結果
問題 | No.950 行列累乗 |
ユーザー | haruki_K |
提出日時 | 2019-12-14 01:51:13 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
RE
|
実行時間 | - |
コード長 | 12,305 bytes |
コンパイル時間 | 2,676 ms |
コンパイル使用メモリ | 211,200 KB |
実行使用メモリ | 17,496 KB |
最終ジャッジ日時 | 2024-06-28 01:00:33 |
合計ジャッジ時間 | 17,827 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge1 |
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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 | 8 ms
5,248 KB |
testcase_01 | RE | - |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 43 ms
5,376 KB |
testcase_06 | AC | 2 ms
5,376 KB |
testcase_07 | AC | 2 ms
5,376 KB |
testcase_08 | AC | 2 ms
5,376 KB |
testcase_09 | AC | 2 ms
5,376 KB |
testcase_10 | AC | 3 ms
5,376 KB |
testcase_11 | AC | 2 ms
5,376 KB |
testcase_12 | RE | - |
testcase_13 | AC | 3 ms
5,376 KB |
testcase_14 | AC | 3 ms
5,376 KB |
testcase_15 | RE | - |
testcase_16 | AC | 3 ms
5,376 KB |
testcase_17 | AC | 2 ms
5,376 KB |
testcase_18 | AC | 2 ms
5,376 KB |
testcase_19 | AC | 2 ms
5,376 KB |
testcase_20 | AC | 2 ms
5,376 KB |
testcase_21 | RE | - |
testcase_22 | AC | 548 ms
14,960 KB |
testcase_23 | AC | 47 ms
5,376 KB |
testcase_24 | AC | 581 ms
12,952 KB |
testcase_25 | AC | 58 ms
5,376 KB |
testcase_26 | AC | 59 ms
5,376 KB |
testcase_27 | RE | - |
testcase_28 | AC | 498 ms
13,968 KB |
testcase_29 | AC | 430 ms
13,096 KB |
testcase_30 | AC | 577 ms
13,248 KB |
testcase_31 | AC | 463 ms
12,532 KB |
testcase_32 | AC | 594 ms
16,952 KB |
testcase_33 | AC | 631 ms
13,812 KB |
testcase_34 | AC | 635 ms
16,808 KB |
testcase_35 | AC | 543 ms
13,952 KB |
testcase_36 | AC | 2 ms
5,376 KB |
testcase_37 | AC | 8 ms
5,376 KB |
testcase_38 | AC | 9 ms
5,376 KB |
testcase_39 | AC | 2 ms
5,376 KB |
testcase_40 | AC | 80 ms
5,912 KB |
testcase_41 | AC | 59 ms
5,972 KB |
testcase_42 | RE | - |
testcase_43 | AC | 693 ms
17,236 KB |
testcase_44 | AC | 713 ms
17,364 KB |
testcase_45 | AC | 879 ms
17,496 KB |
testcase_46 | AC | 715 ms
17,364 KB |
testcase_47 | AC | 2 ms
5,376 KB |
testcase_48 | AC | 710 ms
17,236 KB |
testcase_49 | AC | 753 ms
17,152 KB |
testcase_50 | AC | 820 ms
17,364 KB |
testcase_51 | AC | 819 ms
17,240 KB |
testcase_52 | AC | 14 ms
5,504 KB |
testcase_53 | AC | 14 ms
5,376 KB |
testcase_54 | AC | 2 ms
5,376 KB |
testcase_55 | AC | 2 ms
5,376 KB |
testcase_56 | AC | 12 ms
5,376 KB |
testcase_57 | AC | 2 ms
5,376 KB |
testcase_58 | AC | 2 ms
5,376 KB |
testcase_59 | AC | 2 ms
5,376 KB |
testcase_60 | AC | 2 ms
5,376 KB |
ソースコード
// >>> TEMPLATES #include <bits/stdc++.h> using namespace std; #define rep(i,n) for (int i = 0; i < int(n); i++) #define rep1(i,n) for (int i = 1; i <= int(n); i++) #define repR(i,n) for (int i = int(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = int(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second #ifdef LOCAL #define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__) #define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl; #define debug if (1) void dump_impl(const char*) { cerr << endl; } template <class T, class... U> void dump_impl(const char *s, T const& x, U const& ...y) { const char *o = "({[", *e = "]})"; for (int i = 0; *s != '\0'; cerr << *s++) { if (count(o,o+3,*s)) i++; if (count(e,e+3,*s)) i--; if (!i && *s == ',') break; } cerr << " = " << x; if (*s == ',') cerr << ", ", s++; dump_impl(s, y...); } #else #define dump(...) #define say(x) #define debug if (0) #endif using ll = long long; using ld = long double; template <class T> using pque_max = priority_queue<T>; template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >; template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type> ostream& operator<<(ostream& os, T const& v) { os << "{"; for (auto const& x : v) os << " " << x; return os << " }"; } template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; } template <size_t i, class T> typename enable_if<i >= tuple_size<T>::value>::type output_tuple(ostream&, T const&) { } template <size_t i = 0, class T> typename enable_if<i < tuple_size<T>::value>::type output_tuple(ostream& os, T const& t) { os << (i ? " " : "") << get<i>(t); output_tuple<i+1,T>(os,t); } template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) { return output_tuple(os,t), os; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template <class F> struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward<F>(f)) {} template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); } }; struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template <class T, size_t d> struct vec_impl { using type = vector<typename vec_impl<T,d-1>::type>; template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); } }; template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } }; template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type; template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); } template <class T> void quit(T const& x) { cout << x << endl; exit(0); } template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; } template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; } template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); } #define int ll #define double ld template <class T> int sz(T const& x) { return x.size(); } const ll INF = (1LL<<62)-1; // ~ 4.6e18 // <<< // >>> runtime modint class runtime_modint { using ll = long long; using M = runtime_modint; ll x; public: static ll& mod() { static ll mod = 0; return mod; } runtime_modint(ll x = 0) : x((assert(mod() > 0), ((x%=mod()) < 0 ? x+mod() : x))) { } constexpr ll val() const { return x; } constexpr bool operator==(M const& r) const { return x == r.x; } constexpr bool operator!=(M const& r) const { return x != r.x; } M operator+() const { return *this; } M operator-() const { return M()-*this; } M& operator+=(M const& r) { if ((x += r.x) >= mod()) x -= mod(); return *this; } M& operator-=(M const& r) { if ((x += mod()-r.x) >= mod()) x -= mod(); return *this; } M& operator*=(M const& r) { return *this = *this * r; } M operator*(M const& r) const { M t; t.x = (x*r.x) % mod(); return t; } M& operator/=(M const& r) { return *this *= r.inv(); } M operator+(M const& r) const { return M(*this) += r; } M operator-(M const& r) const { return M(*this) -= r; } M operator/(M const& r) const { return M(*this) /= r; } friend M operator+(ll x, M const& y) { return M(x)+y; } friend M operator-(ll x, M const& y) { return M(x)-y; } friend M operator*(ll x, M const& y) { return M(x)*y; } friend M operator/(ll x, M const& y) { return M(x)/y; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } M inv() const { assert(x > 0); ll t = 1, v = x, q = 0, r = 0; while (v != 1) { q = mod() / v; r = mod() % v; if (r * 2 < v) { t *= -q; t %= mod(); v = r; } else { t *= q + 1; t %= mod(); v -= r; } } if (t < 0) t += mod(); M y; y.x = t; return y; } static ll gen() { // assume mod():prime if (mod() == 2) return 1; vector<int> ps; int n = mod()-1; for (int i = 2; i*i <= n; ++i) { if (n % i) continue; ps.push_back(i); do n /= i; while (n % i == 0); } if (n > 1) ps.push_back(n); n = mod()-1; auto check = [&](M g) { for (int p : ps) if (g.pow(n/p) == 1) return false; return true; }; for (int g = 2; g <= n; ++g) if (check(g)) return g; return -1; } int log(M y) { assert(x > 0); int s = 1; while (s*s < mod()) s++; unordered_map<int,int> m; M c = 1; rep (i,s) { if (!m.count(c.val())) m[c.val()] = i; c *= *this; } M d = pow(-s); c = y; rep (i,s) { if (m.count(c.val())) { int ans = i*s + m[c.val()]; if (ans > 0) return ans; } c *= d; } return -1; } }; ostream& operator<<(ostream& os, runtime_modint r) { return os << r.val(); } istream& operator>>(istream& is, runtime_modint &r) { ll x; is >> x; r = x; return is; } using mint = runtime_modint; // <<< // >>> matrix template <class T> struct Matrix { int n,m; vector<vector<T> > a; Matrix() {} Matrix(int n, int m) : n(n), m(m), a(n) { assert(n > 0 && m > 0); rep (i,n) a[i].resize(m); } Matrix(initializer_list<initializer_list<T> > init) { for (auto ls : init) { a.emplace_back(); for (auto x : ls) a.back().emplace_back(x); } n = a.size(); assert(n > 0); m = a[0].size(); assert(m > 0); } vector<T> const& operator[](int i) const { assert(0 <= i && i < n); return a[i]; } vector<T> & operator[](int i) { assert(0 <= i && i < n); return a[i]; } bool operator==(Matrix const& x) const { if (n != x.n || m != x.m) return false; rep (i,n) rep (j,m) if (a[i][j] != x[i][j]) return false; return true; } bool operator!=(Matrix const& x) const { return !(*this == x); } Matrix& operator+=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] += x[i][j]; return *this; } Matrix& operator-=(Matrix const& x) { assert(n == x.n && m == x.m); rep (i,n) rep (j,m) a[i][j] -= x[i][j]; return *this; } Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; } Matrix operator-(Matrix const& x) const { return Matrix(*this) -= x; } Matrix operator*(Matrix const& x) const { assert(m == x.n); Matrix ret(n,x.m); rep (i,n) rep (j,m) rep (k,x.m) ret[i][k] += a[i][j] * x[j][k]; return ret; } Matrix& operator*=(Matrix const& x) { auto res = (*this)*x; swap(a, res.a); return *this; } Matrix operator+() const { return *this; } Matrix operator-() const { Matrix x = *this; rep (i,n) rep (j,m) x[i][j] = -x[i][j]; return x; } Matrix& operator*=(T const& c) { rep (i,n) rep (j,m) a[i][j] *= c; return *this; } Matrix operator*(T const& c) const { return Matrix(*this) *= c; } friend Matrix operator*(T const& c, Matrix const& x) { Matrix ret = x; rep (i,x.n) rep (j,x.m) ret[i][j] = c*x[i][j]; return ret; } Matrix& operator/=(T const& c) { rep (i,n) rep (j,m) a[i][j] /= c; return *this; } Matrix operator/(T const& c) const { return Matrix(*this) /= c; } static Matrix identity(int n) { Matrix ret(n,n); rep (i,n) ret[i][i] = 1; return ret; } Matrix pow(ll k) const { assert(n == m); assert(k >= 0); Matrix v = *this, r = Matrix::identity(n); for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v; return r; } }; template <class T> istream& operator>>(istream& is, Matrix<T>& x) { rep (i,x.n) rep (j,x.m) is >> x[i][j]; return is; } template <class T> ostream& operator<<(ostream& os, Matrix<T> const& x) { rep (i,x.n) { os << "\n("; rep (j,x.m) os << " " << x[i][j]; os << " )"; } return os << "\n"; } // <<< bool operator<(Matrix<mint> const& a, Matrix<mint> const& b) { auto aa = make_v<int,2>(2,2); auto bb = make_v<int,2>(2,2); rep (i,2) rep (j,2) aa[i][j] = a[i][j].val(); rep (i,2) rep (j,2) bb[i][j] = b[i][j].val(); return aa < bb; } mint det(Matrix<mint> const& x) { assert(x.n == 2 && x.m == 2); return x[0][0]*x[1][1] - x[0][1]*x[1][0]; } mint trace(Matrix<mint> const& x) { assert(x.n == 2 && x.m == 2); return x[0][0] + x[1][1]; } Matrix<mint> inv(Matrix<mint> const& x) { assert(x.n == 2 && x.m == 2); assert(det(x) != 0); Matrix<mint> ret = { { x[1][1], -x[0][1] }, { -x[1][0], x[0][0] } }; return ret * det(x).inv(); } int32_t main() { int p; cin >> p; mint::mod() = p; Matrix<mint> a(2,2),b(2,2); cin >> a.a >> b.a; const int NN = 20; rep1 (i,NN) if (a.pow(i) == b) quit(i); Matrix<mint> zero(2,2), id = Matrix<mint>::identity(2); if (a == zero || a*a == zero) quit(-1); if (det(a) == 0) { auto t = trace(a); assert(t != 0); set<int> s; rep (i,2) rep (j,2) if (a[i][j] != 0) s.insert((b[i][j]/a[i][j]).val()); if (s.empty() || sz(s) > 1) quit(-1); int x = *s.begin(); dump(t,x); int ans = t.log(x*t); dump(ans); if (a.pow(ans) != b) quit(-1); else quit(ans); } assert(det(a) != 0); b *= inv(a); int r = det(b) == 1 ? 0 : det(a).log(det(b)); int m = det(a).log(1); b *= inv(a).pow(r); a = a.pow(m); dump(r,m,a,b); int s = 1; while (s*s < 2*p) s++; map<Matrix<mint>, int> mp; auto c = id; rep (i,s) { if (!mp.count(c)) mp[c] = i; c *= a; } auto d = inv(a).pow(s); c = b; rep (i,s) { if (mp.count(c)) { int q = i*s + mp[c]; quit(1+r+q*m); } c *= d; } quit(-1); }