結果

問題 No.2441 行列累乗
ユーザー Astral__Astral__
提出日時 2023-08-25 21:22:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 9,918 bytes
コンパイル時間 2,340 ms
コンパイル使用メモリ 217,040 KB
最終ジャッジ日時 2025-02-16 13:39:17
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
other AC * 20
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ソースコード

diff # 

#include<bits/stdc++.h>
#define PPque priority_queue<tuple<ll, ll, ll>, vector<tuple<ll, ll, ll>>, greater<tuple<ll, ll, ll>>>
#define Pque  priority_queue<pair<ll, ll>, vector<pair<ll, ll>>, greater<pair<ll, ll>>>
#define pque priority_queue<int, vector<int>, greater<int>>
#define umap unordered_map
#define uset unordered_set
#define rep(i, s, f) for(ll i = s; i <= f; i++)
#define per(i, s, f) for(ll i = s; i >= f; i--)
#define all0(x) (x).begin() ,(x).end()
#define all(x) (x).begin() + 1, (x).end()
#define vvvi vector<vector<vector<int>>>
#define vvvl vector<vector<vector<ll>>>
#define vvvc vector<vector<vector<char>>>
#define vvvd vector<vector<vector<double>>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvs vector<vector<string>>
#define vvc vector<vector<char>>
#define vvp vector<vector<pair<ll, ll>>>
#define vvb vector<vector<bool>>
#define vvd vector<vector<double>>
#define vp vector<pair<ll, ll>>
#define vi vector<int>
#define vl vector<ll>
#define vs vector<string>
#define vc vector<char>
#define vb vector<bool>
#define vd vector<double>
#define P pair<ll, ll>
#define TU tuple<ll, ll, ll>
#define rrr(l, r) mt()%(r-l+1)+l
#define ENDL '\n'
#define ull unsigned long long
#define debug(a, s) rep(i, s, a.size()-1) {cout << a.at(i) << " ";}cout << endl;
#define Debug(a, s) rep(i, s, a.size()-1) {rep(j, s, a.at(i).size()-1) {cout << a.at(i).at(j) << " ";}cout << endl;}
typedef long long ll;
using namespace std;

////////////////////////////////////////////////////////////////////////////////////////////////////////////
//これが本当の組み込み関数ってね（笑）

template <typename T>
T or_less(vector<T> &A, T x) { //x以下で最大要素の添字 前提: sort済み 存在しない: -1
  return distance(A.begin(), upper_bound(A.begin(), A.end(), x)-1);
}
template <typename T>
T under(vector<T> &A, T x) { //x未満の最大要素の添字　前提: sort済み 存在しない: -1
  return distance(A.begin(), lower_bound(A.begin(), A.end(), x)-1);
}
template <typename T>
T or_more(vector<T> &A, T x) { //x以上で最小要素の添字　　前提: sort済み 存在しない: N .   //distanceのA.beginは添字を出すために常にA.begin() NG: A.begin() + 1
  return distance(A.begin(), lower_bound(A.begin(), A.end(), x));
}
template <typename T>
T over(vector<T> &A, T x) { //xより大きい最小要素の添字前提: sort済み 存在しない: N
  return distance(A.begin(), upper_bound(A.begin(), A.end(), x));
}
void compress(vector<ll> &A) {//小さい順に順位、大きい順にしたいならreverseはNG最後に変換
    vector<ll> temp = A;
    sort(temp.begin()+1, temp.end());
    for (int i = 1; i <= int(A.size()-1); i++) {
        A.at(i) = distance(temp.begin(), lower_bound(temp.begin()+1, temp.end(), A.at(i)));
    }
}
ll LIS1(vl &A) {//at(0)は番兵、広義単調増加
  ll N = A.size()-1;
  vl L(N+1, 1001001001001001001LL);
  L.at(0) = -1 * 1001001001001001001LL;
  ll ans = 0;
  rep(i, 1, N) {
    ll idx = over<ll>(L, A.at(i));
    L.at(idx) = A.at(i);
    ans = max(ans, idx);
  }
  return ans;
}
ll LIS2(vl &A) {//狭義単調増加
  ll N = A.size() - 1;
  vl L(N+1, 1001001001001001001LL);
  L.at(0) = -1 * 1001001001001001001LL;
  ll ans = 0;
  rep(i, 1, N) {
    ll idx = or_more<ll>(L, A.at(i));
    L.at(idx) = A.at(i);
    ans = max(ans, idx);
  }
  return ans;
}
//////////////////////////////////////////////////////////////////////
//数学系
///////////////////////////////////////////////////////////////////////
ll POWER(ll a, ll b, ll mod) {
    a %= mod;
    vector<ll> pow (61);
    pow.at(0) = a;
    bitset<60> bina(b);
    ll answer = 1;
    for (int i = 1; i <= 60; i++) {
      pow.at(i) = pow.at(i-1) * pow.at(i-1) % mod;
        if (bina.test(i-1)) {
            answer = (answer*pow.at(i-1)) % mod;
        }
    }
    return answer;
}
ll Div(ll a, ll b, ll mod) {
    return a * POWER(b, mod-2, mod) % mod;
}

ll round(ll x, ll i) {
    return ll(x + 5 * pow(10, i-1))/ll(pow(10, i)) * ll(pow(10, i));
}
template <typename T> //約分
void normalize(T &mol, T &deno) {
    T mol_temp = abs(mol);
    T deno_temp = abs(deno);
    T GCD = gcd(mol_temp, deno_temp);
    mol /= GCD;
    deno /= GCD;
}
vvl mat_mul(vvl &a, vvl &b, ll mod) {//0-indexed && 正方行列
  ll n = a.size();
  vvl res(n , vl(n, 0));
 
  rep(i, 0, n-1) {
    rep(j, 0, n-1) {
      rep(k, 0, n-1) {
        res.at(i).at(j) += a.at(i).at(k) * b.at(k).at(j);
        res.at(i).at(j) %= mod;
      }
    }
  }
  return res;
}
vvl mat_pow(vvl &a, ll b, ll mod) {//0-indexed && 正方行列
  bitset<60> bina(b);
  vvl power = a;
  int N = a.size();
  vvl res(N, vl(N, 0));
  rep(i, 0, N-1) {
    res.at(i).at(i) = 1;
  }
  rep(i, 1, 60) {
    if (bina.test(i-1)) {
      res = mat_mul(res, power, mod);
    }
    power = mat_mul(power, power, mod);
  }
  return res;
}

vvl comb(ll n, ll mod) {//計算にO(N^2)　読み取りにO(1)
  vvl v(n+1, vl(n+1, 0));
  rep(i, 0, v.size() - 1) {
    v.at(i).at(0) = 1;
    v.at(i).at(i) = 1;
  }

  rep(i, 1, v.size()-1) {
    rep(j, 1, i) {
      v.at(i).at(j) = v.at(i-1).at(j-1) + v.at(i-1).at(j);
      v.at(i).at(j) %= mod;
    }
  }
  return v;
}

ll nCk(int n, int k, ll mod) {//毎回O(max(分子、　分母))
  ll ue = 1;
  ll sita = 1;
  for (int i = 1; i <= k; i++) {
      sita *= i;
      sita %= mod;
  }
  for (int i = 1; i <= k; i++) {
    ue *= (n-i+1);
    ue %= mod;
  }
  return Div(ue, sita, mod);
}
ll gaiseki(P a, P b) { //原点を中心としてaからbの方向　０以下なら角aObが180°以上
  return a.first * b.second - a.second * b.first;
}

ll gaiseki(P a, P b, P c) { //cを中心としてaからbの方向
  return (a.first - c.first) * (b.second - c.second) - (a.second - c.second) * (b.first - c.first);

}
ll nto10(string S, ll base) {
  ll res = 0;
  reverse(all0(S));
  while(!S.empty()) {
    ll num = S.back() - '0';
    if(num < 0 || num > 9) num = 9 + S.back() - 'a' + 1;
    res = res * base + num;
    S.pop_back();
  }
  return res;
}
string toN(ll N, ll base) {
  if(N == 0) return "0";
  string ans ="";
  ll MOD = abs(base);
  while(N != 0) {
    ll first = N % MOD;
    while(first < 0) first += MOD;
    ans += to_string(first);
    N -= first;
    N /= base;
  }
  reverse(all0(ans));
  return ans;
}
vp factrization(ll N) {
  vp res;
  for (int i = 2; i * i <= N; i++) {
    ll cnt = 0;
    while(N % i == 0) {
      cnt++;
      N /= i;
    }
    if(cnt != 0) res.push_back(P(i, cnt));
  }
  if(N != 1) res.push_back(P(N, 1));
  return res;
}
struct comb_fast {//must素数
  vl fac;
  vl facinv;
  vl inv;
  ll mod_comb;
  comb_fast (ll n, ll mod) {
    mod_comb = mod;
    fac.assign(n+1, 1);
    facinv.assign(n+1, 1);
    inv.assign(n+1, 1);
    rep(i, 2, n) {
      fac.at(i) = fac.at(i-1) * i % mod_comb;
      inv.at(i) = mod_comb - inv.at(mod_comb%i) * (mod_comb/i)%mod_comb;
      facinv.at(i) = facinv.at(i-1) * inv.at(i) % mod_comb;
    }
  }
  ll get(ll n, ll k) {
    if(n < k) return 0;
    if(n < 0 || k < 0) return 0;
    return fac.at(n) * (facinv.at(k) * facinv.at(n-k)%mod_comb)%mod_comb;
  }
};

double KAKUDO(double rad) {
  double res = rad * 180 / 3.141592653589793;
  return res;
}
double RAD(double kakudo) {
  return kakudo / 180 * 3.141592653589793;
}
double KAKUDO(P from, P to, P inside) {
  from.first -= inside.first; from.second -= inside.second;
  to.first -= inside.first; to.second -= inside.second;
  double kakudor = atan2(from.first, from.second);
  kakudor = KAKUDO(kakudor);
  double kakudol = atan2(to.first, to.second);
  kakudol = KAKUDO(kakudol);
  double res = kakudol - kakudor;
  if(res < 0)res += 360;
  if(res > 360) res -= 360;
  return res;
}
ll extgcd (ll a, ll b,  ll &x, ll &y) {
  if(b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  ll d = extgcd(b, a%b, y, x);
  y -= a/b * x;
  return d;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//グローバル変数を置くところ（情報工学意識高め）
ll int_max = 1001001001;
ll ll_max = 1001001001001001001LL;
const double pi = 3.141592653589793;
vl dx{0, 1, 0, -1, 0, 1, 1, -1, -1};
vl dy{0, 0, -1, 0, 1, 1, -1, -1, 1};
//#pragma GCC optimize ("-O3")
//ll mod = 1000000007;
//ll mod = 998244353;

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
template<typename T>
struct Matrix  {
  int h, w;
  vector<vector<T>> d;
  Matrix() {}
  Matrix(int h, int w, T val = 0): h(h), w(w), d(h, vector<T>(w, val)){}
  Matrix& unit() {
    assert(h == w);
    rep(i, 0, h-1) {
      d[i][i] = 1;
    }
   return *this;
  }
  const vector<T>& operator[](int i) const{return d[i];}
  vector<T>& operator[](int i) {return d[i];}
  Matrix operator*(const Matrix&a) const{
    assert(w == a.h);
    Matrix r(h, a.w);
    rep(i, 0, h-1) {
      rep(k, 0, w-1) {
        rep(j, 0, a.w-1) {
          r[i][j] += d[i][k] * a[k][j];
        }
      }
    }
    return r;
  }
  Matrix pow(ll t) const {
    assert(h == w);
    if(!t) return Matrix(h, h).unit();
    if(t == 1) return *this;
    Matrix r = pow(t >> 1);
    r = r * r;
    if(t&1) r = r*(*this);
    return r;
  }
};


void solve() {
  Matrix<ll>  A(2, 2);
 cin >>  A[0][0];
 cin >> A[0][1];
 cin >> A[1][0];
 cin >> A[1][1];
 Matrix<ll> ans = A.pow(3);

 rep(i, 0, 1) {
  rep(j, 0, 1) {
    cout << ans[i][j] << " ";
  }
  cout << endl;
 }

 
  





}
//stringでの数字の下から1桁目は 正:S.at(N-1)  誤:S.at(0)
//if(S.at(i) == 1　← charなのに1...?
// modは取りましたか...?(´・ω・｀)



int main() {
  ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  cout << fixed << setprecision(15);
  solve();
  return 0;
}
0