#684513 (C++17) No.1632 Sorting Integers (GCD of M)

提出ソース

結果

問題	No.1632 Sorting Integers (GCD of M)
ユーザー	haruki_K
提出日時	2021-07-30 21:57:11
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	RE
実行時間	-
コード長	13,818 bytes
コンパイル時間	2,437 ms
コンパイル使用メモリ	211,880 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-16 00:04:23
合計ジャッジ時間	5,291 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

このコードへのチャレンジ
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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
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	2 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	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	1 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 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	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 ms 5,376 KB
testcase_25	AC	2 ms 5,376 KB
testcase_26	AC	2 ms 5,376 KB
testcase_27	AC	2 ms 5,376 KB
testcase_28	AC	2 ms 5,376 KB
testcase_29	AC	2 ms 5,376 KB
testcase_30	AC	2 ms 5,376 KB
testcase_31	AC	2 ms 5,376 KB
testcase_32	AC	2 ms 5,376 KB
testcase_33	AC	2 ms 5,376 KB
testcase_34	AC	2 ms 5,376 KB
testcase_35	AC	2 ms 5,376 KB
testcase_36	AC	1 ms 5,376 KB
testcase_37	AC	2 ms 5,376 KB
testcase_38	AC	2 ms 5,376 KB
testcase_39	AC	2 ms 5,376 KB
testcase_40	AC	2 ms 5,376 KB
testcase_41	AC	2 ms 5,376 KB
testcase_42	AC	2 ms 5,376 KB
testcase_43	AC	2 ms 5,376 KB
testcase_44	AC	2 ms 5,376 KB
testcase_45	AC	2 ms 5,376 KB
testcase_46	AC	2 ms 5,376 KB
testcase_47	AC	2 ms 5,376 KB
testcase_48	AC	2 ms 5,376 KB
testcase_49	AC	2 ms 5,376 KB
testcase_50	AC	2 ms 5,376 KB
testcase_51	AC	2 ms 5,376 KB
testcase_52	AC	2 ms 5,376 KB
testcase_53	AC	2 ms 5,376 KB
testcase_54	AC	2 ms 5,376 KB
testcase_55	AC	2 ms 5,376 KB
testcase_56	AC	2 ms 5,376 KB
testcase_57	AC	2 ms 5,376 KB
testcase_58	AC	2 ms 5,376 KB
testcase_59	RE	-
testcase_60	RE	-
testcase_61	RE	-
testcase_62	RE	-

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#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) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define rng(x, l, r) begin(x) + (l), begin(x) + (r)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class A, class B> constexpr auto mp(A &&a, B &&b) { return make_pair(forward<A>(a), forward<B>(b)); }
template <class... T> constexpr auto mt(T&&... x) { return make_tuple(forward<T>(x)...); }
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) 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; }
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, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)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{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class T> vector<T> &operator--(vector<T> &v) { for (T &x : v) --x; return v; }
template <class T> vector<T> &operator++(vector<T> &v) { for (T &x : v) ++x; return v; }
// <<<
// >>> matrix (array)
template <class T>
decltype(T::one()) semi_ring_one(signed) { return T::one(); }
template <class T>
constexpr T semi_ring_one(long) { return 1; }
template <class T, size_t N, size_t M>
struct Matrix {
    int n = N, m = M;
    array<array<T, M>, N> a;
    Matrix() : a() {}
    Matrix(initializer_list<initializer_list<T>> init) {
        size_t i = 0;
        for (auto ls : init) {
            size_t j = 0;
            for (auto const& x : ls) {
                a[i][j] = x;
                j++;
            }
            assert((int)j == m);
            i++;
        }
        assert((int)i == n);
    }
    array<T, M> const& operator[](int i) const {
        assert(0 <= i); assert(i < n);
        return a[i];
    }
    array<T, M> & operator[](int i) {
        assert(0 <= i); assert(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+() const { return *this; }
    Matrix operator+(Matrix const& x) const { return Matrix(*this) += x; }
    Matrix& operator+=(Matrix const& x) {
        assert(n == x.n); assert(m == x.m);
        rep (i, n) rep (j, m) a[i][j] += x[i][j];
        return *this;
    }
    template <size_t L>
    Matrix<T, N, L> operator*(Matrix<T, M, L> const& x) const {
        assert(m == x.n);
        Matrix<T, N, L> ret;
        rep (i, n) rep (j, m) rep (k, x.m) ret[i][k] += a[i][j] * x[j][k];
        return ret;
    }
    Matrix& operator*=(Matrix<T, M, M> const& x) {
        auto res = (*this)*x;
        swap(a, res.a);
        return *this;
    }
    Matrix operator*(T const& c) const { return Matrix(*this) *= c; }
    Matrix& operator*=(T const& c) {
        rep (i, n) rep (j, m) a[i][j] *= c;
        return *this;
    }
    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;
    }
    static Matrix identity() {
        assert(N == M);
        Matrix ret;
        rep (i, N) ret[i][i] = semi_ring_one<T>(0);
        return ret;
    }
    Matrix pow(ll k) const {
        assert(n == m); assert(k >= 0);
        Matrix v = *this, r = Matrix::identity();
        for (; k > 0; k >>= 1, v *= v) if (k&1) r *= v;
        return r;
    }
#if 1
    Matrix operator-() const {
        Matrix x = *this;
        rep (i, n) rep (j, m) x[i][j] = -x[i][j];
        return x;
    }
    Matrix& operator-=(Matrix const& x) {
        assert(n == x.n); assert(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/=(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;
    }
#endif
    friend istream& operator>>(istream& is, Matrix& x) {
        rep (i, x.n) rep (j, x.m) is >> x[i][j];
        return is;
    }
#ifdef LOCAL
    friend string to_s(Matrix const& x) {
        string ret;
        rep (i, x.n) {
            ret += "\n(";
            rep (j, x.m) ret += " " + to_s(x[i][j]);
            ret += " )";
        }
        return ret += "\n";
    }
#endif
};

// <<<
// >>> runtime modint

template <int id> class runtime_modint {
    using u32 = uint32_t;
    using i32 = int32_t;
    using i64 = int64_t;
    using M = runtime_modint;
    u32 x;
    struct barrett {
        uint32_t mod;
        uint64_t inv;
        barrett() : mod(0), inv(0) { }
        barrett(uint32_t mod) : mod(mod), inv((uint64_t)(-1) / mod + 1) { }
        uint32_t operator()(uint32_t a, uint32_t b) const {
            return operator()(uint64_t(a) * b);
        }
        uint32_t operator()(uint64_t a) const {
            const __uint128_t c = a;
            const uint64_t q = (c * inv) >> 64;
            uint32_t x = c - q * mod;
            if (mod <= x) x += mod;
            return x;
        }
    };
    inline static barrett bar;
public:
    static void set_mod(u32 new_mod) { bar = barrett(new_mod); }
    static int mod() { return bar.mod; }
    runtime_modint(i64 x = 0) {
        assert(mod() > 0);
        if (x < 0) {
            x = -x;
            this->x = bar(x);
            if (this->x > 0) this->x = mod() - this->x;
        } else {
            this->x = bar(x);
        }
    }
    i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    bool operator==(M const& r) const { return x == r.x; }
    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) { i64 t = i64(x) + r.x; if (t >= mod()) t -= mod(); x = t; return *this; }
    M& operator-=(M const& r) { i64 t = i64(x) + mod()-r.x; if (t >= mod()) t -= mod(); x = t; return *this; }
    M& operator*=(M const& r) { x = bar(x, r.x); return *this; }
    M& operator/=(M const& r) { return *this *= r.inv(); }
    M operator+(M r) const { return M(*this) += r; }
    M operator-(M r) const { return M(*this) -= r; }
    M operator*(M r) const { return M(*this) *= r; }
    M operator/(M r) const { return M(*this) /= r; }
    friend M operator+(i64 x, M y) { return M(x)+y; }
    friend M operator-(i64 x, M y) { return M(x)-y; }
    friend M operator*(i64 x, M y) { return M(x)*y; }
    friend M operator/(i64 x, M y) { return M(x)/y; }
    M pow(i64 n) const { // 0^0 = 1
        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 {
        uint32_t a = x, b = mod();
        int64_t u = 1, v = 0;
        while (b) {
            int64_t q = a / b;
            swap(a -= q * b, b);
            swap(u -= q * v, v);
        }
        assert(a == 1);
        return u;
    }
    static i64 gen() { // assume mod():prime
        if (mod() == 2) return 1;
        assert(mod() >= 3);
        for (int i = 2; i*i <= mod(); i++) assert(mod() % i != 0);
        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;
    }

    // return minimum k >= (allow_zero ? 0 : 1) s.t. this->pow(k) == y
    // return -1 if not found
    int log(M y, bool allow_zero = false) {
        if (allow_zero and pow(0) == y) return 0;
        auto x = *this;
        M z = 1;
        int k = 0;
        while ((1u << k) < mod()) {
            z *= x, k++;
            if (z == y) return k;
        }
        u32 g = gcd(z.x, mod());
        if (y.x % g != 0) return -1;

        auto old_bar = bar;
        bar = barrett(mod()/g);
        x.x %= mod(), y.x /= g, z.x /= g;
        unordered_map<u32, u32> m;
        int s = 0;
        M w = 1;
        for ( ; s*s < mod(); s++) m[(y*w).x] = s, w *= x;
        while (k < mod()) {
            z *= w, k += s;
            if (m.count(z.x)) {
                swap(bar, old_bar);
                return k - m[z.x];
            }
        }
        swap(bar, old_bar);
        return -1;
    }
#ifdef LOCAL
//    friend string to_s(M r) { return to_s(r.val(), M::mod()); }
    friend string to_s(M r) { return to_s(r.val()); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};

using mint = runtime_modint<-1>;

// <<<

int32_t main() {
    int n; cin >> n;
    vector<int> c(10);
    rep1 (i, 9) cin >> c[i];

    int g = 0;
    rep1 (i, 9) rep1 (j, 9) if (c[i] > 0 and c[j] > 0) {
        g = gcd(g, abs(i-j)*9);
    }
    dump(g);

    if (n == 1) g = 1e9 + 7;

    mint::set_mod(g);
    using M = Matrix<mint, 2, 2>;
    auto A = M::identity();
    rep1 (i, 9) {
        M B = {
            { 10, i },
            { 0, 1 }
        };
        A = B.pow(c[i]) * A;
    }

    int x = A[0][1].val();
    dump(x);

    if (n == 1) {
        cout << x << '\n';
    } else {
        cout << gcd(g, x) << '\n';
    }


}

yukicoder

結果

テストケース

ソースコード