Problem p01486 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#define int long long
using ll = long long;
using vi = vector<int>;
using vl = vector<long long>;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
#define ITR(i, c) for (auto i = begin(c); i != end(c); ++i)
#define FORE(x, c) for (auto &x : c)
#define REPF(i, a, n) for (int i = a, i##_len = (int)(n); i < i##_len; ++i)
#define REP(i, n) REPF(i, 0, n)
#define REPR(i, n) for (int i = (int)(n); i >= 0; --i)
#define REPW(i, n) for (i = 0; i < (int)(n); ++i)
#define ALL(c) begin(c), end(c)
#define RALL(c) rbegin(c), rend(c) // c++14
#define SZ(c) ((int)c.size())
#define EXIST(c, x) (c.find(x) != end(c))
#define OUTOFRANGE(y, x, h, w) (y < 0 || x < 0 || y >= h || x >= w)
#define dump(...)
const int DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
          DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
#define INF (1001001001)
#define INFLL (1001001001001001001ll)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  ITR(i, v) os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  ITR(i, v) is >> *i;
  return is;
}
template <class T> istream &operator>>(istream &is, pair<T, T> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
//------------------------------------------------------------------------------
struct before_main_function {
  before_main_function() {
#ifdef int
#undef INF
#define INF INFLL
#define stoi stoll
#endif
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
  }
} before_main_function;
//------------------------------------------------------------------------------

unordered_map<string, bool> dp;
bool solve(string s) {
  if (EXIST(dp, s))
    return dp[s];
  if (s == "")
    return dp[s] = true;
  int n = SZ(s);
  if (s[0] != 'm' || s[n - 1] != 'w')
    return dp[s] = false;
  REP(i, n) {
    if (s[i] == 'e') {
      if (solve(s.substr(1, i - 1)) and solve(s.substr(i + 1, n - i - 2))) {
        return dp[s] = true;
      }
    }
  }
  return dp[s] = false;
}
signed main() {
  string s;
  cin >> s;
  cout << (solve(s) ? "Cat" : "Rabbit") << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define int long long
using ll = long long;
using vi = vector<int>;
using vl = vector<long long>;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
#define ITR(i, c) for (auto i = begin(c); i != end(c); ++i)
#define FORE(x, c) for (auto &x : c)
#define REPF(i, a, n) for (int i = a, i##_len = (int)(n); i < i##_len; ++i)
#define REP(i, n) REPF(i, 0, n)
#define REPR(i, n) for (int i = (int)(n); i >= 0; --i)
#define REPW(i, n) for (i = 0; i < (int)(n); ++i)
#define ALL(c) begin(c), end(c)
#define RALL(c) rbegin(c), rend(c) // c++14
#define SZ(c) ((int)c.size())
#define EXIST(c, x) (c.find(x) != end(c))
#define OUTOFRANGE(y, x, h, w) (y < 0 || x < 0 || y >= h || x >= w)
#define dump(...)
const int DX[9] = {0, 1, 0, -1, 1, 1, -1, -1, 0},
          DY[9] = {-1, 0, 1, 0, -1, 1, 1, -1, 0};
#define INF (1001001001)
#define INFLL (1001001001001001001ll)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  ITR(i, v) os << *i << (i == end(v) - 1 ? "" : " ");
  return os;
}
template <class T> istream &operator>>(istream &is, vector<T> &v) {
  ITR(i, v) is >> *i;
  return is;
}
template <class T> istream &operator>>(istream &is, pair<T, T> &p) {
  is >> p.first >> p.second;
  return is;
}
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
//------------------------------------------------------------------------------
struct before_main_function {
  before_main_function() {
#ifdef int
#undef INF
#define INF INFLL
#define stoi stoll
#endif
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
  }
} before_main_function;
//------------------------------------------------------------------------------

bool solve(string s) {
  if (s == "")
    return true;
  int n = SZ(s);
  if (s[0] != 'm' || s[n - 1] != 'w')
    return false;
  REP(i, n) {
    if (s[i] == 'e') {
      if (solve(s.substr(1, i - 1)) and solve(s.substr(i + 1, n - i - 2))) {
        return true;
      }
    }
  }
  return false;
}
signed main() {
  string s;
  cin >> s;
  cout << (solve(s) ? "Cat" : "Rabbit") << endl;
  return 0;
}