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

#include <bits/stdc++.h>

using namespace std;

#define N 4
#define N2 16
#define LIMIT 100

int dx[4] = {0, -1, 0, 1};
int dy[4] = {1, 0, -1, 0}; // 注意这块有的数据可能因为走的方向不同而导致TLE
char dir[4] = {'r', 'u', 'l', 'd'};
int MDT[N2][N2];

struct Puzzle {
  int f[N2], space, MD;
};

Puzzle state;
int limit;
int path[LIMIT];

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;
}

bool isSolved() {
  for (int i = 0; i < N2; i++) {
    if (state.f[i] != i + 1)
      return false;
  }
  return true;
}

bool dfs(int depth, int pre) {
  if (state.MD == 0)
    return 1;
  if (depth + state.MD > limit)
    return false;
  int sx = state.space / N;
  int sy = state.space % N;
  Puzzle tmp;
  for (int r = 0; r < 4; r++) {
    int tx = sx + dx[r];
    int ty = sy + dy[r];
    if (tx < 0 || ty < 0 || tx >= N || ty >= N)
      continue;
    if (max(pre, r) - min(pre, r) == 2)
      continue; // 去重
    tmp = state;
    state.MD -= MDT[tx * N + ty][state.f[tx * N + ty] - 1];
    state.MD += MDT[sx * N + sy][state.f[tx * N + ty] - 1];
    swap(state.f[sx * N + sy], state.f[tx * N + ty]);
    state.space = tx * N + ty;
    if (dfs(depth + 1, r)) {
      path[depth] = r;
      return true;
    }
    state = tmp;
  }
  return false;
}

string iterative_deepening(Puzzle in) {
  in.MD = getallMD(in); // 初始状态的曼哈顿距离
  for (limit = in.MD; limit <= LIMIT; limit++) {
    state = in;
    if (dfs(0, -100)) {
      string ans = "";
      for (int i = 0; i < limit; i++) {
        ans += dir[path[i]];
      }
      return ans;
    }
  }
  return "unsolvable";
}

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;
    }
  }
  string ans = iterative_deepening(in);
  cout << ans.size() << endl;
  return 0;
}


Error: MLE

Fixed submission:


#include <bits/stdc++.h>

using namespace std;

#define N 4
#define N2 16

int dx[4] = {0, -1, 0, 1};
int dy[4] = {-1, 0, 1, 0};
char dir[4] = {'r', 'u', 'l', 'd'};
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;
}

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 || ty < 0 || tx >= N || 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;
}