Problem p02668 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
#define double ld
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \\
  if (false)                                                                   \\
  cerr
#endif

const double PI = 2 * acos(0.0);
#define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\\n\\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int M = 1e9 + 7;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

const int N = 5050;

int dp[N][N];

void insum(int &a, int b) { a = (a + b) % M; }

void smain() {

  int n, m;
  cin >> n >> m;

  for (int j = 1; j <= m; ++j) {
    dp[n - 1][j] = pw(2, j);
  }

  for (int i = n - 2; i >= 0; --i) {
    /* no 01 */;
    for (int j = 1; j <= m; ++j) {
      insum(dp[i][j], (ll)dp[i + 1][j] * (j + 1) % M);
      dp[i + 1][j] = (ll)dp[i + 1][j] * j % M;
    }
    /* at least one 01 */;
    int sum = 0;
    for (int j = 1; j <= m; ++j) {
      sum = (ll)sum * 2 % M;
      insum(sum, dp[i + 1][j - 1]);
      insum(dp[i][j], sum);
      //            for (int k = 1; k < j; ++k) {
      //                insum(dp[i][j], (ll) dp[i + 1][k] * pw(2, j - k - 1) %
      //                M);
      //            }
    }
  }
  cout << dp[0][m];
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#include <random>

using namespace std;

typedef unsigned long long ull;
typedef long long ll;
typedef double ld;
// #define ll __int128
// #define int ll
// #define int ll
// #define char ll
#define double ld
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<vvc> vvvc;
typedef pair<int, int> pii;
typedef pair<pii, pii> piii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<pii> vpi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<short> vs;
typedef vector<vs> vvs;
typedef vector<vvs> vvvs;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<vvl> vvvl;
typedef vector<ld> vld;
typedef vector<vld> vvld;
typedef vector<vvld> vvvld;
typedef vector<string> vst;
typedef vector<vst> vvst;
typedef pair<ld, ld> pld;

#define inmin(a, b) a = min(a, (b))
#define inmax(a, b) a = max(a, (b))
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define sqr(x) ((x) * (x))
#define fori(i, n) for (int i = 0; i < int(n); ++i)
#define SZ(a) ((int)((a).size()))
#define triple(T) tuple<T, T, T>
#define quad(T) tuple<T, T, T, T>
#define watch(x) cerr << (#x) << " = " << (x) << endl;

#ifdef MAX_HOME
#define cerr cout
#else
#define cerr                                                                   \\
  if (false)                                                                   \\
  cerr
#endif

const double PI = 2 * acos(0.0);
#define rand shittttty_shit
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng_64(chrono::steady_clock::now().time_since_epoch().count());

const string DIGITS = "0123456789";
const string ALPH = "abcdefghijklmnopqrstuvwxyz";

template <class T0, class T1>
inline ostream &operator<<(ostream &out, pair<T0, T1> &a) {
  return out << "{" << a.first << ", " << a.second << "}";
}

template <class T0, class T1>
inline istream &operator>>(istream &in, pair<T0, T1> &a) {
  return in >> a.first >> a.second;
}

template <class T0, class T1, class T2>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << "}";
}

template <class T0, class T1, class T2, class T3>
inline ostream &operator<<(ostream &out, tuple<T0, T1, T2, T3> &a) {
  return out << "{" << get<0>(a) << ", " << get<1>(a) << ", " << get<2>(a)
             << ", " << get<3>(a) << "}";
}

template <class T> inline ostream &operator<<(ostream &out, vector<T> &a) {
  out << "[";
  fori(i, a.size()) out << a[i]
                        << vector<string>{", ", "]  "}[i + 1 == a.size()];
  return out;
}

void smain();

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifdef MAX_HOME
  freopen("input.txt", "r", stdin);
  clock_t start = clock();
#endif
  cout << setprecision(12) << fixed;
  smain();
#ifdef MAX_HOME
  cout << "\\n\\nTOTAL EXECUTION TIME: "
       << float(clock() - start) / CLOCKS_PER_SEC << endl;
#endif
  return 0;
}

const int M = 1e9 + 7;

int pw(int a, int n = M - 2) {
  int ret = 1;
  while (n) {
    if (n & 1)
      ret = (ll)ret * a % M;
    a = (ll)a * a % M;
    n >>= 1;
  }
  return ret;
}

const int N = 5050;

int dp[N][N];

void insum(int &a, int b) { a = (a + b) % M; }

void smain() {

  int n, m;
  cin >> n >> m;

  for (int j = 1; j <= m; ++j) {
    dp[n - 1][j] = pw(2, j);
  }

  for (int i = n - 2; i >= 0; --i) {
    /* no 01 */;
    for (int j = 1; j <= m; ++j) {
      insum(dp[i][j], (ll)dp[i + 1][j] * (j + 1) % M);
      dp[i + 1][j] = (ll)dp[i + 1][j] * j % M;
    }
    /* at least one 01 */;
    for (int j = 1; j <= m; ++j) {
      for (int k = 1; k < j; ++k) {
        insum(dp[i][j], (ll)dp[i + 1][k] * pw(2, j - k - 1) % M);
      }
    }
  }
  cout << dp[0][m];
}