#408416 (C++14) No.950 行列累乗

提出ソース

結果

問題	No.950 行列累乗
ユーザー	haruki_K
提出日時	2019-12-14 01:58:34
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	928 ms / 2,000 ms
コード長	12,454 bytes
コンパイル時間	2,636 ms
コンパイル使用メモリ	209,204 KB
実行使用メモリ	17,440 KB
最終ジャッジ日時	2023-09-10 09:40:49
合計ジャッジ時間	17,533 ms
ジャッジサーバーID （参考情報）	judge15 / judge14

このコードへのチャレンジ
（要ログイン）

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 4,464 KB
testcase_01	AC	9 ms 4,380 KB
testcase_02	AC	1 ms 4,380 KB
testcase_03	AC	2 ms 4,380 KB
testcase_04	AC	2 ms 4,376 KB
testcase_05	AC	43 ms 4,924 KB
testcase_06	AC	3 ms 4,376 KB
testcase_07	AC	2 ms 4,376 KB
testcase_08	AC	2 ms 4,376 KB
testcase_09	AC	2 ms 4,380 KB
testcase_10	AC	2 ms 4,380 KB
testcase_11	AC	2 ms 4,380 KB
testcase_12	AC	1 ms 4,380 KB
testcase_13	AC	2 ms 4,376 KB
testcase_14	AC	2 ms 4,376 KB
testcase_15	AC	1 ms 4,380 KB
testcase_16	AC	2 ms 4,380 KB
testcase_17	AC	1 ms 4,376 KB
testcase_18	AC	1 ms 4,380 KB
testcase_19	AC	2 ms 4,380 KB
testcase_20	AC	1 ms 4,376 KB
testcase_21	AC	25 ms 5,912 KB
testcase_22	AC	564 ms 14,980 KB
testcase_23	AC	47 ms 4,956 KB
testcase_24	AC	585 ms 12,904 KB
testcase_25	AC	57 ms 4,516 KB
testcase_26	AC	60 ms 4,928 KB
testcase_27	AC	16 ms 4,672 KB
testcase_28	AC	522 ms 14,104 KB
testcase_29	AC	439 ms 13,000 KB
testcase_30	AC	606 ms 13,120 KB
testcase_31	AC	482 ms 12,344 KB
testcase_32	AC	623 ms 16,952 KB
testcase_33	AC	644 ms 13,904 KB
testcase_34	AC	656 ms 17,012 KB
testcase_35	AC	575 ms 13,776 KB
testcase_36	AC	1 ms 4,376 KB
testcase_37	AC	9 ms 4,380 KB
testcase_38	AC	9 ms 4,412 KB
testcase_39	AC	2 ms 4,376 KB
testcase_40	AC	81 ms 6,160 KB
testcase_41	AC	61 ms 6,008 KB
testcase_42	AC	24 ms 5,944 KB
testcase_43	AC	697 ms 17,216 KB
testcase_44	AC	748 ms 17,212 KB
testcase_45	AC	928 ms 17,128 KB
testcase_46	AC	737 ms 17,440 KB
testcase_47	AC	1 ms 4,376 KB
testcase_48	AC	743 ms 17,156 KB
testcase_49	AC	754 ms 17,124 KB
testcase_50	AC	853 ms 17,216 KB
testcase_51	AC	859 ms 17,304 KB
testcase_52	AC	14 ms 5,656 KB
testcase_53	AC	14 ms 5,584 KB
testcase_54	AC	2 ms 4,380 KB
testcase_55	AC	1 ms 4,376 KB
testcase_56	AC	11 ms 5,356 KB
testcase_57	AC	2 ms 4,380 KB
testcase_58	AC	2 ms 4,376 KB
testcase_59	AC	1 ms 4,376 KB
testcase_60	AC	2 ms 4,380 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

raw source code

// >>> 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);
    if (p == 2) quit(-1);

    Matrix<mint> zero(2,2), id = Matrix<mint>::identity(2);
    if (a == zero || a*a == zero) quit(-1);

    if (det(a) == 0) {
        say("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 (ans == -1) quit(-1);
        if (a.pow(ans) != b) quit(-1); else quit(ans);
    }
    assert(det(a) != 0);
    say("det(a) != 0");
    b *= inv(a);

    int r = det(b) == 1 ? 0 : det(a).log(det(b));
    int m = det(a).log(1);
    dump(r,m);
    if (r == -1) quit(-1);

    b *= inv(a).pow(r);
    a = a.pow(m);
    dump(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);

}

yukicoder

結果

テストケース

ソースコード