Problem p02632 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#ifdef __DEBUG__
#define DBG(X) cout << #X << " = " << (X) << endl;
#define SAY(X) cout << (X) << endl;
#else
#define DBG(X)
#define SAY(X)
#endif

using namespace std;

using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

int dx[] = {1, 0, -1, 0, 1, -1, 1, -1};
int dy[] = {0, 1, 0, -1, 1, 1, -1, -1};
const int INT_INF = (int)(2e9);
const ll LL_INF = (ll)(2e18);

inline void fast_io() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
};
template <typename T, typename S>
inline ostream &operator<<(ostream &os, const pair<T, S> p) {
  cout << "[" << p.first << ";" << p.second << "]";
  return os;
}
template <typename T, typename S>
inline ostream &operator<<(ostream &os, const map<T, S> p) {
  for (auto el : p)
    cout << "[" << el.first << ";" << el.second << "]";
  return os;
}
template <typename T>
inline ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T>
inline ostream &operator<<(ostream &os, const deque<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T> inline ostream &operator<<(ostream &os, const set<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T> inline vector<T> fetch_vec(int sz) {
  vector<T> ret(sz);
  for (auto &elem : ret)
    cin >> elem;
  return ret;
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
const ll mod = 1e9 + 7;
using modint = ModInt<mod>;

template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(int k) const { return _fact[k]; }

  inline T rfact(int k) const { return _rfact[k]; }

  inline T inv(int k) const { return _inv[k]; }

  T P(int n, int r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T H(int n, int r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

int K;
string S;
void input() {
  fast_io();
  cin >> K >> S;
}

int WAsolve() {
  // これだと重複するパターンが存在する。
  int N = S.length();
  Combination<modint> combi(N + K + 1);
  modint ans = combi.C(N + K, N);
  ans *= modint(26).pow(K);
  cout << ans << endl;
  return 0;
}

int TLEsolve() {
  int N = S.length();
  vector<vector<modint>> dp(N + K + 1, vector<modint>(N + 2, 0));
  dp[0][0] = 1;
  for (int i = 0; i < N + K; i++) {
    for (int j = 0; j <= N; j++) {
      if (j < N)
        dp[i + 1][j] += dp[i][j] * 25;
      else
        dp[i + 1][j] += dp[i][j] * 26;
      dp[i + 1][j + 1] += dp[i][j];
    }
  }
  cout << dp[N + K][N] << endl;
  return 0;
  // 本質的にはパスカルの三角形
}

int solve() {
  int N = S.length();
  Combination<modint> combi(N + K + 1);
  modint ans = 0;
  for (int l = N - 1; l <= N + K - 1; l++) {
    int r = (N + K) - (l + 1);
    ans += combi.C(l, N - 1) * modint(25).pow(l - N + 1) * modint(26).pow(r);
  }
  cout << ans << endl;
  return 0;
}

int main() {
  input();
  solve();
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#ifdef __DEBUG__
#define DBG(X) cout << #X << " = " << (X) << endl;
#define SAY(X) cout << (X) << endl;
#else
#define DBG(X)
#define SAY(X)
#endif

using namespace std;

using ll = long long int;
using ull = unsigned long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

int dx[] = {1, 0, -1, 0, 1, -1, 1, -1};
int dy[] = {0, 1, 0, -1, 1, 1, -1, -1};
const int INT_INF = (int)(2e9);
const ll LL_INF = (ll)(2e18);

inline void fast_io() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
};
template <typename T, typename S>
inline ostream &operator<<(ostream &os, const pair<T, S> p) {
  cout << "[" << p.first << ";" << p.second << "]";
  return os;
}
template <typename T, typename S>
inline ostream &operator<<(ostream &os, const map<T, S> p) {
  for (auto el : p)
    cout << "[" << el.first << ";" << el.second << "]";
  return os;
}
template <typename T>
inline ostream &operator<<(ostream &os, const vector<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T>
inline ostream &operator<<(ostream &os, const deque<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T> inline ostream &operator<<(ostream &os, const set<T> &v) {
  for (auto el : v)
    cout << el << " ";
  return os;
}
template <typename T> inline vector<T> fetch_vec(int sz) {
  vector<T> ret(sz);
  for (auto &elem : ret)
    cin >> elem;
  return ret;
}

template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
const ll mod = 1e9 + 7;
using modint = ModInt<mod>;

template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(int k) const { return _fact[k]; }

  inline T rfact(int k) const { return _rfact[k]; }

  inline T inv(int k) const { return _inv[k]; }

  T P(int n, int r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T H(int n, int r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

int K;
string S;
void input() {
  fast_io();
  cin >> K >> S;
}

int WAsolve() {
  // これだと重複するパターンが存在する。
  int N = S.length();
  Combination<modint> combi(N + K + 1);
  modint ans = combi.C(N + K, N);
  ans *= modint(26).pow(K);
  cout << ans << endl;
  return 0;
}

int solve() {
  int N = S.length();
  vector<vector<modint>> dp(N + K + 1, vector<modint>(N + 2, 0));
  dp[0][0] = 1;
  for (int i = 0; i < N + K; i++) {
    for (int j = 0; j <= N; j++) {
      if (j < N)
        dp[i + 1][j] += dp[i][j] * 25;
      else
        dp[i + 1][j] += dp[i][j] * 26;
      dp[i + 1][j + 1] += dp[i][j];
    }
  }
  cout << dp[N + K][N] << endl;
  return 0;
}

int main() {
  input();
  solve();
  return 0;
}