結果

問題 No.2122 黄金比で擬似乱数生成
ユーザー tokusakuraitokusakurai
提出日時 2022-11-04 23:36:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 130 ms / 2,000 ms
コード長 10,566 bytes
コンパイル時間 2,289 ms
コンパイル使用メモリ 208,460 KB
最終ジャッジ日時 2025-02-08 18:24:07
ジャッジサーバーID
(参考情報)
judge5 / judge1
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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

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 10000;
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int &p) const { return x == p.x; }
bool operator!=(const Mod_Int &p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
using mint = Mod_Int<MOD>;
template <typename T>
struct Matrix {
vector<vector<T>> A;
Matrix(int m, int n) : A(m, vector<T>(n, 0)) {}
int height() const { return A.size(); }
int width() const { return A.front().size(); }
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int l) {
Matrix ret(l, l);
for (int i = 0; i < l; i++) ret[i][i] = 1;
return ret;
}
Matrix &operator*=(const Matrix &B) {
int m = height(), n = width(), p = B.width();
assert(n == B.height());
Matrix ret(m, p);
for (int i = 0; i < m; i++) {
for (int k = 0; k < n; k++) {
for (int j = 0; j < p; j++) ret[i][j] += A[i][k] * B[k][j];
}
}
swap(A, ret.A);
return *this;
}
Matrix operator*(const Matrix &B) const { return Matrix(*this) *= B; }
Matrix pow(long long k) const {
int m = height(), n = width();
assert(m == n);
Matrix now = *this, ret = I(n);
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
bool eq(const T &a, const T &b) const {
return a == b;
// return abs(a-b) <= EPS;
}
// (rank, det)
pair<int, T> row_reduction(vector<T> &b) {
int m = height(), n = width(), check = 0, rank = 0;
T det = 1;
assert(b.size() == m);
for (int j = 0; j < n; j++) {
int pivot = check;
for (int i = check; i < m; i++) {
if (A[i][j] != 0) pivot = i;
// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T
}
if (check != pivot) det *= T(-1);
swap(A[check], A[pivot]), swap(b[check], b[pivot]);
if (eq(A[check][j], T(0))) {
det = T(0);
continue;
}
rank++;
det *= A[check][j];
T r = T(1) / A[check][j];
for (int k = j + 1; k < n; k++) A[check][k] *= r;
b[check] *= r;
A[check][j] = T(1);
for (int i = 0; i < m; i++) {
if (i == check) continue;
if (!eq(A[i][j], 0)) {
for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[check][k];
b[i] -= A[i][j] * b[check];
}
A[i][j] = T(0);
}
if (++check == m) break;
}
return make_pair(rank, det);
}
pair<int, T> row_reduction() {
vector<T> b(height(), T(0));
return row_reduction(b);
}
//
Matrix inverse() {
if (height() != width()) return Matrix(0, 0);
int n = height();
Matrix ret = I(n);
for (int j = 0; j < n; j++) {
int pivot = j;
for (int i = j; i < n; i++) {
if (A[i][j] != 0) pivot = i;
// if(abs(A[i][j]) > abs(A[pivot][j])) pivot = i; // T
}
swap(A[j], A[pivot]), swap(ret[j], ret[pivot]);
if (eq(A[j][j], T(0))) return Matrix(0, 0);
T r = T(1) / A[j][j];
for (int k = j + 1; k < n; k++) A[j][k] *= r;
for (int k = 0; k < n; k++) ret[j][k] *= r;
A[j][j] = T(1);
for (int i = 0; i < n; i++) {
if (i == j) continue;
if (!eq(A[i][j], T(0))) {
for (int k = j + 1; k < n; k++) A[i][k] -= A[i][j] * A[j][k];
for (int k = 0; k < n; k++) ret[i][k] -= A[i][j] * ret[j][k];
}
A[i][j] = T(0);
}
}
return ret;
}
// Ax = b 1
vector<vector<T>> Gausiann_elimination(vector<T> b) {
int m = height(), n = width();
row_reduction(b);
vector<vector<T>> ret;
vector<int> p(m, n);
vector<bool> is_zero(n, true);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (!eq(A[i][j], T(0))) {
p[i] = j;
break;
}
}
if (p[i] < n)
is_zero[p[i]] = false;
else if (!eq(b[i], T(0)))
return {};
}
vector<T> x(n, T(0));
for (int i = 0; i < m; i++) {
if (p[i] < n) x[p[i]] = b[i];
}
ret.push_back(x);
for (int j = 0; j < n; j++) {
if (!is_zero[j]) continue;
x[j] = T(1);
for (int i = 0; i < m; i++) {
if (p[i] < n) x[p[i]] = -A[i][j];
}
ret.push_back(x), x[j] = T(0);
}
return ret;
}
};
using mat = Matrix<mint>;
int main() {
int K = 10000;
string S;
ll M, L;
cin >> S >> M >> L;
vector<vector<int>> next(61, vector<int>(K));
rep(i, K) {
mat A(2, 2);
A[0][0] = i;
A[0][1] = 1;
A[1][0] = 1;
A = A.pow(M);
mint x = A[1][0];
if (M % 2 == 1) x--;
next[0][i] = x.x;
}
rep(i, 60) {
rep(j, K) {
next[i + 1][j] = next[i][next[i][j]]; //
}
}
int s = stoi(S);
rep(i, 61) {
if (flg(L, i)) s = next[i][s];
}
string T = to_string(s);
while (sz(T) < 4) T = '0' + T;
cout << T << '\n';
}
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