Add dominoes exercise (#64)

* Add dominoes exercise

* Simplify 'new'

* Refactor

config.json

@@ -258,6 +258,14 @@
         ],
         "prerequisites": [],
         "difficulty": 3
+      },
+      {
+        "slug": "dominoes",
+        "name": "Dominoes",
+        "uuid": "4bf12182-491e-4da7-a51a-3d96a2649d8a",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 10
       }
     ],
     "foregone": [

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/config.json

@@ -0,0 +1,18 @@
+{
+  "authors": [
+    "misicnenad"
+  ],
+  "files": {
+    "solution": [
+      "src/lib.cairo",
+      "Scarb.toml"
+    ],
+    "test": [
+      "src/tests.cairo"
+    ],
+    "example": [
+      ".meta/example.cairo"
+    ]
+  },
+  "blurb": "Make a chain of dominoes."
+}

exercises/practice/dominoes/.meta/example.cairo

@@ -0,0 +1,145 @@
+use core::dict::Felt252DictTrait;
+
+type Domino = (u8, u8);
+
+/// A table keeping track of available dominoes.
+///
+/// Effectively a 6x6 matrix represented as a dynamic array. Each position denotes whether a domino
+/// is available with that column dots and row dots. Positions are mirrored ((3,4) == (4,3)), except
+/// for positions with equal row and column numbers.
+#[derive(Destruct)]
+struct AvailabilityTable {
+    d: Felt252Dict<u8>,
+    len: usize
+}
+
+fn index(x: u8, y: u8) -> u8 {
+    (x - 1) * 6 + (y - 1)
+}
+
+#[generate_trait]
+impl AvailabilityTableImpl of AvailabilityTableTrait {
+    fn new() -> AvailabilityTable {
+        AvailabilityTable { d: Default::default(), len: 36 }
+    }
+
+    fn get(ref self: AvailabilityTable, x: u8, y: u8) -> u8 {
+        let i = index(x, y);
+        assert!(i.into() < self.len, "Index out of bounds");
+        self.d.get(i.into())
+    }
+
+    fn set(ref self: AvailabilityTable, x: u8, y: u8, c: u8) {
+        self.d.insert(index(x, y).into(), c);
+    }
+
+    fn add(ref self: AvailabilityTable, x: u8, y: u8) {
+        let c = self.get(x, y);
+        self.set(x, y, c + 1);
+        if x != y { // Not the diagonal
+            let c = self.get(y, x);
+            self.set(y, x, c + 1);
+        }
+    }
+
+    fn remove(ref self: AvailabilityTable, x: u8, y: u8) {
+        // For this toy code hard explicit fail is best
+        assert!(self.get(x, y) > 0, "no stones to remove: ({:?}, {:?})", x, y);
+
+        let c = self.get(x, y);
+        self.set(x, y, c - 1);
+        if x != y { // Not the diagonal
+            let c = self.get(y, x);
+            self.set(y, x, c - 1);
+        }
+    }
+
+    fn pop_first(ref self: AvailabilityTable, x: u8) -> Option<u8> {
+        // the "double" has precedence, otherwise an invalid chain might occur
+        if self.get(x, x) > 0 {
+            self.remove(x, x);
+            return Option::Some(x);
+        }
+
+        let mut y = 1;
+        loop {
+            if y == 7 {
+                break Option::None;
+            }
+            if self.get(x, y) > 0 {
+                self.remove(x, y);
+                break Option::Some(y);
+            }
+            y += 1;
+        }
+    }
+}
+
+fn chain(dominoes: @Array<Domino>) -> Option<Array<Domino>> {
+    match dominoes.len() {
+        0 => Option::Some(array![]),
+        1 => {
+            let domino: Domino = *dominoes[0];
+            let (x, y) = domino;
+            if x == y {
+                Option::Some(array![domino])
+            } else {
+                Option::None
+            }
+        },
+        _ => {
+            // First check if the total number of each amount of dots is even, if not it's not
+            // possible to complete a cycle. This follows from that it's an Eulerian path.
+            let mut d: Felt252Dict<u8> = Default::default();
+            let mut i = 0;
+            while i < dominoes
+                .len() {
+                    let (x, y): Domino = *dominoes[i];
+                    d.insert(x.into(), d.get(x.into()) + 1);
+                    d.insert(y.into(), d.get(y.into()) + 1);
+                    i += 1;
+                };
+            let mut i = 0;
+            let even_dot_types = loop {
+                if i == 6 {
+                    break true;
+                }
+                if d.get(i.into()) % 2 != 0 {
+                    break false;
+                }
+                i += 1;
+            };
+            if !even_dot_types {
+                return Option::None;
+            }
+            let chain = chain_worker(dominoes);
+            if chain.len() == dominoes.len() {
+                Option::Some(chain)
+            } else {
+                Option::None
+            }
+        }
+    }
+}
+
+fn chain_worker(dominoes: @Array<Domino>) -> Array<Domino> {
+    let mut t = AvailabilityTableTrait::new();
+    let mut i = dominoes.len() - 1;
+    let first = *dominoes[i];
+    while i != 0 {
+        i -= 1;
+        let (x, y): Domino = *dominoes[i];
+        t.add(x, y);
+    };
+    let mut chain: Array<Domino> = array![];
+    chain.append(first);
+    let (_, mut x) = first;
+    while let Option::Some(y) = t.pop_first(x) {
+        chain.append((x, y));
+        x = y;
+    };
+    chain
+}
+
+#[cfg(test)]
+mod tests;

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/Scarb.toml

@@ -0,0 +1,9 @@
+[package]
+name = "dominoes"
+version = "0.1.0"
+edition = "2023_11"
+
+# See more keys and their definitions at https://docs.swmansion.com/scarb/docs/reference/manifest.html
+
+[dependencies]
+alexandria_sorting = { git = "https://github.com/keep-starknet-strange/alexandria.git" }

exercises/practice/dominoes/src/lib.cairo

@@ -0,0 +1,5 @@
+fn chain(dominoes: @Array<(u8, u8)>) -> Option<Array<(u8, u8)>> {
+    panic!(
+        "From the given dominoes '{dominoes:?}' construct a proper dominoes chain or return None if it is not possible."
+    )
+}