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

#include <cassert>
#include <cmath>
#include <iostream>
#include <stdio.h>
#include <string>
using namespace std;
#define N 4
#define N2 16
#define LIMIT 100

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

static const int dx[4] = {0, -1, 0, 1};
static const int dy[4] = {1, 0, -1, 0};
static const char dir[4] = {'r', 'u', 'l', 'd'};
int MDT[N2][N2];
Puzzle state;
int limit;
int path[LIMIT];

int get(Puzzle pz) {
  int sum = 0, i;
  for (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 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 iterdeep(Puzzle in) {
  in.MD = get(in);

  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 = iterdeep(in);
  cout << ans.size() << endl;

  return 0;
}

Error: MLE

Fixed submission:

#include <cmath>
#include <iostream>
#include <map>
#include <queue>
#include <string>
using namespace std;
#define N 4
#define N2 16

struct Puzzle {
  int f[N2];
  int space;
  string path;

  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;
  }
};

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

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

string bfs(Puzzle s) {
  queue<Puzzle> Q;
  map<Puzzle, bool> V;
  Puzzle u, v;
  s.path = "";
  Q.push(s);
  V[s] = true;

  while (!Q.empty()) {
    u = Q.front();
    Q.pop();
    if (isTarget(u))
      return u.path;
    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;
      swap(v.f[u.space], v.f[tx * N + ty]);
      v.space = tx * N + ty;
      if (!V[v]) {

        V[v] = true;
        v.path += dir[r];
        Q.push(v);
      }
    }
  }
  return "unsolvable";
}

int main() {
  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 = bfs(in);
  cout << ans.size() << endl;

  return 0;
}