#869217 (C++14) No.2303 Frog on Grid

提出ソース
結果

問題	No.2303 Frog on Grid
ユーザー	t98slider
提出日時	2023-05-13 15:56:31
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	51 ms / 2,000 ms
コード長	14,093 bytes
コンパイル時間	3,285 ms
コンパイル使用メモリ	209,400 KB
実行使用メモリ	14,444 KB
最終ジャッジ日時	2024-05-06 21:55:32
合計ジャッジ時間	4,674 ms
ジャッジサーバーID （参考情報）	judge2 / 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 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	48 ms 12,744 KB
testcase_03	AC	24 ms 7,748 KB
testcase_04	AC	47 ms 12,508 KB
testcase_05	AC	49 ms 13,532 KB
testcase_06	AC	25 ms 8,116 KB
testcase_07	AC	46 ms 12,164 KB
testcase_08	AC	47 ms 12,324 KB
testcase_09	AC	12 ms 5,464 KB
testcase_10	AC	23 ms 7,372 KB
testcase_11	AC	13 ms 5,440 KB
testcase_12	AC	26 ms 8,856 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 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	51 ms 14,308 KB
testcase_19	AC	51 ms 14,444 KB
testcase_20	AC	51 ms 14,312 KB
testcase_21	AC	51 ms 14,440 KB
testcase_22	AC	51 ms 14,436 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

template<const unsigned int MOD> struct prime_modint {
    using mint = prime_modint;
    unsigned int v;
    prime_modint() : v(0) {}
    prime_modint(unsigned int a) { a %= MOD; v = a; }
    prime_modint(unsigned long long a) { a %= MOD; v = a; }
    prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    static constexpr int mod() { return MOD; }
    mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
    mint& operator--() {if(v == 0)v = MOD; v--; return *this;}
    mint operator++(int) { mint result = *this; ++*this; return result; }
    mint operator--(int) { mint result = *this; --*this; return result; }
    mint& operator+=(const mint& rhs) { v += rhs.v; if(v >= MOD) v -= MOD; return *this; }
    mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
    mint& operator*=(const mint& rhs) {
        v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint r = 1, x = *this;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const { assert(v); return pow(MOD - 2); }
    friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint& lhs, const mint& rhs) { return (lhs.v == rhs.v); }
    friend bool operator!=(const mint& lhs, const mint& rhs) { return (lhs.v != rhs.v); }
    friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
//using mint = prime_modint<1000000007>;
using mint = prime_modint<998244353>;

constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

template<class mint> struct fft_info {
    const int g = primitive_root(mint::mod());
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }

    int ceil_pow2(int n) {
        int x = 0;
        while ((1U << x) < (unsigned int)(n)) x++;
        return x;
    }

    int bsf(unsigned int n) {
    #ifdef _MSC_VER
        unsigned long index;
        _BitScanForward(&index, n);
        return index;
    #else
        return __builtin_ctz(n);
    #endif
    }

    constexpr long long safe_mod(long long x, long long m) {
        x %= m;
        if (x < 0) x += m;
        return x;
    }

    constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
        if (m == 1) return 0;
        unsigned int _m = (unsigned int)(m);
        unsigned long long r = 1;
        unsigned long long y = safe_mod(x, m);
        while (n) {
            if (n & 1) r = (r * y) % _m;
            y = (y * y) % _m;
            n >>= 1;
        }
        return r;
    }

    constexpr int primitive_root(int m) {
        if (m == 2) return 1;
        if (m == 167772161) return 3;
        if (m == 469762049) return 3;
        if (m == 754974721) return 11;
        if (m == 998244353) return 3;
        int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        int x = (m - 1) / 2;
        while (x % 2 == 0) x /= 2;
        for (int i = 3; (long long)(i)*i <= x; i += 2) {
            if (x % i == 0) {
                divs[cnt++] = i;
                while (x % i == 0) x /= i;
            }
        }
        if (x > 1) divs[cnt++] = x;
        for (int g = 2;; g++) {
            bool ok = true;
            for (int i = 0; i < cnt; i++) {
                if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return g;
        }
    }

    void butterfly(std::vector<mint>& a) {
        int n = int(a.size());
        int h = ceil_pow2(n);

        int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
        while (len < h) {
            if (h - len == 1) {
                int p = 1 << (h - len - 1);
                mint rot = 1;
                for (int s = 0; s < (1 << len); s++) {
                    int offset = s << (h - len);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p] * rot;
                        a[i + offset] = l + r;
                        a[i + offset + p] = l - r;
                    }
                    if (s + 1 != (1 << len)) rot *= rate2[bsf(~(unsigned int)(s))];
                }
                len++;
            } else {
                // 4-base
                int p = 1 << (h - len - 2);
                mint rot = 1, imag = root[2];
                for (int s = 0; s < (1 << len); s++) {
                    mint rot2 = rot * rot;
                    mint rot3 = rot2 * rot;
                    int offset = s << (h - len);
                    for (int i = 0; i < p; i++) {
                        auto mod2 = 1ULL * mint::mod() * mint::mod();
                        auto a0 = 1ULL * a[i + offset].v;
                        auto a1 = 1ULL * a[i + offset + p].v * rot.v;
                        auto a2 = 1ULL * a[i + offset + 2 * p].v * rot2.v;
                        auto a3 = 1ULL * a[i + offset + 3 * p].v * rot3.v;
                        auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).v * imag.v;
                        auto na2 = mod2 - a2;
                        a[i + offset] = a0 + a2 + a1 + a3;
                        a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                        a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                        a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                    }
                    if (s + 1 != (1 << len))
                        rot *= rate3[bsf(~(unsigned int)(s))];
                }
                len += 2;
            }
        }
    }

    void butterfly_inv(std::vector<mint>& a) {
        int n = int(a.size());
        int h = ceil_pow2(n);

        int len = h;
        while (len) {
            if (len == 1) {
                int p = 1 << (h - len);
                mint irot = 1;
                for (int s = 0; s < (1 << (len - 1)); s++) {
                    int offset = s << (h - len + 1);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p];
                        a[i + offset] = l + r;
                        a[i + offset + p] = (unsigned long long)(mint::mod() + l.v - r.v) * irot.v;
                    }
                    if (s + 1 != (1 << (len - 1))) irot *= irate2[bsf(~(unsigned int)(s))];
                }
                len--;
            } else {
                // 4-base
                int p = 1 << (h - len);
                mint irot = 1, iimag = iroot[2];
                for (int s = 0; s < (1 << (len - 2)); s++) {
                    mint irot2 = irot * irot;
                    mint irot3 = irot2 * irot;
                    int offset = s << (h - len + 2);
                    for (int i = 0; i < p; i++) {
                        auto a0 = 1ULL * a[i + offset + 0 * p].v;
                        auto a1 = 1ULL * a[i + offset + 1 * p].v;
                        auto a2 = 1ULL * a[i + offset + 2 * p].v;
                        auto a3 = 1ULL * a[i + offset + 3 * p].v;
                        auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.v).v;

                        a[i + offset] = a0 + a1 + a2 + a3;
                        a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.v;
                        a[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.v;
                        a[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.v;
                    }
                    if (s + 1 != (1 << (len - 2))) irot *= irate3[bsf(~(unsigned int)(s))];
                }
                len -= 2;
            }
        }
    }

    std::vector<mint> convolution_naive(const std::vector<mint>& a, const std::vector<mint>& b) {
        int n = int(a.size()), m = int(b.size());
        std::vector<mint> ans(n + m - 1);
        if (n < m) {
            for (int j = 0; j < m; j++) {
                for (int i = 0; i < n; i++) {
                    ans[i + j] += a[i] * b[j];
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ans[i + j] += a[i] * b[j];
                }
            }
        }
        return ans;
    }

    std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
        int n = int(a.size()), m = int(b.size());
        int z = 1 << ceil_pow2(n + m - 1);
        a.resize(z), butterfly(a);
        b.resize(z), butterfly(b);
        for (int i = 0; i < z; i++) a[i] *= b[i];
        butterfly_inv(a);
        a.resize(n + m - 1);
        mint iz = mint(z).inv();
        for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
        return a;
    }
};

template <class mint> std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    static fft_info<mint> info;
    if (std::min(n, m) <= 60) return info.convolution_naive(a, b);
    return info.convolution_fft(a, b);
}

template <unsigned int mod = 998244353, class T>
std::vector<T> convolution(std::vector<T>& a, std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = prime_modint<mod>;
    std::vector<mint> a2(n), b2(m), c2;
    for (int i = 0; i < n; i++) a2[i] = mint(a[i]);
    for (int i = 0; i < m; i++) b2[i] = mint(b[i]);

    static fft_info<mint> info;
    if (std::min(n, m) <= 60) c2 = info.convolution_naive(a2, b2);
    else c2 = info.convolution_fft(a2, b2);

    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) c[i] = c2[i].v;
    return c;
}

std::vector<long long> convolution_ll(std::vector<long long>& a, std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    auto safe_mod = [&](long long x, long long m) {
        x %= m;
        if (x < 0) x += m;
        return x;
    };

    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static constexpr unsigned long long i1 = 190329765; //inv_gcd(MOD2 * MOD3, MOD1).second
    static constexpr unsigned long long i2 = 58587104; //inv_gcd(MOD1 * MOD3, MOD2).second
    static constexpr unsigned long long i3 = 187290749; //inv_gcd(MOD1 * MOD2, MOD3).second

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        long long diff = c1[i] - safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }
    return c;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int H, W;
    cin >> H >> W;
    vector<mint> fact(H + W + 1), inv(H + W + 1), a(H + 1), b(W + 1);
    fact[0] = 1;
    for(int i = 1; i <= H + W; i++) fact[i] = i * fact[i - 1];
    inv[H + W] = 1 / fact[H + W];
    for(int i = H + W; i >= 1; i--) inv[i - 1] = i * inv[i];

    for(int i = 0; i <= H / 2; i++) a[H - i] = inv[i] * inv[H - 2 * i];
    for(int i = 0; i <= W / 2; i++) b[W - i] = inv[i] * inv[W - 2 * i];

    auto c = convolution(a, b);

    mint ans;
    for(int i = (H + W) / 2; i <= H + W; i++) ans += fact[i] * c[i];

    cout << ans << '\n';
}
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結果

テストケース

ソースコード
