Problem p02246 (C++) — buggy submission, verdict: Runtime Error

#include <cassert>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <string>
using namespace std;
const int dx[4] = {0, -1, 0, 1};
const int dy[4] = {1, 0, -1, 0};
const char dir[4] = {'r', 'u', 'l', 'd'};
const int N = 4;
const int N2 = 16;
const int LIMIT = 45;
int MDT[N2][N2];
struct Puzzle {
  int f[N2], space;
  int 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)
      ;
    else
      sum += MDT[i][pz.f[i] - 1];
  }

  return sum;
}
int check(int x, int y) {
  if (x < 0 || y < 0 || x >= N || y >= N)
    return 0;
  return 1;
}
int dfs(int depth, int prev) {
  if (state.MD == 0)
    return 1;
  if (depth + state.MD > limit)
    return 0;

  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 (!check(tx, ty))
      continue;
    if (max(prev, r) - min(prev, r) == 2)
      continue;

    tmp = state;

    int nt, ns;
    nt = tx * N + ty;
    ns = sx * N + sy;
    state.MD -= MDT[nt][state.f[nt] - 1];
    state.MD += MDT[ns][state.f[nt] - 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 1;
    }
    state = tmp;
  }
  return 0;
}
string iterative_deepening(Puzzle in) {
  in.MD = getALLMD(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;
    }
  }
}
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 = iterative_deepening(in);

  cout << ans.size() << endl;
  return 0;
}

Error: 0

Fixed submission:

#include <cassert>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <string>
using namespace std;
const int N = 4;
const int N2 = 16;
const int LIMIT = 40;
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;
  int 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 isSolved() {
  for (int i = 0; i < N2; i++)
    if (state.f[i] != i + 1)
      return false;
}
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 iterative_deepening(Puzzle in) {
  in.MD = getALLMD(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;
    }
  }
}
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 = iterative_deepening(in);

  cout << ans.size() << endl;
  return 0;
}