
+    tally := tally.set! first firstCount
+    let second := stone.2.val
+    let secondCount := tally[second]! + 1
+    tally := tally.set! second secondCount
+  for entry in tally do
+    if (entry &&& 1) != 0 then return false
+
+  let mut parents : Array Nat := List.range 7 |> List.toArray
+  for stone in dominoes do
+    let firstRoot := findRoot parents stone.1.val
+    let secondRoot := findRoot parents stone.2.val
+    parents := parents.set! secondRoot firstRoot
+
+  let mut count := 0
+  for i in [0:7] do
+    if (tally[i]! > 0) && (i == parents[i]!) then count := count + 1
+  return count ≤ 1
+
+end Dominoes

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

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "keiravillekode"
+  ],
+  "files": {
+    "solution": [
+      "Dominoes.lean"
+    ],
+    "test": [
+      "DominoesTest.lean"
+    ],
+    "example": [
+      ".meta/Example.lean"
+    ]
+  },
+  "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.lean

@@ -0,0 +1,10 @@
+namespace Dominoes
+
+def Half := { x : Nat // x ≥ 1 ∧ x ≤ 6 }
+
+def Stone := Half × Half
+
+def canChain (dominoes : List Stone) : Bool :=
+  sorry
+
+end Dominoes

exercises/practice/dominoes/DominoesTest.lean

@@ -0,0 +1,95 @@
+import LeanTest
+import Dominoes
+
+open LeanTest
+
+def dominoesTests : TestSuite :=
+  (TestSuite.empty "Dominoes")
+  |>.addTest "empty input = empty output" (do
+      return assertTrue (Dominoes.canChain []))
+  |>.addTest "singleton input = singleton output" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨1, by decide⟩)
+      ]))
+  |>.addTest "singleton that can't be chained" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩)
+      ]))
+  |>.addTest "three elements" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩)
+      ]))
+  |>.addTest "can reverse dominoes" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨1, by decide⟩, ⟨3, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩)
+      ]))
+  |>.addTest "can't be chained" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨4, by decide⟩, ⟨1, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩)
+      ]))
+  |>.addTest "disconnected - simple" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨1, by decide⟩),
+        (⟨2, by decide⟩, ⟨2, by decide⟩)
+      ]))
+  |>.addTest "disconnected - double loop" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨1, by decide⟩),
+        (⟨3, by decide⟩, ⟨4, by decide⟩),
+        (⟨4, by decide⟩, ⟨3, by decide⟩)
+      ]))
+  |>.addTest "disconnected - single isolated" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨4, by decide⟩, ⟨4, by decide⟩)
+      ]))
+  |>.addTest "need backtrack" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨2, by decide⟩, ⟨4, by decide⟩),
+        (⟨2, by decide⟩, ⟨4, by decide⟩)
+      ]))
+  |>.addTest "separate loops" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨1, by decide⟩, ⟨1, by decide⟩),
+        (⟨2, by decide⟩, ⟨2, by decide⟩),
+        (⟨3, by decide⟩, ⟨3, by decide⟩)
+      ]))
+  |>.addTest "nine elements" (do
+      return assertTrue (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨5, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨4, by decide⟩),
+        (⟨1, by decide⟩, ⟨6, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨4, by decide⟩),
+        (⟨5, by decide⟩, ⟨6, by decide⟩)
+      ]))
+  |>.addTest "separate three-domino loops" (do
+      return assertFalse (Dominoes.canChain [
+        (⟨1, by decide⟩, ⟨2, by decide⟩),
+        (⟨2, by decide⟩, ⟨3, by decide⟩),
+        (⟨3, by decide⟩, ⟨1, by decide⟩),
+        (⟨4, by decide⟩, ⟨5, by decide⟩),
+        (⟨5, by decide⟩, ⟨6, by decide⟩),
+        (⟨6, by decide⟩, ⟨4, by decide⟩)
+      ]))
+
+def main : IO UInt32 := do
+  runTestSuitesWithExitCode [dominoesTests]

exercises/practice/dominoes/lakefile.toml

@@ -0,0 +1,15 @@
+name = "dominoes"
+version = "0.1.0"
+defaultTargets = ["DominoesTest"]
+testDriver = "DominoesTest"
+
+[[lean_lib]]
+name = "LeanTest"
+srcDir = "vendor/LeanTest"
+
+[[lean_lib]]
+name = "Dominoes"
+
+[[lean_exe]]
+name = "DominoesTest"
+root = "DominoesTest"

exercises/practice/dominoes/lean-toolchain

@@ -0,0 +1 @@
+leanprover/lean4:v4.25.2