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

// 15 Puzzle
#include <iostream>
#include <map>
#include <queue>
#include <string>

using namespace std;

static const int N = 4;
static const int N2 = 16;
static const int LIMIT = 100;
static const char dir[4] = {'u', 'l', 'd', 'r'};
static const int dx[4] = {0, -1, 0, 1};
static const int dy[4] = {1, 0, -1, 0};

int MDT[N2][N2];
int path[LIMIT];

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

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(Puzzle p, int limit, int depth, int prev) {
  if (p.MD == 0)
    return true;
  if (depth + p.MD > limit)
    return false;

  int sx = p.space % N;
  int sy = p.space / N;
  Puzzle q;

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

string iterative_deepening(Puzzle in) {
  in.MD = getAllMD(in);
  for (int limit = in.MD; limit <= LIMIT; limit++) {
    if (dfs(in, limit, 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;
    }
  }

  cout << iterative_deepening(in).size() << endl;
}


Error: TLE

Fixed submission:

// 15 Puzzle
#include <iostream>
#include <map>
#include <queue>
#include <string>

using namespace std;

static const int N = 4;
static const int N2 = 16;
static const int LIMIT = 100;
static const char dir[4] = {'u', 'l', 'd', 'r'};
static const int dx[4] = {0, -1, 0, 1};
static const int dy[4] = {1, 0, -1, 0};

int MDT[N2][N2];
int path[LIMIT];

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

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 isTarget(Puzzle p) {
  for (int i = 0; i < N2; i++) {
    if (p.f[i] != (i + 1))
      return false;
  }
  return true;
}

bool dfs(Puzzle p, int limit, int depth, int prev) {
  if (p.MD == 0)
    return true;
  if (depth + p.MD > limit)
    return false;

  int sx = p.space % N;
  int sy = p.space / N;
  Puzzle q;

  for (int r = 0; r < 4; r++) {
    if (max(prev, r) - min(prev, r) == 2)
      continue;
    int tx = sx + dx[r];
    int ty = sy + dy[r];
    if (tx < 0 || ty < 0 || tx >= N || ty >= N)
      continue;
    q = p;
    q.space = tx + N * ty;
    swap(q.f[q.space], q.f[p.space]);
    q.MD -= MDT[q.space][p.f[q.space] - 1];
    q.MD += MDT[p.space][p.f[q.space] - 1];
    if (dfs(q, limit, depth + 1, dir[r])) {
      path[depth] = r;
      return true;
    }
  }
  return false;
}

string iterative_deepening(Puzzle in) {
  in.MD = getAllMD(in);
  for (int limit = in.MD; limit <= LIMIT; limit++) {
    if (dfs(in, limit, 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;
    }
  }

  cout << iterative_deepening(in).size() << endl;
}