Problem p02246 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;

const int N = 4;
const int LIMIT = 100;
int dx[4] = {0, 1, 0, -1}, dy[4] = {-1, 0, 1, 0};
int limit;
int puz[N * N];
int zero;
int esti;
int MDT[N * N][N * N];

int dfs(int dep, int pre) {
  if (esti == 0)
    return dep;
  if (dep >= limit)
    return LIMIT;

  int ret = LIMIT;
  for (int i = 0; i < 4; i++) {
    if ((i + 2) % 4 == pre)
      continue;
    int y = zero / N, x = zero % N;
    int ny = y + dy[i], nx = x + dx[i];
    if (ny < 0 || nx < 0 || ny >= N || nx >= N)
      continue;
    int tmp[N * N];
    int tmp_zero = zero;
    int tmp_esti = esti;
    for (int j = 0; j < N * N; j++)
      tmp[j] = puz[j];
    int ch_id = ny * N + nx;
    int ch_dat = puz[ch_id];
    esti -= MDT[zero][N * N - 1];
    esti -= MDT[ny * N + nx][ch_dat];
    esti += MDT[zero][ch_dat];
    esti += MDT[ny * N + nx][N * N - 1];
    swap(puz[zero], puz[ch_id]);
    zero = ch_id;
    ret = min(ret, dfs(dep + 1, i));
    for (int j = 0; j < N * N; j++)
      puz[j] = tmp[j];
    zero = tmp_zero;
    esti = tmp_esti;
  }

  return ret;
}

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

  for (int i = 0; i < N * N; i++) {
    cin >> puz[i];
    if (puz[i] == 0) {
      zero = i;
      puz[i] = N * N - 1;
    } else {
      puz[i]--;
    }
    esti += abs(i / N - puz[i] / N) + abs(i % N - puz[i] % N);
  }

  for (int i = esti; i <= LIMIT; i++) {
    limit = i;
    int ans = dfs(0, -1);
    if (ans < 100) {
      cout << ans << endl;
      break;
    }
  }

  return 0;
}


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

const int N = 4;
const int LIMIT = 100;
int dx[4] = {0, 1, 0, -1}, dy[4] = {-1, 0, 1, 0};
int limit;
int puz[N * N];
int zero;
int esti;
int MDT[N * N][N * N];

int dfs(int dep, int pre) {
  if (esti == 0)
    return dep;
  if (dep + esti >= limit)
    return LIMIT;

  int ret = LIMIT;
  for (int i = 0; i < 4; i++) {
    if ((i + 2) % 4 == pre)
      continue;
    int y = zero / N, x = zero % N;
    int ny = y + dy[i], nx = x + dx[i];
    if (ny < 0 || nx < 0 || ny >= N || nx >= N)
      continue;
    int tmp[N * N];
    int tmp_zero = zero;
    int tmp_esti = esti;
    for (int j = 0; j < N * N; j++)
      tmp[j] = puz[j];
    int ch_id = ny * N + nx;
    int ch_dat = puz[ch_id];
    esti -= MDT[zero][N * N - 1];
    esti -= MDT[ny * N + nx][ch_dat];
    esti += MDT[zero][ch_dat];
    esti += MDT[ny * N + nx][N * N - 1];
    swap(puz[zero], puz[ch_id]);
    zero = ch_id;
    ret = min(ret, dfs(dep + 1, i));
    for (int j = 0; j < N * N; j++)
      puz[j] = tmp[j];
    zero = tmp_zero;
    esti = tmp_esti;
  }

  return ret;
}

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

  for (int i = 0; i < N * N; i++) {
    cin >> puz[i];
    if (puz[i] == 0) {
      zero = i;
      puz[i] = N * N - 1;
    } else {
      puz[i]--;
    }
    esti += abs(i / N - puz[i] / N) + abs(i % N - puz[i] % N);
  }

  for (int i = esti; i <= LIMIT; i++) {
    limit = i;
    int ans = dfs(0, -1);
    if (ans < 100) {
      cout << ans << endl;
      break;
    }
  }

  return 0;
}