algo(geometry): add polyominoes

README.md

@@ -26,6 +26,7 @@ In this repository, you'll find algorithms and data structure implementations fo
 - Geometry
   - [convex hull](/algorithms/geometry/convex-hull.cpp)
   - [point to segment](/algorithms/geometry/point-to-segment.cpp)
+  - [polyominoes](/algorithms/geometry/polyominoes.cpp)
 
 - Graphs
   - [articulation points](/algorithms/graphs/articulation-points.cpp)

algorithms/geometry/polyominoes.cpp

@@ -0,0 +1,85 @@
+// We consider the rotations
+// as distinct (0, 10, 10+9, 10+9+8...)
+vi pos = {0, 10, 19, 27, 34, 40, 45, 49, 52, 54, 55};
+
+const int MAXP = 10;
+
+struct Poly {
+  ii v[MAXP];
+  int64_t id;
+  int n;
+
+  Poly() {
+    n = 1;
+    v[0] = {0, 0};
+    normalize();
+  }
+
+  Poly(vii &vp) {
+    n = vp.size();
+    for (int i = 0; i < n; i++) v[i] = vp[i];
+    normalize();
+  }
+
+  ii &operator[](int i) { return v[i]; }
+
+  bool add(int a, int b) {
+    for (int i = 0; i < n; i++) {
+      auto [f, s] = v[i];
+      if (f == a and s == b) return false;
+    }
+
+    v[n++] = ii{a, b};
+    normalize();
+    return true;
+  }
+
+  void normalize() {
+    int mx = 100, my = 100;
+    for (int i = 0; i < n; i++) {
+      auto [f, s] = v[i];
+      mx = min(mx, f), my = min(my, s);
+    }
+
+    id = 0;
+    for (int i = 0; i < n; i++) {
+      auto &[f, s] = v[i];
+      f -= mx, s -= my;
+      id |= (1LL << (pos[f] + s));
+    }
+  }
+
+  bool operator<(Poly oth) { return id < oth.id; }
+};
+
+vector<Poly> poly[MAXP + 1];
+
+void buildPoly(int mxN) {
+  for (int i = 0; i <= mxN; i++) poly[i].clear();
+
+  Poly init;
+  queue<Poly> q;
+  unordered_set<int64_t> used;
+  q.push(init);
+  used.insert(init.id);
+  while (not q.empty()) {
+    Poly u = q.front();
+    q.pop();
+    poly[u.n].emplace_back(u);
+
+    if (u.n == mxN) continue;
+
+    for (int i = 0; i < u.n; i++) {
+      for (auto [dx, dy] : dir4) {
+        Poly to = u;
+        auto [f, s] = to[i];
+        bool ok = to.add(f + dx, s + dy);
+
+        if (ok and not used.count(to.id)) {
+          q.push(to);
+          used.insert(to.id);
+        }
+      }
+    }
+  }
+}

algorithms/geometry/polyominoes.tex

@@ -0,0 +1,5 @@
+\subsection{Polynominoes}
+
+Geometric figure made by equal squares, connected between themselves in a way that at least one side of each square coincide with a side of another square.
+
+Watch out: the number of polynominoes increases fastly (size 12 has 63.600 figures)