結果

問題 No.2122 黄金比で擬似乱数生成
ユーザー ecotteaecottea
提出日時 2022-11-04 23:07:57
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 366 ms / 2,000 ms
コード長 11,036 bytes
コンパイル時間 4,270 ms
コンパイル使用メモリ 244,968 KB
実行使用メモリ 5,760 KB
最終ジャッジ日時 2024-07-18 22:12:19
合計ジャッジ時間 7,187 ms
ジャッジサーバーID
(参考情報)
judge5 / judge2
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ファイルパターン 結果
other AC * 26
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ソースコード

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#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004004004004004LL;
double EPS = 1e-12;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
// Visual Studio
#ifdef _MSC_VER
#include "local.hpp"
// gcc
#else
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
#endif //
//--------------AtCoder --------------
#include <atcoder/all>
using namespace atcoder;
//using mint = modint1000000007;
//using mint = modint998244353;
using mint = modint; // mint::set_mod(m);
istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
//----------------------------------------
//
/*
*
*
* Matrix(m, n) : O(m n)
* m * n
*
* Matrix(n) : O(n^2)
* n * n
*
* Matrix(a) : O(m n)
* a
*
* A + B : O(m n)
* m * n A, B += 使
*
* A - B : O(m n)
* m * n A, B -= 使
*
* c * A A * c : O(m n)
* m * n A c *= 使
*
* A * x : O(m n)
* m * n A n x
*
* x * A : O(m n)
* m x m * n A
*
* A * B : O(l m n)
* l * m A m * n B
*
* pow(d) : O(n^3 log d)
* d
*/
template <class T> struct Matrix {
int m, n; // m n
vector<vector<T>> v; //
//
Matrix() : m(0), n(0) {}
Matrix(const int& m_, const int& n_) : m(m_), n(n_), v(m_, vector<T>(n_)) {}
Matrix(const int& n_) : m(n_), n(n_), v(n_, vector<T>(n_)) { rep(i, n) v[i][i] = 1; }
Matrix(const vector<vector<T>>& a) : m(sz(a)), n(sz(a[0])), v(a) {}
//
Matrix(const Matrix& b) = default;
Matrix& operator=(const Matrix& b) = default;
//
friend istream& operator>>(istream& is, Matrix& a) {
rep(i, a.m) rep(j, a.n) is >> a.v[i][j];
return is;
}
//
vector<T> const& operator[](int i) const { return v[i]; }
vector<T>& operator[](int i) { return v[i]; }
//
bool operator==(const Matrix& b) const { return m == b.m && n == b.n && v == b.v; }
bool operator!=(const Matrix& b) const { return !(*this == b); }
//
Matrix& operator+=(const Matrix& b) {
rep(i, m) rep(j, n) v[i][j] += b.v[i][j];
return *this;
}
Matrix& operator-=(const Matrix& b) {
rep(i, m) rep(j, n) v[i][j] -= b.v[i][j];
return *this;
}
Matrix& operator*=(const T& c) {
rep(i, m) rep(j, n) v[i][j] *= c;
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 T& c) const { return Matrix(*this) *= c; }
friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
Matrix operator-() const { return Matrix(*this) *= T(-1); }
// : O(m n)
vector<T> operator*(const vector<T>& x) const {
vector<T> y(m);
rep(i, m) rep(j, n) y[i] += v[i][j] * x[j];
return y;
}
// : O(m n)
friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
vector<T> y(a.n);
rep(i, a.m) rep(j, a.n) y[j] += x[i] * a.v[i][j];
return y;
}
// O(n^3)
Matrix operator*(const Matrix& b) const {
// verify : https://judge.yosupo.jp/problem/matrix_product
Matrix res(m, b.n);
rep(i, res.m) rep(j, res.n) rep(k, n) res.v[i][j] += v[i][k] * b.v[k][j];
return res;
}
Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }
// O(n^3 log d)
Matrix pow(ll d) const {
Matrix res(n), pow2 = *this;
while (d > 0) {
if ((d & 1) != 0) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Matrix& a) {
rep(i, a.m) {
rep(j, a.n) os << a.v[i][j] << " ";
os << endl;
}
return os;
}
// Mathematica
void print() const {
cerr << "{\n";
rep(i, m) {
cerr << "{";
rep(j, n) cerr << v[i][j] << (j < n - 1 ? "," : "}");
cerr << (i < m - 1 ? ",\n" : "\n");
}
cerr << "}\n";
}
#endif
};
//
/*
* Map_composite(vi s, ll k_max) : O(n log(k_max))
* [0..n) i -> s[i]
* apply() k k_max
*
* int apply(int x, ll k) : O(log(k_max))
* s^k[x]
*
* ll max_right(int x, function<bool(int)>& okQ) : O(log(k_max))
* okQ(s^k[x]) = true okQ(s^(k+1)[x]) = false k
*
*
*/
class Map_composite {
int n, K;
// dp[i][j] : s^(2^i)[j]
vvi dp;
public:
// [0..n) i -> s[i]
Map_composite(const vi& s, ll k_max = 1LL << 62) : n(sz(s)), K(msb(k_max) + 1), dp(K, vi(n)) {
// verify : https://atcoder.jp/contests/abc212/tasks/abc212_f
// s^(2^0)[j] = s[j]
rep(j, n) dp[0][j] = s[j];
rep(i, K - 1) {
rep(j, n) {
// s^(2^(i+1))[j] = s^(2^i)[ s^(2^i)[j] ]
dp[i + 1][j] = dp[i][dp[i][j]];
}
}
}
// s^k[x]
int apply(int x, ll k) const {
// verify : https://atcoder.jp/contests/abc212/tasks/abc212_f
rep(i, K) {
if (k & (1LL << i)) {
x = dp[i][x];
}
}
return x;
}
// okQ[s^k[x]] = true okQ[s^(k+1)[x]] = false k
ll max_right(int x, function<bool(int)>& okQ) const {
// verify : https://atcoder.jp/contests/arc060/tasks/arc060_c
ll res = 0;
repir(i, K - 1, 0) {
res <<= 1;
if (okQ(dp[i][x])) {
res++;
x = dp[i][x];
}
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Map_composite& mc) {
rep(i, mc.K) {
os << (1LL << i) << ":" << endl;
rep(j, mc.n) os << mc.dp[i][j] << " "; os << endl;
}
return os;
}
#endif
};
// m :
void WA() {
int n; ll m, l;
cin >> n >> m >> l;
mint::set_mod(10000);
vi s(10000);
rep(i, 10000) {
Matrix<mint> mat(vvm{ {i, 1}, {1, 0} });
mat = mat.pow(m);
s[i] = mat[0][1].val();
}
Map_composite mc(s, l);
int res = mc.apply(n, l);
cout << setfill('0') << right << setw(4) << res << endl;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n; ll m, l;
cin >> n >> m >> l;
if (l == 0) {
cout << setfill('0') << right << setw(4) << n << endl;
return 0;
}
if (m == 0) {
cout << setfill('0') << right << setw(4) << 0 << endl;
return 0;
}
mint::set_mod(10000);
vi s(10000);
rep(i, 10000) {
Matrix<mint> mat(vvm{ {i, 2, -i, -1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0} });
mat = mat.pow(m);
vm vec{ i * i, i, 0, 0 };
vec = mat * vec;
if (i == n) {
dump(mat);
dump(vec);
}
s[i] = vec[3].val();
}
Map_composite mc(s, l);
int res = mc.apply(n, l);
cout << setfill('0') << right << setw(4) << res << endl;
}
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