feat: n-puzzle

config.yml

@@ -446,6 +446,9 @@ notebook:
     - smawk: SMAWK 算法
       code_ext: hpp
       test_ext: cpp
+    - astar: A* 算法
+      code_ext: hpp
+      test_ext: cpp
     graph:
     - alist: 邻接表
       code_ext: hpp
@@ -1225,6 +1228,9 @@ notebook:
     - texas_holdem: 德州扑克
       code_ext: hpp
       test_ext: cpp
+    - npuzzle_data: N puzzle 数据类
+      code_ext: hpp
+      test_ext: cpp
     fast:
     - rsort32: 32 位整数基数排序
       code_ext: hpp

src/code/game/npuzzle_data.hpp

@@ -0,0 +1,82 @@
+#ifndef TIFALIBS_GAME_NPUZZLE_DATA
+#define TIFALIBS_GAME_NPUZZLE_DATA
+
+#include "../util/abs_constexpr.hpp"
+#include "../util/util.hpp"
+
+namespace tifa_libs::game {
+
+// clang-format off
+enum Dir4 { U, D, L, R };
+// clang-format on
+
+// n = k*k-1
+class NPuzzleData {
+  u32 k, pos0;
+  vec<u32> node_;
+  vec<Dir4> moves_;
+  u32 cost_;
+
+ public:
+  constexpr explicit NPuzzleData(u32 k) : k(k) {}
+
+  constexpr auto const &cost() const { return cost_; }
+  constexpr auto &node() { return node_; }
+  constexpr auto const &node() const { return node_; }
+  constexpr auto const &moves() const { return moves_; }
+
+  constexpr bool solved() {
+    for (u32 i = 0; i < node_.size(); ++i)
+      if (node_[i] != i) return 0;
+    return 1;
+  }
+  constexpr vec<NPuzzleData> next() {
+    auto moves = gen_move();
+    vec<NPuzzleData> ans(moves.size(), *this);
+    for (u32 i = 0; i < moves.size(); ++i) ans[i].move(moves[i]);
+    return ans;
+  }
+  constexpr void move(Dir4 dir) {
+    moves_.push_back(dir);
+    u32 _ = pos0;
+    switch (dir) {
+      case U: pos0 -= k; break;
+      case D: pos0 += k; break;
+      case L: --pos0; break;
+      case R: ++pos0; break;
+    }
+    std::swap(node_[_], node_[pos0]);
+    cost_ = gen_cost();
+  }
+
+  constexpr auto operator<=>(NPuzzleData const &node) const { return node_ <=> node.node_; }
+
+  friend std::istream &operator>>(std::istream &is, NPuzzleData &np) {
+    np.node_.resize(np.k * np.k);
+    for (auto &i : np.node_) is >> i;
+    np.pos0 = u32(std::find(np.node_.begin(), np.node_.end(), 0) - np.node_.begin());
+    np.cost_ = np.gen_cost();
+    return is;
+  }
+
+ private:
+  constexpr vec<Dir4> gen_move() const {
+    vec<Dir4> ans;
+    if (pos0 / k) ans.push_back(U);
+    if (pos0 / k != k - 1) ans.push_back(D);
+    if (pos0 % k) ans.push_back(L);
+    if (pos0 % k != k - 1) ans.push_back(R);
+    return ans;
+  }
+  constexpr u32 gen_cost() const {
+    u32 h1 = 0, h2 = 0;
+    for (u32 i = 0; i < k; ++i)
+      for (u32 j = 0; j < k; ++j)
+        if (u32 _ = node_[k * i + j]; _ != k * i + j && _) ++h1, h2 += u32(abs((i32)i - i32(_ / k)) + abs((i32)j - i32(_ % k)));
+    return std::max(h1, h2) + (u32)moves_.size();
+  }
+};
+
+}  // namespace tifa_libs::game
+
+#endif

src/code/opt/astar.hpp

@@ -0,0 +1,40 @@
+#ifndef TIFALIBS_OPT_ASTAR
+#define TIFALIBS_OPT_ASTAR
+
+#include "../util/traits.hpp"
+
+namespace tifa_libs::opt {
+
+template <class T>
+requires requires(T x, T y) {
+  { x.solved() } -> std::same_as<bool>;
+  { x.next() } -> iterable_c;
+  x.cost() < y.cost();
+  x < y;
+}
+std::optional<T> astar(T const &s) {
+  struct C {
+    constexpr bool operator()(T const &a, T const &b) const { return b.cost() < a.cost(); }
+  };
+  pq<T, C> pq;
+  std::set<T> vis;
+
+  pq.push(s);
+  vis.insert(s);
+  while (!pq.empty()) {
+    T now = pq.top();
+    pq.pop();
+    if (now.solved()) return now;
+    auto nxt = now.next();
+    for (auto i : nxt)
+      if (!vis.count(i)) {
+        pq.push(i);
+        vis.insert(i);
+      }
+  }
+  return std::nullopt;
+}
+
+}  // namespace tifa_libs::opt
+
+#endif

src/code/util/util.hpp

@@ -39,11 +39,14 @@ using vecp = vec<std::pair<U, T>>;
 template <class U, class T>
 using vvecp = vvec<std::pair<U, T>>;
 
-template <class T>
-using pq = std::priority_queue<T>;
+template <class T, class C = std::less<T>>
+using pq = std::priority_queue<T, vec<T>, C>;
 template <class T>
 using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
 
+using strn = std::string;
+using strnv = std::string_view;
+
 #ifdef ONLINE_JUDGE
 #undef assert
 #define assert(x) 42

src/doc_tex/game/npuzzle_data.tex

@@ -0,0 +1,7 @@
+用于求解 \(N\)-puzzle \(N=k^2-1,~k\in\mathbf{N}_{>2}\) 的数据类.
+
+\(N\)-puzzle 是一个滑块游戏. 滑块方盘的长宽均为 \(k\times k\) 个方块, 其中 \(N\) 个位置放序号打乱的方块, 剩下一个为空位. 与空位同行或同列的方块可以通过水平或垂直滑动来移动. 拼图的目标是按编号顺序排列方块
+
+求解时需使用 \fullref{sec:a*-算法}
+
+\inputminted{cpp}{src/src/npuzzle_data_usage.txt}

src/doc_tex/opt/astar.tex

@@ -0,0 +1,9 @@
+\paragraph{要求}
+
+数据类 \verb|T| 需可比较且需具有如下成员函数:
+
+\verb|bool solved()|: 返回当前状态是否满足终止条件
+
+\verb|U next()|: 返回当前状态的所有后继, 返回类型 \verb|U| 需可迭代
+
+\verb|W cost()|: 返回当前状态的估价, 返回类型 \verb|W| 需可比较

src/src/npuzzle_data_usage.txt

@@ -0,0 +1,9 @@
+int k = 4; // 15-puzzle
+
+NPuzzleData start(k);
+// 读入局面
+std::cin >> start;
+// 输出当前局面
+std::cout << start.node();
+// 输出操作步骤
+std::cout << astar(start)->moves();

src/test_cpverifier/aizu/alds1_13_c.test.cpp

@@ -0,0 +1,16 @@
+#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/1/ALDS1/all/ALDS1_13_C"
+
+#include "../../code/game/npuzzle_data.hpp"
+#include "../../code/opt/astar.hpp"
+
+int main() {
+  std::ios::sync_with_stdio(false);
+  std::cin.tie(nullptr);
+  tifa_libs::game::NPuzzleData start(4);
+  std::cin >> start;
+  for (auto& i : start.node())
+    if (i) --i;
+    else i = 15;
+  std::cout << tifa_libs::opt::astar(start)->moves().size() << '\n';
+  return 0;
+}

src/test_cpverifier/hackerrank/n-puzzle.test.cpp

@@ -0,0 +1,22 @@
+#define PROBLEM "https://www.hackerrank.com/challenges/n-puzzle/problem"
+
+#include "../../code/game/npuzzle_data.hpp"
+#include "../../code/opt/astar.hpp"
+
+int main() {
+  std::ios::sync_with_stdio(false);
+  std::cin.tie(nullptr);
+  u32 n;
+  std::cin >> n;
+  tifa_libs::game::NPuzzleData start(n);
+  std::cin >> start;
+  auto v = tifa_libs::opt::astar(start)->moves();
+  std::cout << v.size() << '\n';
+  for (auto i : v) switch (i) {
+      case tifa_libs::game::U: std::cout << "UP\n"; break;
+      case tifa_libs::game::D: std::cout << "DOWN\n"; break;
+      case tifa_libs::game::L: std::cout << "LEFT\n"; break;
+      case tifa_libs::game::R: std::cout << "RIGHT\n"; break;
+    }
+  return 0;
+}