#549005 (C++17) No.1241 Eternal Tours

提出ソース

結果

問題	No.1241 Eternal Tours
ユーザー	hitonanode
提出日時	2020-09-06 12:41:46
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	15,043 bytes
コンパイル時間	2,438 ms
コンパイル使用メモリ	128,448 KB
実行使用メモリ	7,124 KB
最終ジャッジ日時	2024-11-29 10:59:09
合計ジャッジ時間	41,927 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	35 ms 6,816 KB
testcase_04	AC	5 ms 6,820 KB
testcase_05	AC	3 ms 6,816 KB
testcase_06	AC	2 ms 6,820 KB
testcase_07	AC	4 ms 6,820 KB
testcase_08	AC	9 ms 6,820 KB
testcase_09	AC	5 ms 6,820 KB
testcase_10	AC	5 ms 6,816 KB
testcase_11	AC	6 ms 6,820 KB
testcase_12	AC	3 ms 6,816 KB
testcase_13	AC	6 ms 6,820 KB
testcase_14	WA	-
testcase_15	AC	3 ms 6,820 KB
testcase_16	WA	-
testcase_17	WA	-
testcase_18	WA	-
testcase_19	WA	-
testcase_20	AC	69 ms 6,816 KB
testcase_21	AC	449 ms 6,820 KB
testcase_22	WA	-
testcase_23	AC	1,382 ms 6,820 KB
testcase_24	AC	2 ms 6,820 KB
testcase_25	AC	2 ms 6,820 KB
testcase_26	AC	3 ms 6,816 KB
testcase_27	AC	2 ms 6,816 KB
testcase_28	WA	-
testcase_29	AC	57 ms 7,000 KB
testcase_30	AC	2 ms 6,820 KB
testcase_31	AC	34 ms 6,820 KB
testcase_32	WA	-
testcase_33	WA	-
testcase_34	WA	-
testcase_35	WA	-
testcase_36	AC	2 ms 6,820 KB
testcase_37	AC	2 ms 6,816 KB
testcase_38	WA	-
testcase_39	WA	-
testcase_40	WA	-
testcase_41	WA	-
testcase_42	WA	-
testcase_43	WA	-

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

#include <cassert>
#include <algorithm>
#include <array>
#include <chrono>
#include <iostream>
#include <set>
#include <tuple>
#include <vector>
using namespace std;

// Berlekamp-Massey 解法（与える項の数が足りず想定WA）

template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr ModInt pow(lint n) const {
        return power(n);
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }
};
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false);

constexpr int nttprimes[3] = {998244353, 167772161, 469762049};

// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT>
void ntt(std::vector<MODINT> &a, bool is_inverse = false)
{
    int n = a.size();
    if (n == 1) return;
    static const int mod = MODINT::get_mod();
    static const MODINT root = MODINT::get_primitive_root();
    assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);

    static std::vector<MODINT> w{1}, iw{1};
    for (int m = w.size(); m < n / 2; m *= 2)
    {
        MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw;
        w.resize(m * 2), iw.resize(m * 2);
        for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
    }

    if (!is_inverse) {
        for (int m = n; m >>= 1;) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
#ifdef __clang__
                    a[i + m] *= w[k];
                    std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);
#else
                    MODINT x = a[i], y = a[i + m] * w[k];
                    a[i] = x + y, a[i + m] = x - y;
#endif
                }
            }
        }
    }
    else {
        for (int m = 1; m < n; m *= 2) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
#ifdef __clang__
                    std::tie(a[i], a[i + m]) = std::make_pair(a[i] + a[i + m], a[i] - a[i + m]);
                    a[i + m] *= iw[k];
#else
                    MODINT x = a[i], y = a[i + m];
                    a[i] = x + y, a[i + m] = (x - y) * iw[k];
#endif
                }
            }
        }
        int n_inv = MODINT(n).inv();
        for (auto &v : a) v *= n_inv;
    }
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
    int sz = a.size();
    assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
    std::vector<ModInt<MOD>> ap(sz), bp(sz);
    for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
    if (a == b) {
        ntt(ap, false);
        bp = ap;
    }
    else {
        ntt(ap, false);
        ntt(bp, false);
    }
    for (int i = 0; i < sz; i++) ap[i] *= bp[i];
    ntt(ap, true);
    return ap;
}
long long extgcd_ntt_(long long a, long long b, long long &x, long long &y)
{
    long long d = a;
    if (b != 0) d = extgcd_ntt_(b, a % b, y, x), y -= (a / b) * x;
    else x = 1, y = 0;
    return d;
}
long long modinv_ntt_(long long a, long long m)
{
    long long x, y;
    extgcd_ntt_(a, m, x, y);
    return (m + x % m) % m;
}
long long garner_ntt_(int r0, int r1, int r2, int mod)
{
    using mint2 = ModInt<nttprimes[2]>;
    static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
    static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv();
    static const long long m01_inv_m2 = mint2(m01).inv();

    int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
    auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
    return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner)
{
    int sz = 1, n = a.size(), m = b.size();
    while (sz < n + m) sz <<= 1;
    if (sz <= 16) {
        std::vector<MODINT> ret(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
        }
        return ret;
    }
    int mod = MODINT::get_mod();
    if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes))
    {
        a.resize(sz), b.resize(sz);
        if (a == b) { ntt(a, false); b = a; }
        else ntt(a, false), ntt(b, false);
        for (int i = 0; i < sz; i++) a[i] *= b[i];
        ntt(a, true);
        a.resize(n + m - 1);
    }
    else {
        std::vector<int> ai(sz), bi(sz);
        for (int i = 0; i < n; i++) ai[i] = a[i].val;
        for (int i = 0; i < m; i++) bi[i] = b[i].val;
        auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
        auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
        auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
        a.resize(n + m - 1);
        for (int i = 0; i < n + m - 1; i++) {
            a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod);
        }
    }
    return a;
}

constexpr int md = 998244353;
using mint = ModInt<md>;


// Berlekamp–Massey algorithm
// <https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm>
// Complexity: O(N^2)
// input: S = sequence from field K
// return: L          = degree of minimal polynomial,
//         C_reversed = monic min. polynomial (size = L + 1, reversed order, C_reversed[0] = 1))
// Formula: convolve(S, C_reversed)[i] = 0 for i >= L
// Example:
// - [1, 2, 4, 8, 16]   -> (1, [1, -2])
// - [1, 1, 2, 3, 5, 8] -> (2, [1, -1, -1])
// - [0, 0, 0, 0, 1]    -> (5, [1, 0, 0, 0, 0, 998244352]) (mod 998244353)
// - []                 -> (0, [1])
// - [0, 0, 0]          -> (0, [1])
// - [-2]               -> (1, [1, 2])
template <typename Tfield>
std::pair<int, std::vector<Tfield>> linear_recurrence(const std::vector<Tfield> &S)
{
    int N = S.size();
    using poly = std::vector<Tfield>;
    poly C_reversed{1}, B{1};
    int L = 0, m = 1;
    Tfield b = 1;

    // adjust: C(x) <- C(x) - (d / b) x^m B(x)
    auto adjust = [](poly C, const poly &B, Tfield d, Tfield b, int m) -> poly {
        C.resize(std::max(C.size(), B.size() + m));
        Tfield a = d / b;
        for (unsigned i = 0; i < B.size(); i++) C[i + m] -= a * B[i];
        return C;
    };

    for (int n = 0; n < N; n++) {
        Tfield d = S[n];
        for (int i = 1; i <= L; i++) d += C_reversed[i] * S[n - i];

        if (d == 0) m++;
        else if (2 * L <= n) {
            poly T = C_reversed;
            C_reversed = adjust(C_reversed, B, d, b, m);
            L = n + 1 - L;
            B = T;
            b = d;
            m = 1;
        }
        else C_reversed = adjust(C_reversed, B, d, b, m++);
    }
    return std::make_pair(L, C_reversed);
}

// Calculate x^N mod f(x)
// Known as `Kitamasa method` (Fast version based on FFT)
// Input: f_reversed: monic, reversed (f_reversed[0] = 1)
// Complexity: O(K lg K lgN) (K: deg. of f)
// Example: (4, [1, -1, -1]) -> [2, 3]
//          ( x^4 = (x^2 + x + 2)(x^2 - x - 1) + 3x + 2 )
// Reference: <http://misawa.github.io/others/fast_kitamasa_method.html>
//            <http://sugarknri.hatenablog.com/entry/2017/11/18/233936>
template <typename Tfield>
std::vector<Tfield> monomial_mod_polynomial(long long N, const std::vector<Tfield> &f_reversed)
{
    assert(!f_reversed.empty() and f_reversed[0] == 1);
    int K = f_reversed.size() - 1;
    if (!K) return {};
    int D = 64 - __builtin_clzll(N);
    std::vector<Tfield> ret(K, 0);
    ret[0] = 1;
    auto self_conv = [](std::vector<Tfield> x) -> std::vector<Tfield> {
        return nttconv(x, x);
    };
    for (int d = D; d--;)
    {
        ret = self_conv(ret);
        for (int i = 2 * K - 2; i >= K; i--)
        {
            for (int j = 1; j <= K; j++) ret[i - j] -= ret[i] * f_reversed[j];
        }
        ret.resize(K);
        if ((N >> d) & 1)
        {
            std::vector<Tfield> c(K);
            c[0] = -ret[K - 1] * f_reversed[K];
            for (int i = 1; i < K; i++)
            {
                c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i];
            }
            ret = c;
        }
    }
    return ret;
}


template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
    os << '[';
    for (auto v : vec)
        os << v << ',';
    os << ']';
    return os;
}
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl


int main()
{
    int X, Y;
    long long T;
    long long a, b, c, d;
    cin >> X >> Y >> T >> a >> b >> c >> d;
    auto START = std::chrono::system_clock::now();

    T = (T - 1) % (md - 1) + 1;

    long long dist = abs(a - c) + abs(b - d);
    if (dist > T)
    {
        puts("0");
        return 0;
    }

    mint primitive_root = 3;

    mint rx = primitive_root.pow((md - 1) / (1 << (X + 1))), rxi = rx.inv();
    mint ry = primitive_root.pow((md - 1) / (1 << (Y + 1))), ryi = ry.inv();

    mint rxa = rx.pow(a), rxai = rxa.inv();
    mint ryb = ry.pow(b), rybi = ryb.inv();

    mint rxc = rx.pow(c), rxci = rxc.inv();
    mint ryd = ry.pow(d), rydi = ryd.inv();

    mint rxpow = 1, rxpowi = 1, rypow, rypowi;
    mint rxapow = 1, rxapowi = 1, rybpow, rybpowi;
    mint rxcpow = 1, rxcpowi = 1, rydpow, rydpowi;

    vector<mint> coeffs;
    vector<mint> fkls;

    for (int k = 0; k < 1 << X; k++)
    {
        rypow = 1, rypowi = 1;
        rybpow = 1, rybpowi = 1;
        rydpow = 1, rydpowi = 1;
        for (int l = 0; l < 1 << Y; l++)
        {
            fkls.emplace_back(rxpow + rxpowi + rypow + rypowi + 1);
            coeffs.emplace_back((rxapow - rxapowi) * (rybpow - rybpowi) * (rxcpow - rxcpowi) * (rydpow - rydpowi) * mint(1 << (X + Y + 2)).inv());

            rypow *= ry, rypowi *= ryi;
            rybpow *= ryb, rybpowi *= rybi;
            rydpow *= ryd, rydpowi *= rydi;
        }
        rxpow *= rx, rxpowi *= rxi;
        rxapow *= rxa, rxapowi *= rxai;
        rxcpow *= rxc, rxcpowi *= rxci;
    }
    vector<mint> fklpow;
    dbg(dist);
    dbg(T);
    for (auto x : fkls) fklpow.emplace_back(x.pow(dist));
    vector<mint> seq;

    for (long long t = dist; t - dist <= 10000; t++)
    {
        if (chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now() - START).count() > 2000) break;
        mint tmp = 0;
        for (int kl = 0; kl < 1 << (X + Y); kl++) {
            tmp += coeffs[kl] * fklpow[kl];
            fklpow[kl] *= fkls[kl];
        }
        if (t == T)
        {
            cout << tmp << '\n';
            return 0;
        }
        seq.emplace_back(tmp);
    }

    dbg(seq.size());

    auto [L, poly_reversed] = linear_recurrence(seq);

    dbg(L);

    auto g = monomial_mod_polynomial(T - dist, poly_reversed);
    mint ret = 0;
    for (int i = 0; i < int(g.size()); i++) ret += seq.at(i) * g.at(i);

    cout << ret << '\n';
}

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結果

テストケース

ソースコード