結果
問題 | No.2122 黄金比で擬似乱数生成 |
ユーザー |
|
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 |
ソースコード
#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;}// 行基本変形を用いて簡約化を行い、(rank, det) の組を返す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 が小数の場合はこちら}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);}// 行基本変形を行い、逆行列を求める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 が小数の場合はこちら}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 の解の 1 つと解空間の基底の組を返す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';}