結果

問題 No.1595 The Final Digit
ユーザー saki0080
提出日時 2021-07-10 02:40:11
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 7,893 bytes
コンパイル時間 2,315 ms
コンパイル使用メモリ 202,728 KB
最終ジャッジ日時 2025-01-22 23:38:12
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 17
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a) for (int i = 0; i < (int)(a); i++)
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
typedef long long ll;
template<typename T>istream& operator>>(istream&i,vector<T>&v){rep(j,sz(v))i>>v[j];return i;}
template<typename T>string join(const vector<T>&v){stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);}
template<typename T>ostream& operator<<(ostream&o,const vector<T>&v){if(sz(v))o<<join(v);return o;}
template<typename T1,typename T2>istream& operator>>(istream&i,pair<T1,T2>&v){return i>>v.first>>v.second;}
template<typename T1,typename T2>ostream& operator<<(ostream&o,const pair<T1,T2>&v){return o<<v.first<<","<<v.second;}
template<typename T>bool mins(T& x,const T&y){if(x>y){x=y;return true;}else return false;}
template<typename T>bool maxs(T& x,const T&y){if(x<y){x=y;return true;}else return false;}
template<typename T>T dup(T x, T y){return (x+y-1)/y;}
template<typename T>ll suma(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
int keta(ll n) { int ret = 0; while (n>0) { n/=10; ret++; } return ret; }

#ifdef _DEBUG
inline void dump() { cerr << endl; }
template <typename Head> void dump(Head &&head) { cerr << head; dump(); }
template <typename Head, typename... Tail> void dump(Head &&head, Tail &&... tail) { cerr << head << ", "; dump(forward<Tail>(tail)...); }
#define debug(...) do { cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false)
#else
#define dump(...)
#define debug(...)
#endif

template <typename T> struct edge {
  int src, to;
  T cost;
  edge(int to, T cost) : src(-1), to(to), cost(cost) {}
  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}
  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;

const ll LINF = 1LL << 60;
const int INF = 1001001001;

/////////////////////////////////////////////////////////////////////

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, h) 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) {
    assert(h == a.h && w == a.w);
    rep(i, h) rep(j, w) d[i][j] += a[i][j];
    return *this;
  }
  Matrix& operator-=(const Matrix& a) {
    assert(h == a.h && w == a.w);
    rep(i, h) rep(j, w) d[i][j] -= a[i][j];
    return *this;
  }
  Matrix& operator*=(const Matrix& a) {
    assert(w == a.h);
    Matrix r(h, a.w);
    rep(i, h) rep(k, w) rep(j, a.w) {
      r[i][j] += d[i][k] * a[k][j];
    }
    rep(i, h) rep(j, w) d[i][j] = r[i][j];
    return *this;
  }
  Matrix& operator/=(const Matrix& a) {
    assert(h == a.h && w == a.w);
    return *this *= a.inv();
  }

  Matrix operator+(const Matrix& a) const { return Matrix(*this) += a; }
  Matrix operator-(const Matrix& a) const { return Matrix(*this) -= a; }
  Matrix operator*(const Matrix& a) const { return Matrix(*this) *= a; }
  Matrix operator/(const Matrix& a) const { return Matrix(*this) /= a; }

  bool operator==(const Matrix& a) {
    assert(h == a.h && w == a.w);
    rep(i, h) rep(j, w) if (d[i][j] != a[i][j]) return false;
    return true;
  }

  Matrix& operator+=(const T& a) { rep(i, h) rep(j, w) d[i][j] += a; return *this; }
  Matrix& operator-=(const T& a) { rep(i, h) rep(j, w) d[i][j] -= a; return *this; }
  Matrix& operator*=(const T& a) { rep(i, h) rep(j, w) d[i][j] *= a; return *this; }
  Matrix& operator/=(const T& a) { rep(i, h) rep(j, w) d[i][j] /= a; return *this; }
  Matrix operator+(const T& a) const { return Matrix(*this) += a; }
  Matrix operator-(const T& a) const { return Matrix(*this) -= a; }
  Matrix operator*(const T& a) const { return Matrix(*this) *= a; }
  Matrix operator/(const T& a) const { return Matrix(*this) /= a; }

  Matrix pow(ll t) const {
    assert(h == w);
    if (!t) return Matrix<T>(h, h).unit();
    if (t == 1) return *this;
    Matrix<T> r = pow(t>>1);
    r = r*r;
    if (t&1) r = r*(*this);
    return r;
  }

  T det() {
    assert(h == w);
    Matrix b(*this);
    T ret = 1;
    for (int i=0; i<w; i++) {
      int idx = -1;
      for (int j=i; j<w; 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<w; j++) b[i][j] /= vv;
      for (int j=i+1; j<w; j++) {
        T a = b[j][i];
        for (int k=0; k<w; k++) b[j][k] -= b[i][k] * a;
      }
    }
    return ret;
  }

  Matrix inv() const {
    assert(h == w);
    Matrix b(*this);
    Matrix invb(h, w);
    rep(i, h) rep(j, w) invb[i][j] = (i==j) ? 1 : 0;
    rep(i, h) {
      T buf = (T)(1)/b[i][i];
      rep(j, w) { b[i][j] *= buf; invb[i][j] *= buf; }
      rep(j, w) {
        if (i != j) {
          buf = b[j][i];
          rep(k, w) { b[j][k] -= b[i][k] * buf; invb[j][k] -= invb[i][k] * buf; }
        }
      }
    }
    return invb;
  }

  Matrix trans() const {
    Matrix b(w, h);
    rep(i, h) rep(j, w) b[j][i] = d[i][j];
    return b;
  }

  Matrix rot(int deg) const {
    deg %= 4;
    int rh = h, rw = w;
    if (deg&1) swap(rh, rw);
    Matrix b(rh, rw);
    if (deg == 0) return *this;
    if (deg == 1) rep(i, h) rep(j, w) b[j][h-i-1] = d[i][j];
    if (deg == 2) rep(i, h) rep(j, w) b[h-i-1][w-j-1] = d[i][j];
    if (deg == 3) rep(i, h) rep(j, w) b[w-j-1][i] = d[i][j];
    return b;
  }

  void show() {
    rep(i, h) {
      rep(j, w) { if (j > 0) cout << " "; cout << d[i][j]; }
      cout << "\n";
    }
  }
};

template<int mod>
struct ModInt {
  ll x;
  ModInt(ll x=0):x((x%mod+mod)%mod){}
  ModInt operator-() const { return ModInt(-x); }
  ModInt& operator+=(const ModInt a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  ModInt& operator-=(const ModInt a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  ModInt& operator*=(const ModInt a) { (x *= a.x) %= mod; return *this; }
  ModInt operator+(const ModInt a) const { return ModInt(*this)+=a; }
  ModInt operator-(const ModInt a) const { return ModInt(*this)-=a; }
  ModInt operator*(const ModInt a) const { return ModInt(*this)*=a; }
  ModInt pow(ll t) const {
    if (!t) return 1;
    ModInt a = *this, r = 1;
    while (t) {
      if (t & 1) r *= a;
      a *= a;
      t >>= 1;
    }
    return r;
  }
  ModInt inv() const {
    ll a = x;
    ll b = mod;
    ll c = 1, d = 0;
    while (b) {
      ll t = a/b;
      a -= t*b; swap(a, b);
      c -= t*d; swap(c, d);
    }
    c %= mod;
    if (c < 0) c += mod;
    return c;
  }
  ModInt& operator/=(const ModInt a) { return (*this) *= a.inv(); }
  ModInt operator/(const ModInt a) const { return ModInt(*this)/=a; }
  bool operator==(const ModInt a) const { return x == a.x; }
  bool operator!=(const ModInt a) const { return x != a.x; }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) {
    ll t;
    is >> t;
    a = ModInt(t);
    return (is);
  }
};

using mint = ModInt<10>;

void solve()
{
  ll p,q,r,k; cin>>p>>q>>r>>k;

  Matrix<mint> mat(3, 3);
  Matrix<mint> a(3, 1);
  a[0][0] = r;
  a[1][0] = q;
  a[2][0] = p;

  mat[0][0] = 1; mat[0][1] = 1; mat[0][2] = 1;
  mat[1][0] = 1; mat[1][1] = 0; mat[1][2] = 0;
  mat[2][0] = 0; mat[2][1] = 1; mat[2][2] = 0;

  Matrix<mint> ans = mat.pow(k-3) * a;
  rep(i, 3) debug(ans[i][0]);
  cout << ans[0][0] << "\n";

}

int main()
{
  int t;
  t = 1;
  // cin>>t;
  while (t--) solve();

  return 0;
}
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