#427205 (C++14) No.981 一般冪乗根

提出ソース

結果

問題	No.981 一般冪乗根
ユーザー	haruki_K
提出日時	2020-02-07 23:20:45
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	TLE (最新) AC (最初)
実行時間	-
コード長	7,431 bytes
コンパイル時間	1,709 ms
コンパイル使用メモリ	179,200 KB
実行使用メモリ	6,820 KB
最終ジャッジ日時	2024-10-09 14:45:38
合計ジャッジ時間	96,999 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

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	5,635 ms 5,248 KB
testcase_01	AC	5,513 ms 5,248 KB
testcase_02	AC	5,320 ms 6,816 KB
testcase_03	AC	5,405 ms 6,816 KB
testcase_04	AC	5,325 ms 6,816 KB
testcase_05	AC	161 ms 6,816 KB
testcase_06	AC	162 ms 6,820 KB
testcase_07	AC	162 ms 6,816 KB
testcase_08	AC	162 ms 6,816 KB
testcase_09	AC	161 ms 6,820 KB
testcase_10	AC	162 ms 6,816 KB
testcase_11	AC	161 ms 6,820 KB
testcase_12	AC	161 ms 6,816 KB
testcase_13	AC	163 ms 6,820 KB
testcase_14	AC	161 ms 6,816 KB
testcase_15	AC	163 ms 6,816 KB
testcase_16	AC	161 ms 6,816 KB
testcase_17	AC	161 ms 6,816 KB
testcase_18	AC	161 ms 6,816 KB
testcase_19	AC	162 ms 6,820 KB
testcase_20	AC	161 ms 6,816 KB
testcase_21	AC	161 ms 6,816 KB
testcase_22	AC	162 ms 6,820 KB
testcase_23	AC	161 ms 5,248 KB
testcase_24	AC	163 ms 5,248 KB
testcase_25	AC	5,484 ms 5,248 KB
testcase_26	TLE	-
testcase_27	AC	5 ms 5,248 KB
testcase_28	AC	4,954 ms 5,248 KB
evil_60bit1.txt	RE	-
evil_60bit2.txt	RE	-
evil_60bit3.txt	RE	-
evil_hack	AC	3 ms 5,248 KB
evil_hard_random	RE	-
evil_hard_safeprime.txt	RE	-
evil_hard_tonelli0	RE	-
evil_hard_tonelli1	RE	-
evil_hard_tonelli2	RE	-
evil_hard_tonelli3	RE	-
evil_sefeprime1.txt	RE	-
evil_sefeprime2.txt	RE	-
evil_sefeprime3.txt	RE	-
evil_tonelli1.txt	RE	-
evil_tonelli2.txt	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;
#define int ll
#define double ld
#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
#define INF (numeric_limits<int>::max()/2-1)
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
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) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; 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> 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> 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{}); }
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(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
// <<<
// >>> runtime modint
class runtime_modint {
    using i32 = int32_t;
    using i64 = int64_t;
    using M = runtime_modint;
    i32 x;
public:
    static i32& mod() { static i32 mod = 0; return mod; }
    runtime_modint(i64 x = 0)
        : x((assert(mod() > 0), ((x%=mod()) < 0 ? x+mod() : x))) { }
    i64 val() 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) { return *this = *this * r; }
    M operator*(M const& r) const { M t; t.x = (i64(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);
        i64 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 i64 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;
    }
};
#ifdef LOCAL
string to_s(runtime_modint r) { return to_s(r.val(), runtime_modint::mod()); }
#endif
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;
// <<<
ll extgcd(ll a, ll b, ll &x, ll &y) {
    for (ll v = x = 1, u = y = 0; b; ) {
        ll q = a/b;
        swap(a -= q*b, b);
        swap(x -= q*u, u);
        swap(y -= q*v, v);
    }
    if (a < 0) a = -a, x = -x, y = -y;
    return a;
}

void solve() {
    int p,k,a; cin >> p >> k >> a;
    mint::mod() = p;
    mint gen = mint::gen();
    int n = gen.log(a);
    int x,y;
    int gcd = extgcd(k,p-1,x,y);
    if (n%gcd != 0) {
        cout << -1 << endl;
        return;
    }
    cout << gen.pow(n/gcd*x) << endl;
}

int32_t main() {
    int t; cin >> t;
    while (t--) solve();
}

yukicoder

結果

テストケース

ソースコード