#344420 (C++14) No.658 テトラナッチ数列 Hard

提出ソース
結果

問題	No.658 テトラナッチ数列 Hard
ユーザー	もりを
提出日時	2019-05-02 23:24:14
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	403 ms / 2,000 ms
コード長	13,733 bytes
コンパイル時間	1,812 ms
コンパイル使用メモリ	180,536 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-06-10 04:15:13
合計ジャッジ時間	4,170 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 5,248 KB
testcase_01	AC	1 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	3 ms 5,376 KB
testcase_04	AC	144 ms 5,376 KB
testcase_05	AC	165 ms 5,376 KB
testcase_06	AC	206 ms 5,376 KB
testcase_07	AC	232 ms 5,376 KB
testcase_08	AC	261 ms 5,376 KB
testcase_09	AC	396 ms 5,376 KB
testcase_10	AC	403 ms 5,376 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
//#define int long long
//TEMPLATE START---------------8<---------------8<---------------8<---------------8<---------------//
typedef long long ll;       typedef long double ld;  typedef pair<int,int> pii; typedef pair<ll,ll> pll;  typedef vector<int> vi;   typedef vector<ll> vl;
typedef vector<string> vst; typedef vector<bool> vb; typedef vector<ld> vld;    typedef vector<pii> vpii; typedef vector<pll> vpll; typedef vector<vector<int> > vvi;
const int INF = (0x7FFFFFFFL); const ll INFF = (0x7FFFFFFFFFFFFFFFL); const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const int MOD = 1e9 + 7;       const int MODD = 998244353;            const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const double PI = acos(-1.0);  const double EPS = 1e-9;               const string Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
int dx[9] = { 1, 0, -1,  0,  1, -1, -1, 1, 0 };
int dy[9] = { 0, 1,  0, -1, -1, -1,  1, 1, 0 };
#define ln '\n'
#define scnaf scanf
#define sacnf scanf
#define sancf scanf
#define SS(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t){cin >> t;}template<typename First, typename...Rest> void MACRO_VAR_Scan(First& first, Rest&...rest){cin >> first;MACRO_VAR_Scan(rest...);}
#define SV(type,c,n) vector<type> c(n);for(auto& i:c)cin >> i;
#define SVV(type,c,n,m) vector<vector<type>> c(n,vector<type>(m));for(auto& r:c)for(auto& i:r)cin >> i;
template<class T,class U>ostream &operator<<(ostream &o,const pair<T,U>&j){o<<"{"<<j.first<<", "<<j.second<<"}";return o;}
template<class T,class U>ostream &operator<<(ostream &o,const map<T,U>&j){o<<"{";for(auto t=j.begin();t!=j.end();++t)o<<(t!=j.begin()?", ":"")<<*t;o<<"}";return o;}
template<class T>ostream &operator<<(ostream &o,const set<T>&j){o<<"{";for(auto t=j.begin();t!=j.end();++t)o<<(t!=j.begin()?", ":"")<<*t;o<<"}";return o;}
template<class T>ostream &operator<<(ostream &o,const vector<T>&j){o<<"{";for(int i=0;i<(int)j.size();++i)o<<(i>0?", ":"")<<j[i];o<<"}";return o;}
inline int print(void){cout << endl; return 0;}
template<class Head> int print(Head&& head){cout << head;print();return 0;} template<class Head,class... Tail> int print(Head&& head,Tail&&... tail){cout<<head<<" ";print(forward<Tail>(tail)...);return 0;}
inline int debug(void){cerr << endl; return 0;}
template<class Head> int debug(Head&& head){cerr << head;debug();return 0;} template<class Head,class... Tail> int debug(Head&& head,Tail&&... tail){cerr<<head<<" ";debug(forward<Tail>(tail)...);return 0;}
template<typename T> void PA(T &a){int ASIZE=sizeof(a)/sizeof(a[0]);for(int ii=0;ii<ASIZE;++ii){cout<<a[ii]<<" \n"[ii==ASIZE-1];}}
template<typename T> void PV(T &v){int VSIZE=v.size();for(int ii=0;ii<VSIZE;++ii){cout<<v[ii]<<" \n"[ii==VSIZE-1];}}
#define ER(x)  cerr << #x << " = " << (x) << endl;
#define ERV(v) {cerr << #v << " : ";for(const auto& xxx : v){cerr << xxx << " ";}cerr << "\n";}
inline int YES(bool x){cout<<((x)?"YES":"NO")<<endl;return 0;} inline int Yes(bool x){cout<<((x)?"Yes":"No")<<endl;return 0;}  inline int yes(bool x){cout<<((x)?"yes":"no")<<endl;return 0;}
inline int yES(bool x){cout<<((x)?"yES":"nO")<<endl;return 0;} inline int Yay(bool x){cout<<((x)?"Yay!":":(")<<endl;return 0;}
template<typename A,typename B> void sankou(bool x,A a,B b){cout<<((x)?(a):(b))<<endl;}
#define _overload3(_1,_2,_3,name,...) name
#define _REP(i,n) REPI(i,0,n)
#define REPI(i,a,b) for(ll i=ll(a);i<ll(b);++i)
#define REP(...) _overload3(__VA_ARGS__,REPI,_REP,)(__VA_ARGS__)
#define _RREP(i,n) RREPI(i,n,0)
#define RREPI(i,a,b) for(ll i=ll(a);i>=ll(b);--i)
#define RREP(...) _overload3(__VA_ARGS__,RREPI,_RREP,)(__VA_ARGS__)
#define EACH(e,v) for(auto& e : v)
#define PERM(v) sort((v).begin(),(v).end());for(bool c##p=1;c##p;c##p=next_permutation((v).begin(),(v).end()))
#define ADD(a,b) a=(a+ll(b))%MOD
#define MUL(a,b) a=(a*ll(b))%MOD
inline ll MOP(ll x,ll n,ll m=MOD){ll r=1;while(n>0){if(n&1)(r*=x)%=m;(x*=x)%=m;n>>=1;}return r;}
inline ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}inline ll lcm(ll a,ll b){return a*b/gcd(a,b);}inline ll POW(ll a,ll b){ll c=1ll;do{if(b&1)c*=1ll*a;a*=1ll*a;}while(b>>=1);return c;}
template<typename T,typename A,typename B> inline bool between(T x,A a,B b) {return ((a<=x)&&(x<b));}template<class T> inline T sqr(T x){return x*x;}
template<typename A,typename B> inline bool chmax(A &a,const B &b){if(a<b){a=b;return 1;}return 0;}
template<typename A,typename B> inline bool chmin(A &a,const B &b){if(a>b){a=b;return 1;}return 0;}
#define tmax(x,y,z) max((x),max((y),(z)))
#define tmin(x,y,z) min((x),min((y),(z)))
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define SORT(v) sort((v).begin(),(v).end())
#define RSORT(v) sort((v).rbegin(),(v).rend())
#define EXIST(s,e) (find((s).begin(),(s).end(),(e))!=(s).end())
#define EXISTST(s,c) (((s).find(c))!=string::npos)
#define POSL(x,val) (lower_bound(x.begin(),x.end(),val)-x.begin())
#define POSU(x,val) (upper_bound(x.begin(),x.end(),val)-x.begin())
#define GEQ(x,val) (int)(x).size() - POSL((x),(val))
#define GREATER(x,val) (int)(x).size() - POSU((x),(val))
#define LEQ(x,val) POSU((x),(val))
#define LESS(x,val) POSL((x),(val))
#define SZV(a) int((a).size())
#define SZA(a) sizeof(a)/sizeof(a[0])
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define MEMINF(a) memset(a,0x3f,sizeof(a))
#define FILL(a,b) memset(a,b,sizeof(a))
#define UNIQUE(v) sort((v).begin(),(v).end());(v).erase(unique((v).begin(),(v).end()),(v).end())
struct abracadabra{
  abracadabra(){
    cin.tie(0); ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(5);
  };
} ABRACADABRA;

//TEMPLATE END---------------8<---------------8<---------------8<---------------8<---------------//

/*
・ModInt
[備考] Mod演算のための構造体
[使用例]
modint M;                   // 剰余系MOD(1e9+7)における演算ができる
ModInt<mod> N;              // 剰余系modにおける演算ができる
*/

template< int MODULO > struct ModInt {
  using uint32 = uint_fast32_t;
  using uint64 = uint_fast64_t;
  uint64 x; ModInt() : x(0) {}
  ModInt(uint64 y) : x(set(y % MODULO + MODULO)) {}
  static uint64 set(const uint64 &y) { return (y < MODULO) ? y : y - MODULO; }
  static ModInt make(const uint64 &y) { ModInt ret = y; return ret; }
  ModInt operator+(const ModInt &m) const { return make(set(x + m.x)); }
  ModInt operator-(const ModInt &m) const { return make(set(x + MODULO - m.x)); }
  ModInt operator*(const ModInt &m) const { return make(x * m.x % MODULO); }
  ModInt operator/(const ModInt &m) const { return make(x) * ~make(m.x); }
  ModInt &operator+=(const ModInt &m) { return *this = *this + m; }
  ModInt &operator-=(const ModInt &m) { return *this = *this - m; }
  ModInt &operator*=(const ModInt &m) { return *this = *this * m; }
  ModInt &operator/=(const ModInt &m) { return *this = *this / m; }
  ModInt &operator^=(const uint64 &y) { return *this = *this ^ y; }
  ModInt operator~ () const { return *this ^ (MODULO - 2); }
  ModInt operator- () const { return make(set(MODULO - x)); }
  ModInt operator! () const { init(uint32(*this)); return fact[uint32(*this)]; }
  ModInt operator& () const { init(uint32(*this)); return finv[uint32(*this)]; }
  ModInt operator++() { return *this = make(set(x + 1)); }
  ModInt operator--() { return *this = make(set(x + MODULO - 1)); }
  bool operator==(const ModInt &m) const { return x == m.x; }
  bool operator!=(const ModInt &m) const { return x != m.x; }
  bool operator< (const ModInt &m) const { return x <  m.x; }
  bool operator<=(const ModInt &m) const { return x <= m.x; }
  bool operator> (const ModInt &m) const { return x >  m.x; }
  bool operator>=(const ModInt &m) const { return x >= m.x; }
  explicit operator   bool() const { return x; }
  explicit operator uint64() const { return x; }
  ModInt operator^(uint64 y) const {
    uint64 t = x, u = 1;
    while (y) { if (y & 1) (u *= t) %= MODULO; (t *= t) %= MODULO; y >>= 1; }
    return make(u);
  }
  friend ostream &operator<<(ostream &os, const ModInt< MODULO > &m) { return os << m.x; }
  friend istream &operator>>(istream &is, ModInt< MODULO > &m) { uint64 y; is >> y; m = make(y); return is; }
  static vector< ModInt > fact, finv, invs;
  static void init(uint32 n) {
    uint32 m = fact.size();
    if (n < m) return;
    fact.resize(n + 1, 1);
    finv.resize(n + 1, 1);
    invs.resize(n + 1, 1);
    if (m == 0) m = 1;
    for (uint32 i = m; i <= n; ++i) fact[i] = fact[i - 1] * ModInt(i);
    finv[n] = ModInt(1) / fact[n];
    for (uint32 i = n; i >= m; --i) finv[i - 1] = finv[i] * make(i);
    for (uint32 i = m; i <= n; ++i) invs[i] = finv[i] * fact[i - 1];
  }
  static ModInt C(uint64 n, uint64 r) {
    if (r == 0) return make(1);
    if (r <  0) return make(0);
    if (n <  0) return make(r & 1 ? MODULO - 1 : 1) * C(-n + r - 1, r);
    if (n == 0 || n < r) return make(0);
    init(n);
    return fact[n] * finv[n - r] * finv[r];
  }
  static ModInt P(uint64 n, uint64 r) {
    if (n < r || r < 0) return make(0);
    init(n);
    return fact[n] * finv[n - r];
  }
  static ModInt H(uint64 n, uint64 r) {
    if (n < 0 || r < 0) return make(0);
    if (!n && !r) return make(1);
    init(n + r - 1);
    return C(n + r - 1, r);
  }
  static ModInt montmort(uint32 n) {
    ModInt res;
    init(n);
    for (uint32 k = 2; k <= n; ++k) {
      if (k & 1) res -= finv[k];
      else res += finv[k];
    }
    return res *= fact[n];
  }
  static ModInt LagrangePolynomial(vector<ModInt> &y, ModInt t) {
    uint32 n = y.size() - 1;
    if (t.x <= n) return y[t.x];
    init(n + 1);
    ModInt res, num(1);
    for (uint32 i = 0; i <= n; ++i) num *= t - make(i);
    for (uint32 i = 0; i <= n; ++i) {
      ModInt tmp = y[i] * num / (t - make(i)) * finv[i] * finv[n - i];
      if ((n - i) & 1) res -= tmp;
      else res += tmp;
    }
    return res;
  }
};
template< int MODULO >
vector<ModInt< MODULO >> ModInt< MODULO >::fact = vector<ModInt< MODULO >>();
template< int MODULO >
vector<ModInt< MODULO >> ModInt< MODULO >::finv = vector<ModInt< MODULO >>();
template< int MODULO >
vector<ModInt< MODULO >> ModInt< MODULO >::invs = vector<ModInt< MODULO >>();
using modint = ModInt< MOD >;
using mint = ModInt< 17 >;

/*
・行列演算
[使用例]
Matrix<ll> mat(n,m);      // n行m列の行列を定義
mat[i][j];                // i行j列目の要素を取得
mat.determinant();        // matの行列式を計算
mat ^= k;                 // matのk乗を計算
*/

template< class T > struct Matrix {
  vector< vector< T > > A;
  Matrix() {}
  Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}
  Matrix(size_t n) : A(n, vector< T >(n, 0)) {};
  size_t height() const { return (A.size()); }
  size_t  width() const { return (A[0].size()); }
  inline const vector< T > &operator[](int k) const { return (A.at(k)); }
  inline       vector< T > &operator[](int k)       { return (A.at(k)); }
  static Matrix I(size_t n) {
    Matrix mat(n);
    for (int i = 0; i < n; ++i) mat[i][i] = 1;
    return (mat);
  }
  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < m; ++j)
        (*this)[i][j] += B[i][j];
    return (*this);
  }
  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }
  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector< vector< T > > C(n, vector< T >(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }
  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while (k > 0) {
      if (k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }
  Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
  Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
  Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
  Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for (int i = 0; i < n; i++) {
      os << "[";
      for (int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }
  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for (int i = 0; i < width(); i++) {
      int idx = -1;
      for (int j = i; j < width(); j++) if (B[j][i] != 0) idx = j;
      if (idx == -1) return (0);
      if (i != idx) { ret *= -1; swap(B[i], B[idx]); }
      ret *= B[i][i];
      T vv = B[i][i];
      for (int j = 0; j < width(); j++) B[i][j] /= vv;
      for (int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for (int k = 0; k < width(); k++) B[j][k] -= B[i][k] * a;
      }
    }
    return (ret);
  }
};

signed main() {

  Matrix< mint > mat(4, 4);
  mat[0][1] = 1;
  mat[1][2] = 1;
  mat[2][3] = 1;
  REP(i, 4) mat[3][i] = 1;

  SS(ll, Q);
  SV(ll, N, Q);

  EACH(n, N) {
    if (n <= 3) cout << 0 << endl;
    else if (n == 4) cout << 1 << endl;
    else {
      cout << (mat ^ n - 4)[3][3] << endl;
    }
  }

}
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結果

テストケース

ソースコード
