Problem p02246 (C++) — buggy submission, verdict: Memory Limit Exceeded

#include <bits/stdc++.h>
using namespace std;

static const int N = 4;
static const int N2 = 16;

static const int dx[] = {0, -1, 0, 1};
static const int dy[] = {1, 0, -1, 0};
int MDT[N2][N2];

struct Puzzle {
  int f[N2], space, MD;
  int cost;
  bool operator<(const Puzzle &p) const {
    for (int i = 0; i < N2; i++) {
      if (f[i] == p.f[i])
        continue;
      return f[i] < p.f[i];
    }
    return false;
  }
};

struct State {
  Puzzle puzzle;
  int estimated;
  bool operator<(const State &s) const { return estimated > s.estimated; }
};

int getAllMD(Puzzle pz) {
  int sum = 0;
  for (int i = 0; i < N2; i++) {
    if (pz.f[i] == N2)
      continue;
    sum += MDT[i][pz.f[i] - 1];
  }
  return sum;
}

inline void dump(Puzzle &u) {
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++)
      cout << u.f[i * N + j] << " ";
    cout << endl;
  }
}

int astar(Puzzle s) {
  priority_queue<State> PQ;
  s.MD = getAllMD(s);
  s.cost = 0;
  map<Puzzle, bool> V;
  Puzzle u, v;
  State initial;
  initial.puzzle = s;
  initial.estimated = getAllMD(s);
  PQ.push(initial);

  while (!PQ.empty()) {
    State st = PQ.top();
    PQ.pop();
    u = st.puzzle;
    if (u.MD == 0)
      return u.cost;
    V[u] = true;

    int sx = u.space / N;
    int sy = u.space % N;
    for (int r = 0; r < 4; r++) {
      int tx = sx + dx[r];
      int ty = sy + dy[r];
      if (tx < 0 or ty < 0 or tx >= N or ty >= N)
        continue;
      v = u;

      v.MD -= MDT[tx * N + ty][v.f[tx * N + ty] - 1];
      v.MD += MDT[sx * N + sy][v.f[tx * N + ty] - 1];

      swap(v.f[sx * N + sy], v.f[tx * N + ty]);
      v.space = tx * N + ty;
      if (!V[v]) {
        v.cost++;
        State news;
        news.puzzle = v;
        news.estimated = v.cost + v.MD;
        PQ.push(news);
      }
    }
  }
  return -1;
}

int main() {
  for (int i = 0; i < N2; i++)
    for (int j = 0; j < N2; j++)
      MDT[i][j] = abs(i / N - j / N) + abs(i % N - j % N);

  Puzzle in;

  for (int i = 0; i < N2; i++) {
    cin >> in.f[i];
    if (in.f[i] == 0) {
      in.f[i] = N2;
      in.space = i;
    }
  }
  cout << astar(in) << endl;
  return 0;
}

Error: MLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;

const short H = 4, W = 4;
set<vector<vector<short>>> memo;

struct STATE {
  short f;
  short g;
  vector<vector<short>> b;

  bool operator<(const STATE &tgt) const {
    return f > tgt.f; // ?¨????
  }
};
inline bool is_searched(const STATE &s) {
  return (memo.find(s.b) != memo.end());
}
inline void searched(const STATE &s) { memo.insert(s.b); }
inline bool is_goal(const STATE &s) {
  for (short i = 0; i < H; i++) {
    for (short j = 0; j < W; j++) {
      if (i == H - 1 and j == W - 1)
        return true;
      if (s.b[i][j] != (i * W) + j + 1)
        return false;
    }
  }
}

inline void where0(const STATE &s, short &h, short &w) {
  for (short i = 0; i < H; i++)
    for (short j = 0; j < W; j++)
      if (s.b[i][j] == 0) {
        h = i;
        w = j;
      }
}

inline short manhattan_dis(const short tgt, const short h, const short w) {
  if (tgt == 0)
    return 0;
  short tgt_h = (tgt - 1) / W;
  short tgt_w = (tgt - 1) % W;
  return abs(tgt_h - h) + abs(tgt_w - w);
}

inline short inversion_number(const vector<vector<short>> &b) {
  short x[16];
  for (short i = 0; i < H; i++)
    for (short j = 0; j < W; j++)
      x[W * i + j] = b[i][j];
  short ans = 0;
  for (int i = 0; i < 16; i++) {
    for (int j = i + 1; j < 16; j++) {
      if (x[i] != 0 and x[j] != 0 and x[i] > x[j])
        ans++;
    }
  }
  return ans / 3 + ans % 3;
}

inline short heuristic(const vector<vector<short>> &b) {
  short ans = 0;
  for (short i = 0; i < H; i++) {
    for (short j = 0; j < W; j++) {
      ans += manhattan_dis(b[i][j], i, j);
    }
  }
  ans = max(ans, inversion_number(b));
  return ans;
}

const short dx[] = {1, 0, -1, 0};
const short dy[] = {0, 1, 0, -1};
inline vector<STATE> adjcency(const STATE &cur) {
  short h, w;
  where0(cur, h, w);
  vector<STATE> ans;
  vector<vector<short>> b = cur.b;

  for (short i = 0; i < 4; i++) { // 4??????
    short nh = h + dy[i], nw = w + dx[i];
    if (nh >= 0 and nh < H and nw >= 0 and nw < W) {
      swap(b[nh][nw], b[h][w]);
      short heu = heuristic(b);
      if (cur.g + 1 + heu <= 45)
        ans.push_back(STATE{(short)(cur.g + 1 + heu), (short)(cur.g + 1), b});
      swap(b[nh][nw], b[h][w]);
    }
  }
  return ans;
}

STATE astar(const STATE &init) {

  priority_queue<STATE>
      pq;        // ?????????????°?????????????????????????????????????
  pq.push(init); // ????????? STATE ????????£??????

  while (pq.size()) { // ?????\\???????????????????????§????????§???
    STATE cur = pq.top();
    pq.pop(); // ?????£??¨????????????????????¶??????????????§???
    if (is_searched(cur))
      continue; // ??????????????¢?´¢????????§...
    if (is_goal(cur))
      return cur; // ??´??????????????´????????????

    searched(cur); // cur ?????¢?´¢???????????¨????????????????????????

    for (STATE &next :
         adjcency(cur)) { // ?????????????????¨?????????????????§???
      if (is_searched(next))
        continue;
      pq.push(next);
    }
  }
  // ???????????\\?????£??????????????¨??????...????????????????????£?????£????????¨???...
  return init;
}

int main() {

  //    cin >> H >> W;
  vector<vector<short>> b(H, vector<short>(W));
  for (short i = 0; i < H; i++)
    for (short j = 0; j < W; j++)
      cin >> b[i][j];

  short h = heuristic(b);
  STATE init{h, 0, b};

  STATE lst = astar(init);
  cout << lst.g << endl;

  //    cout << memo.size() << endl;
}