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

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <string>

using namespace std;

#define N 4
#define N2 16
#define LIMIT 45

int MDT[N2][N2];
const int dx[4]{-1, 0, 1, 0};
const int dy[4]{0, -1, 0, 1};
const char dir[4]{'u', 'l', 'd', 'r'};

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

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

int getAllMd(Puzzle p) {
  int sum = 0;
  for (int i = 0; i < N2; ++i) {
    if (p.f[i] == N2)
      continue;
    sum += MDT[i][p.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;
    //????????????????????£?????????
    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 iterate_deeping(Puzzle p) {

  p.MD = getAllMd(p);

  for (limit = p.MD; limit <= LIMIT; ++limit) {
    state = p;
    if (dfs(0, -100)) {
      string ans = "";
      for (int i = 0; i < limit; ++i) {
        ans += dir[path[i]];
      }
      return ans;
    }
  }
  return "";
}

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 p;
  for (int i = 0; i < N2; ++i) {
    scanf("%d", &p.f[i]);
    if (p.f[i] == 0) {
      p.f[i] = N2;
      p.space = i;
    }
  }
  string ans = iterate_deeping(p);
  cout << ans.size() << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <string>

using namespace std;

#define N 4
#define N2 16
#define LIMIT 1000

int MDT[N2][N2];
const int dx[4]{-1, 0, 1, 0};
const int dy[4]{0, -1, 0, 1};
const char dir[4]{'u', 'l', 'd', 'r'};

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

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

int getAllMd(Puzzle p) {
  int sum = 0;
  for (int i = 0; i < N2; ++i) {
    if (p.f[i] == N2)
      continue;
    sum += MDT[i][p.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;
    //????????????????????£?????????
    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 iterate_deeping(Puzzle p) {

  p.MD = getAllMd(p);

  for (limit = p.MD; limit <= LIMIT; ++limit) {
    state = p;

    if (dfs(0, -100)) {
      string ans = "";
      for (int i = 0; i < limit; ++i) {
        ans += dir[path[i]];
      }
      return ans;
    }
  }
  return "";
}

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 p;
  for (int i = 0; i < N2; ++i) {
    scanf("%d", &p.f[i]);
    if (p.f[i] == 0) {
      p.f[i] = N2;
      p.space = i;
    }
  }
  string ans = iterate_deeping(p);
  cout << ans.size() << endl;
  return 0;
}