結果

問題 No.1595 The Final Digit
ユーザー popofypopofy
提出日時 2021-07-09 23:15:39
言語 C++14
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 8,349 bytes
コンパイル時間 1,864 ms
コンパイル使用メモリ 183,032 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-09-14 10:45:29
合計ジャッジ時間 2,807 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
このコードへのチャレンジ（β）

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 2 ms
4,376 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 2 ms
4,376 KB
testcase_03 AC 1 ms
4,376 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 2 ms
4,376 KB
testcase_06 AC 1 ms
4,380 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 1 ms
4,380 KB
testcase_09 AC 1 ms
4,376 KB
testcase_10 AC 2 ms
4,376 KB
testcase_11 AC 2 ms
4,376 KB
testcase_12 AC 1 ms
4,380 KB
testcase_13 AC 1 ms
4,376 KB
testcase_14 AC 1 ms
4,380 KB
testcase_15 AC 2 ms
4,376 KB
testcase_16 AC 1 ms
4,376 KB
testcase_17 AC 2 ms
4,376 KB
testcase_18 AC 1 ms
4,380 KB
testcase_19 AC 1 ms
4,376 KB
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, n) for (decltype(n) i = 0, i##_len = (n); i < i##_len; ++i)
#define reps(i, n) for (decltype(n) i = 1, i##_len = (n); i <= i##_len; ++i)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pl(s) cout << (s) << "\n";
#define plx(s) {cout << (s) << "\n"; exit(0);}
#define yes(s) cout << ((s)?"Yes":"No") << "\n";
#define bit(n) (1LL << ((int)(n)))
#define get1bit(x,n) (((x) >> (int)(n)) & 1)
#define pcnt(x) __builtin_popcountll(x)
#define flog(x) (63 - __builtin_clzll(x))
#define clog(x) (((x)==1)?0:(64-__builtin_clzll((x)-1)))
#define cdiv(x,y) (((x)+(y)-1)/(y))
#define lb(a,x) distance((a).begin(),lower_bound((a).begin(),(a).end(),(x)))
#define ub(a,x) distance((a).begin(),upper_bound((a).begin(),(a).end(),(x)))
#ifdef __LOCAL
#include <dump.hpp>
#define dump(...) DUMPOUT << "  " << string(#__VA_ARGS__) << ": " << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl << "    ", dump_func(__VA_ARGS__)
#else
#define dump(...)
#endif
using ll = long long; using ld = long double; template<class T> using V = vector<T>;
template<class T> inline bool chmax(T& a, T b) {if (a < b) {a = b; return 1;} return 0;}
template<class T> inline bool chmin(T& a, T b) {if (a > b) {a = b; return 1;} return 0;}
template<class T> istream &operator>>(istream &is, complex<T> &v) {T x, y; is >> x >> y; v.real(x); v.imag(y); return is;}
template<class T> istream &operator>>(istream &is, V<T> &v) {for (auto&& e : v) is >> e;return is;}
template<class T, class U> istream &operator>>(istream &is, pair<T, U> &v) {is >> v.first >> v.second;return is;}
template<class T, size_t n> istream &operator>>(istream &is, array<T, n> &v) {for (auto&& e : v) is >> e;return is;}
template<class T> inline string join(const T& v, string sep = " ") {if (v.size() == 0) return "" ;stringstream ss;for (auto&& e : v) ss << sep << e;return ss.str().substr(1);}
template<class T> inline void uniq(T& a, bool presort = true){if (presort) sort(all(a));a.erase(unique(all(a)),a.end());}
template <class T> vector<T> compress(vector<T> &x){auto ret = x; uniq(ret); rep(i,sz(x)) x[i] = lb(ret, x[i]); return ret;}
template<class T> constexpr bool between(T a, T x, T b) {return (a <= x && x < b);}
template<class T> constexpr bool intersect(T l1, T r1, T l2, T r2) {return max(l1,l2) <= min(r1,r2);}
template<class T> V<T> make_vec(size_t n, T a) {return V<T>(n, a);}
template<class... Ts> auto make_vec(size_t n, Ts... ts) {return V<decltype(make_vec(ts...))>(n, make_vec(ts...));}
template<class T> inline V<T> CUM(V<T> &a) {int n = sz(a); V<T> ret(n+1); rep(i,n) ret[i+1] = a[i] + ret[i]; return ret;}
template<class T> inline V<T> DIF(V<T> &a) {int n = sz(a)-1; V<T> ret(n); rep(i,n) ret[i] = a[i+1] - a[i]; return ret;}
constexpr ll TEN(int n) {return (n == 0) ? 1 : 10 * TEN(n - 1);}
constexpr ll POW(ll x, ll n) {ll ret = 1;while (n > 0) {if (n & 1) ret *= x;x *= x;n >>= 1;}return ret;}
constexpr ll MODPOW(ll x, ll n, ll m) {ll ret = 1;while (n > 0) {if (n&1) ret = ret * x % m;x = x * x % m;n >>= 1;}return ret;}
constexpr ll nC2(ll n) {assert(between(ll(0),n,ll(3037000501)));return n * (n-1)/2;}
constexpr ll NSUM(ll n) {assert(between(ll(0),n,ll(3037000500)));return n * (n+1)/2;}
constexpr ll pos1d(ll y, ll x, ll h, ll w) {assert(between(ll(0),y,h));assert(between(ll(0),x,w));return y*w + x;}
constexpr pair<ll,ll> pos2d(ll p, ll h, ll w) {ll y = p/w, x = p - y*w;assert(between(ll(0),y,h));assert(between(ll(0),x,w));return {y, x};}
V<V<ll>> buildComb(int n = 60) {V<V<ll>> v(n+1, V<ll>(n+1));rep(i,sz(v)) {v[i][0] = 1; v[i][i] = 1;}for (int j = 1; j < sz(v); ++j) for (int k = 1; k < j; ++k) v[j][k] = v[j-1][k-1] + v[j-1][k];return v;}
inline bool palindrome(const string& s){return equal(all(s), s.rbegin());}
inline string upper(string s) {for(auto&& e: s) e = between('a',e,(char)('z'+1)) ? e - ('a'-'A') : e;return s;}
inline string lower(string s) {for(auto&& e: s) e = between('A',e,(char)('Z'+1)) ? e + ('a'-'A') : e;return s;}
inline string replace(string s, map<char, int> &from, V<int> &to) {for (auto&& e: s) e = '0' + (char)(to[from[e]]);return s;}
struct IOS {IOS() {cin.tie(nullptr); ios::sync_with_stdio(false); dump("");}} IO;
constexpr int INF = (1 << 30) - 1; constexpr ll INFL = 1LL << 60;


const int mod = 10;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x=0):x((x%mod+mod)%mod){}
  mint operator-() const { return mint(-x);}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;}
  mint operator+(const mint a) const { return mint(*this) += a;}
  mint operator-(const mint a) const { return mint(*this) -= a;}
  mint operator*(const mint a) const { return mint(*this) *= a;}
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod-2);}
  mint& operator/=(const mint a) { return *this *= a.inv();}
  mint operator/(const mint a) const { return mint(*this) /= a;}
};
istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}

template<typename T>
struct Kitamasa{
  vector<T> a;    // 初期値ベクトル
  vector<T> d;    // 係数ベクトル
  int k;

  Kitamasa(vector<T>& a, vector<T>& d) : a(a), d(d), k((int)a.size()) {}

  // a_n の係数ベクトルを求める
  vector<T> dfs(int64_t n){
      if(n == k)  return d;

      vector<T> res(k);
      if(n & 1 || n < k * 2){
          vector<T> x = dfs(n - 1);
          for(int i = 0; i < k; ++i)  res[i] = d[i] * x[k - 1];
          for(int i = 0; i + 1 < k; ++i)  res[i + 1] += x[i];
      }
      else{
          vector<vector<T>> x(k, vector<T>(k));
          x[0] = dfs(n >> 1);
          for(int i = 0; i + 1 < k; ++i){
              for(int j = 0; j < k; ++j)  x[i + 1][j] = d[j] * x[i][k - 1];
              for(int j = 0; j + 1 < k; ++j)  x[i + 1][j + 1] += x[i][j];
          }
          for(int i = 0; i < k; ++i){
              for(int j = 0; j < k; ++j){
                  res[j] += x[0][i] * x[i][j];
              }
          }
      }

      return res;
  }

  // a_n を求める
  T calc(ll n){
      vector<T> x = dfs(n);
      T res = 0;
      for(int i = 0; i < k; ++i)  res += x[i] * a[i];
      return res;
  }
};

struct Solver {
  V<V<int>> G;
  V<ll> memo;

  void solve() {
    // int n;cin >> n;
    // yes(between(10,n,100));

    // string t = "kyoprotenkei90";
    // map<char,int> mp2;
    // rep(i,sz(t)) {
    //   mp2[t[i]]++;
    // }
    // string s; cin >> s;
    // map<char,int> mp;
    // rep(i,sz(s)) {
    //   mp[s[i]]++;
    // }
    // bool failed = false;
    // for(auto [key,value] : mp2) {
    //   if (mp[key] != value) {
    //     failed = true;
    //     break;
    //   }
    // }
    // yes(!failed)


    // ll n; cin >> n;
    // ll ans = 0;
    // for (ll x = 1; x*x < n*n; ++x) {
    //   ll yy = n*n - x*x;
    //   ll y = sqrt(yy);
    //   if (y > 0 && y*y != n*n - x*x) continue;
    //   //dump(x,y,x*x,y*y);
    //   ++ans;
    // }
    // pl(ans)

    // ll n; cin >> n;
    // V<ll> e(n); cin >> e;
    // ll bn = bit(n);
    // for (ll i = 1; i < bn; ++i) {
    //   ll pa = 0;
    //   bitset<12> bi, bj, bk;
    //   bi = i;
    //   rep(j,n) if (get1bit(i,j)) pa += e[j];
    //   for (ll j = bn-1; j >= 1; --j) {
    //     ll pb = 0, pc = 0;
    //     j &= (bn-1) - i;
    //     bj = j;
    //     ll k = (bn-1) - (i+j);
    //     bk = k;
    //     if (j == 0 || k == 0) continue;
    //     rep(l,n) {
    //       if (get1bit(j,l)) pb += e[l];
    //       if (get1bit(k,l)) pc += e[l];
    //     }
    //     //dump(bi,bj,bk,pa,pb,pc);
    //     if (pa == pb && pb == pc) {
    //       dump(bi,bj,bk,pa,pb,pc);
    //       plx("Yes")
    //     }
    //   }
    // }
    // pl("No")

    ll p, q, r, k; cin >> p >> q >> r >> k;
    V<mint> a(3);
    a[0] = p; a[1] = q; a[2] = r;
    V<mint> b(4,1);
    dump(a);
    auto kita = Kitamasa<mint>(a, b);
    pl(kita.calc(k-1).x)
  }
} solver;
signed main(void) {solver.solve();return 0;}
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