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

#include <bits/stdc++.h>

using namespace std;

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

const int dx[4] = {0, -1, 0, 1};
const int dy[4] = {1, 0, -1, 0};
const 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];

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 dfs(int depth, int prev) {
  if (state.MD == 0) {
    return true;
  }
  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(prev, r) - min(prev, r) == 2) {
      continue;
    }
    tmp = state;
    // 计算曼哈顿距离的差值，同时交换拼图块
    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[tx * N + ty], state.f[sx * N + sy]);
    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++) {
      // 曼哈顿距离，此法太妙
      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);
  //    for(int i=0;i<limit;i++){
  //        cout<<path[i]<<" ";
  //    }
  cout << ans.size() << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

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

const int dx[4] = {0, -1, 0, 1};
const int dy[4] = {1, 0, -1, 0};
const 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];

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 dfs(int depth, int prev) {
  if (state.MD == 0) {
    return true;
  }
  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(prev,r)-min(prev,r)==2){
    //            continue;
    //        }
    tmp = state;
    // 计算曼哈顿距离的差值，同时交换拼图块
    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[tx * N + ty], state.f[sx * N + sy]);
    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++) {
      // 曼哈顿距离，此法太妙
      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);
  //    for(int i=0;i<limit;i++){
  //        cout<<path[i]<<" ";
  //    }
  cout << ans.size() << endl;
  return 0;
}