Problem p01881 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

#define INF 1001000100010001000
#define MOD 1000000007
#define EPS 1e-10
#define int long long
#define rep(i, N) for (int i = 0; i < N; i++)
#define Rep(i, N) for (int i = 1; i < N; i++)
#define For(i, a, b) for (int i = (a); i < (b); i++)
#define pb push_back
#define mp make_pair
#define i_i pair<int, int>
#define vi vector<int>
#define vvi vector<vi>
#define vb vector<bool>
#define vvb vector<vb>
#define vp vector<i_i>
#define all(a) (a).begin(), (a).end()
#define Int(x)                                                                 \\
  int x;                                                                       \\
  scanf("%lld", &x);

int dxy[5] = {0, 1, 0, -1, 0};
// assign

vector<string> board;
vvb used;
int x, y;

bool solve(int a, int b);

signed main() {
  cin >> x >> y;
  board.assign(x, "");

  rep(i, x) { cin >> board[i]; }

  bool ret;
  rep(i, x) {
    rep(j, y) {
      if (board[i][j] == '%') {
        ret = solve(i, j);
      }
    }
  }

  cout << ((ret) ? "Yes" : "No") << endl;

  return 0;
}

bool solve(int a, int b) {
  queue<i_i> q;
  q.push(i_i(a, b));
  used.assign(x, vb(y, false));
  used[a][b] = true;
  bool ret = true, stop = false;

  while (!q.empty()) {
    queue<i_i> nxt;
    while (!q.empty()) {
      int c = q.front().first, d = q.front().second;
      q.pop();
      rep(i, 4) {
        int nx = c + dxy[i], ny = d + dxy[i + 1];
        if (nx < 0 || ny < 0 || x <= nx || y <= ny || used[nx][ny]) {
          continue;
        }
        if (board[nx][ny] == '.') {
          nxt.push(i_i(nx, ny));
        } else if (board[nx][ny] == '$') {
          ret = false;
          stop = true;
        } else if (board[nx][ny] == '@') {
          stop = true;
        }
        used[nx][ny] = true;
      }
    }
    if (stop) {
      return ret;
    }
    q = nxt;
  }
  return false;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

#define INF 1001000100010001000
#define MOD 1000000007
#define EPS 1e-10
#define int long long
#define rep(i, N) for (int i = 0; i < N; i++)
#define Rep(i, N) for (int i = 1; i < N; i++)
#define For(i, a, b) for (int i = (a); i < (b); i++)
#define pb push_back
#define mp make_pair
#define i_i pair<int, int>
#define vi vector<int>
#define vvi vector<vi>
#define vb vector<bool>
#define vvb vector<vb>
#define vp vector<i_i>
#define all(a) (a).begin(), (a).end()
#define Int(x)                                                                 \\
  int x;                                                                       \\
  scanf("%lld", &x);

int dxy[5] = {0, 1, 0, -1, 0};
// assign

vector<string> board;
vvb used;
int x, y;

int solve(int a, int b);

signed main() {
  cin >> x >> y;
  board.assign(x, "");

  rep(i, x) { cin >> board[i]; }

  int pr = 0;
  rep(i, x) {
    rep(j, y) {
      if (board[i][j] == '@') {
        pr = solve(i, j);
      }
    }
  }

  bool ret = true;
  rep(i, x) {
    rep(j, y) {
      if (board[i][j] == '$') {
        if (solve(i, j) <= pr) {
          ret = false;
          break;
        }
      }
    }
  }
  cout << ((ret) ? "Yes" : "No") << endl;

  return 0;
}

int solve(int a, int b) {
  queue<i_i> q;
  q.push(i_i(a, b));
  used.assign(x, vb(y, false));
  used[a][b] = true;
  int ret = 0;

  while (!q.empty()) {
    ret++;
    queue<i_i> nxt;
    while (!q.empty()) {
      int c = q.front().first, d = q.front().second;
      q.pop();
      rep(i, 4) {
        int nx = c + dxy[i], ny = d + dxy[i + 1];
        if (nx < 0 || ny < 0 || x <= nx || y <= ny || used[nx][ny]) {
          continue;
        }
        if (board[nx][ny] == '.') {
          nxt.push(i_i(nx, ny));
        } else if (board[nx][ny] == '$') {
          nxt.push(i_i(nx, ny));
        } else if (board[nx][ny] == '@') {
          nxt.push(i_i(nx, ny));
        } else if (board[nx][ny] == '%') {
          return ret;
        }
        used[nx][ny] = true;
      }
    }
    q = nxt;
  }
  return INF;
}