Problem p02611 (C++) — buggy submission, verdict: Time Limit Exceeded

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) (v).begin(), (v).end()
using ll = long long;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1},
          dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) {
  return a < b ? (a = b, true) : false;
}
template <typename T, typename U> inline bool chmin(T &a, U b) {
  return a > b ? (a = b, true) : false;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt() : val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) const {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1)
        res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) {
    if ((val += x.val) >= mod)
      val -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &x) {
    if ((val += mod - x.val) >= mod)
      val -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &x) {
    val = static_cast<unsigned long long>(val) * x.val % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &x) {
    // assert(__gcd(static_cast<int>(x.val), mod) == 1);
    unsigned a = x.val, b = mod;
    int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() {
    if (++val == mod)
      val = 0;
    return *this;
  }
  ModInt operator++(int) {
    ModInt res = *this;
    ++*this;
    return res;
  }
  ModInt &operator--() {
    val = (val == 0 ? mod : val) - 1;
    return *this;
  }
  ModInt operator--(int) {
    ModInt res = *this;
    --*this;
    return res;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend ostream &operator<<(ostream &os, const ModInt &x) {
    return os << x.val;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    ll val;
    is >> val;
    x = ModInt(val);
    return is;
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000)
      : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i)
      fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0)
      return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0)
      return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0)
      return ModInt(0);
    return k == 0 ? ModInt(1) : nCk(n + k - 1, k);
  }
};

template <typename T> struct Matrix {
  vector<vector<T>> dat;

  Matrix(int m, int n, T val = 0) : dat(m, vector<T>(n, val)) {}

  int height() const { return dat.size(); }

  int width() const { return dat.front().size(); }

  Matrix pow(ll exponent) const {
    int n = height();
    Matrix<T> tmp = *this, res(n, n, 0);
    REP(i, n) res[i][i] = 1;
    while (exponent > 0) {
      if (exponent & 1)
        res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }

  inline const vector<T> &operator[](const int idx) const { return dat[idx]; }
  inline vector<T> &operator[](const int idx) { return dat[idx]; }

  Matrix &operator=(const Matrix &x) {
    int m = x.height(), n = x.width();
    dat.resize(m, vector<T>(n));
    REP(i, m) REP(j, n) dat[i][j] = x[i][j];
    return *this;
  }

  Matrix &operator+=(const Matrix &x) {
    int m = height(), n = width();
    REP(i, m) REP(j, n) dat[i][j] += x[i][j];
    return *this;
  }

  Matrix &operator-=(const Matrix &x) {
    int m = height(), n = width();
    REP(i, m) REP(j, n) dat[i][j] -= x[i][j];
    return *this;
  }

  Matrix &operator*=(const Matrix &x) {
    int m = height(), n = x.width(), l = width();
    vector<vector<T>> res(m, vector<T>(n, 0));
    REP(i, m) REP(j, n) { REP(k, l) res[i][j] += dat[i][k] * x[k][j]; }
    swap(dat, res);
    return *this;
  }

  Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; }

  Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; }

  Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; }
};

int main() {
  const int X = 15;
  Matrix<ModInt> m((X + 1) * 2, (X + 1) * 2), x((X + 1) * 2, 1);
  REP(j, X + 1) REP(p, 2) {
    if (j + 1 <= X && (j >= 5 || !p)) {
      // dp[i][j][p] -> dp[i + 1][k][1] (k > j)
      FOR(k, j + 1, X + 1) m[(X + 1) + k][p * (X + 1) + j] = 1;
    }
    // dp[i][j][p] -> dp[i + 1][j][p ^ 1]
    m[(p ^ 1) * (X + 1) + j][p * (X + 1) + j] = 1;
  }
  x[0][0] = 1;
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    if (n < 5) {
      cout << 0 << '\\n';
    } else {
      Matrix<ModInt> ans = m.pow(n - 4) * x;
      cout << ans[X][0] + ans[(X + 1) + X][0] << '\\n';
    }
  }
  return 0;
}


Error: TLE

Fixed submission:

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, m, n) for (int i = (m); i < (n); ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(v) (v).begin(), (v).end()
using ll = long long;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1},
          dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) {
  return a < b ? (a = b, true) : false;
}
template <typename T, typename U> inline bool chmin(T &a, U b) {
  return a > b ? (a = b, true) : false;
}
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt() : val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) const {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1)
        res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) {
    if ((val += x.val) >= mod)
      val -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &x) {
    if ((val += mod - x.val) >= mod)
      val -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &x) {
    val = static_cast<unsigned long long>(val) * x.val % mod;
    return *this;
  }
  ModInt &operator/=(const ModInt &x) {
    // assert(__gcd(static_cast<int>(x.val), mod) == 1);
    unsigned a = x.val, b = mod;
    int u = 1, v = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(u -= tmp * v, v);
    }
    return *this *= u;
  }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() {
    if (++val == mod)
      val = 0;
    return *this;
  }
  ModInt operator++(int) {
    ModInt res = *this;
    ++*this;
    return res;
  }
  ModInt &operator--() {
    val = (val == 0 ? mod : val) - 1;
    return *this;
  }
  ModInt operator--(int) {
    ModInt res = *this;
    --*this;
    return res;
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend ostream &operator<<(ostream &os, const ModInt &x) {
    return os << x.val;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    ll val;
    is >> val;
    x = ModInt(val);
    return is;
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000)
      : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i)
      fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) const {
    if (n < 0 || n < k || k < 0)
      return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) const {
    if (n < 0 || n < k || k < 0)
      return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) const {
    if (n < 0 || k < 0)
      return ModInt(0);
    return k == 0 ? ModInt(1) : nCk(n + k - 1, k);
  }
};

template <typename T> struct Matrix {
  vector<vector<T>> dat;

  Matrix(int m, int n, T val = 0) : dat(m, vector<T>(n, val)) {}

  int height() const { return dat.size(); }

  int width() const { return dat.front().size(); }

  Matrix pow(ll exponent) const {
    int n = height();
    Matrix<T> tmp = *this, res(n, n, 0);
    REP(i, n) res[i][i] = 1;
    while (exponent > 0) {
      if (exponent & 1)
        res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }

  inline const vector<T> &operator[](const int idx) const { return dat[idx]; }
  inline vector<T> &operator[](const int idx) { return dat[idx]; }

  Matrix &operator=(const Matrix &x) {
    int m = x.height(), n = x.width();
    dat.resize(m, vector<T>(n));
    REP(i, m) REP(j, n) dat[i][j] = x[i][j];
    return *this;
  }

  Matrix &operator+=(const Matrix &x) {
    int m = height(), n = width();
    REP(i, m) REP(j, n) dat[i][j] += x[i][j];
    return *this;
  }

  Matrix &operator-=(const Matrix &x) {
    int m = height(), n = width();
    REP(i, m) REP(j, n) dat[i][j] -= x[i][j];
    return *this;
  }

  Matrix &operator*=(const Matrix &x) {
    int m = height(), n = x.width(), l = width();
    vector<vector<T>> res(m, vector<T>(n, 0));
    REP(i, m) REP(j, n) { REP(k, l) res[i][j] += dat[i][k] * x[k][j]; }
    swap(dat, res);
    return *this;
  }

  Matrix operator+(const Matrix &x) const { return Matrix(*this) += x; }

  Matrix operator-(const Matrix &x) const { return Matrix(*this) -= x; }

  Matrix operator*(const Matrix &x) const { return Matrix(*this) *= x; }
};

int main() {
  const int X = 15;
  Matrix<ModInt> m((X + 1) * 2, (X + 1) * 2), x((X + 1) * 2, 1);
  REP(j, X + 1) REP(p, 2) {
    if (j + 1 <= X && (j >= 5 || !p)) {
      // dp[i][j][p] -> dp[i + 1][k][1] (k > j)
      FOR(k, j + 1, X + 1) m[(X + 1) + k][p * (X + 1) + j] = 1;
    }
    // dp[i][j][p] -> dp[i + 1][j][p ^ 1]
    m[(p ^ 1) * (X + 1) + j][p * (X + 1) + j] = 1;
  }
  x[0][0] = 1;
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    cout << (n < 5 ? ModInt(0)
                   : (m.pow(n - 4) * x)[X][0] +
                         (m.pow(n - 4) * x)[(X + 1) + X][0])
         << '\\n';
  }
  return 0;
}