#558109 (C++17) No.1241 Eternal Tours

提出ソース

結果

問題	No.1241 Eternal Tours
ユーザー	yosupot
提出日時	2020-09-25 21:53:10
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	592 ms / 6,000 ms
コード長	15,007 bytes
コンパイル時間	1,484 ms
コンパイル使用メモリ	131,740 KB
実行使用メモリ	61,596 KB
最終ジャッジ日時	2023-09-10 15:19:49
合計ジャッジ時間	12,028 ms
ジャッジサーバーID （参考情報）	judge12 / judge14

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 4,376 KB
testcase_01	AC	1 ms 4,376 KB
testcase_02	AC	218 ms 19,668 KB
testcase_03	AC	2 ms 4,376 KB
testcase_04	AC	2 ms 4,384 KB
testcase_05	AC	2 ms 4,380 KB
testcase_06	AC	1 ms 4,380 KB
testcase_07	AC	1 ms 4,380 KB
testcase_08	AC	2 ms 4,376 KB
testcase_09	AC	2 ms 4,380 KB
testcase_10	AC	1 ms 4,380 KB
testcase_11	AC	2 ms 4,380 KB
testcase_12	AC	2 ms 4,380 KB
testcase_13	AC	1 ms 4,380 KB
testcase_14	AC	248 ms 12,432 KB
testcase_15	AC	2 ms 4,380 KB
testcase_16	AC	60 ms 5,680 KB
testcase_17	AC	589 ms 61,596 KB
testcase_18	AC	533 ms 24,472 KB
testcase_19	AC	462 ms 19,664 KB
testcase_20	AC	3 ms 4,384 KB
testcase_21	AC	9 ms 4,380 KB
testcase_22	AC	531 ms 40,236 KB
testcase_23	AC	16 ms 4,380 KB
testcase_24	AC	1 ms 4,376 KB
testcase_25	AC	2 ms 4,380 KB
testcase_26	AC	2 ms 4,380 KB
testcase_27	AC	1 ms 4,380 KB
testcase_28	AC	333 ms 19,556 KB
testcase_29	AC	332 ms 19,668 KB
testcase_30	AC	383 ms 19,684 KB
testcase_31	AC	237 ms 11,224 KB
testcase_32	AC	592 ms 61,320 KB
testcase_33	AC	480 ms 20,468 KB
testcase_34	AC	482 ms 19,564 KB
testcase_35	AC	482 ms 19,508 KB
testcase_36	AC	1 ms 4,384 KB
testcase_37	AC	1 ms 4,380 KB
testcase_38	AC	494 ms 20,396 KB
testcase_39	AC	490 ms 19,836 KB
testcase_40	AC	496 ms 19,520 KB
testcase_41	AC	455 ms 61,372 KB
testcase_42	AC	337 ms 19,960 KB
testcase_43	AC	342 ms 19,580 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

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx")
//#undef LOCAL




#include <algorithm>

#include <array>

#include <bitset>

#include <cassert>

#include <complex>

#include <cstdio>

#include <cstring>

#include <iostream>

#include <map>

#include <numeric>

#include <queue>

#include <set>

#include <string>

#include <unordered_map>

#include <unordered_set>

#include <vector>

using namespace std;

using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;



#include <unistd.h>

struct Scanner {
    int fd = -1;
    char line[(1 << 15) + 1];
    size_t st = 0, ed = 0;
    void reread() {
        memmove(line, line + st, ed - st);
        ed -= st;
        st = 0;
        ed += ::read(fd, line + ed, (1 << 15) - ed);
        line[ed] = '\0';
    }
    bool succ() {
        while (true) {
            if (st == ed) {
                reread();
                if (st == ed) return false;
            }
            while (st != ed && isspace(line[st])) st++;
            if (st != ed) break;
        }
        if (ed - st <= 50) {
            bool sep = false;
            for (size_t i = st; i < ed; i++) {
                if (isspace(line[i])) {
                    sep = true;
                    break;
                }
            }
            if (!sep) reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
    bool read_single(T& ref) {
        if (!succ()) return false;
        while (true) {
            size_t sz = 0;
            while (st + sz < ed && !isspace(line[st + sz])) sz++;
            ref.append(line + st, sz);
            st += sz;
            if (!sz || st != ed) break;
            reread();
        }
        return true;
    }
    template <class T, enable_if_t<is_integral<T>::value>* = nullptr>
    bool read_single(T& ref) {
        if (!succ()) return false;
        bool neg = false;
        if (line[st] == '-') {
            neg = true;
            st++;
        }
        ref = T(0);
        while (isdigit(line[st])) {
            ref = 10 * ref + (line[st++] & 0xf);
        }
        if (neg) ref = -ref;
        return true;
    }
    template <class T> bool read_single(V<T>& ref) {
        for (auto& d : ref) {
            if (!read_single(d)) return false;
        }
        return true;
    }
    void read() {}
    template <class H, class... T> void read(H& h, T&... t) {
        bool f = read_single(h);
        assert(f);
        read(t...);
    }
    int read_unsafe() { return 0; }
    template <class H, class... T> int read_unsafe(H& h, T&... t) {
        bool f = read_single(h);
        if (!f) return 0;
        return 1 + read_unsafe(t...);
    }
    Scanner(FILE* fp) : fd(fileno(fp)) {}
};

struct Printer {
  public:
    template <bool F = false> void write() {}
    template <bool F = false, class H, class... T>
    void write(const H& h, const T&... t) {
        if (F) write_single(' ');
        write_single(h);
        write<true>(t...);
    }
    template <class... T> void writeln(const T&... t) {
        write(t...);
        write_single('\n');
    }

    Printer(FILE* _fp) : fp(_fp) {}
    ~Printer() { flush(); }

  private:
    static constexpr size_t SIZE = 1 << 15;
    FILE* fp;
    char line[SIZE], small[50];
    size_t pos = 0;
    void flush() {
        fwrite(line, 1, pos, fp);
        pos = 0;
    }
    void write_single(const char& val) {
        if (pos == SIZE) flush();
        line[pos++] = val;
    }
    template <class T, enable_if_t<is_integral<T>::value>* = nullptr>
    void write_single(T val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char(0x30 | (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }
    void write_single(__int128 val) {
        if (pos > (1 << 15) - 50) flush();
        if (val == 0) {
            write_single('0');
            return;
        }
        if (val < 0) {
            write_single('-');
            val = -val; // todo min
        }
        size_t len = 0;
        while (val) {
            small[len++] = char(0x30 | (val % 10));
            val /= 10;
        }
        for (size_t i = 0; i < len; i++) {
            line[pos + i] = small[len - 1 - i];
        }
        pos += len;
    }

    void write_single(const string& s) {
        for (char c : s) write_single(c);
    }
    void write_single(const char* s) {
        size_t len = strlen(s);
        for (size_t i = 0; i < len; i++) write_single(s[i]);
    }
    template <class T> void write_single(const V<T>& val) {
        auto n = val.size();
        for (size_t i = 0; i < n; i++) {
            if (i) write_single(' ');
            write_single(val[i]);
        }
    }
};


template <uint MD> struct ModInt {
    using M = ModInt;
    static constexpr uint get_mod() { return MD; }
    const static M G;
    uint v;
    ModInt(ll _v = 0) { set_v(uint(_v % MD + MD)); }
    M& set_v(uint _v) {
        v = (_v < MD) ? _v : _v - MD;
        return *this;
    }
    explicit operator bool() const { return v != 0; }
    M operator-() const { return M() - *this; }
    M operator+(const M& r) const { return M().set_v(v + r.v); }
    M operator-(const M& r) const { return M().set_v(v + MD - r.v); }
    M operator*(const M& r) const { return M().set_v(uint(ull(v) * r.v % MD)); }
    M operator/(const M& r) const { return *this * r.inv(); }
    M& operator+=(const M& r) { return *this = *this + r; }
    M& operator-=(const M& r) { return *this = *this - r; }
    M& operator*=(const M& r) { return *this = *this * r; }
    M& operator/=(const M& r) { return *this = *this / r; }
    bool operator==(const M& r) const { return v == r.v; }
    M pow(ll n) const {
        M x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    M inv() const { return pow(MD - 2); }
    friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; }
};
// using Mint = ModInt<998244353>;
// template<> const Mint Mint::G = Mint(3);



// bit op
int popcnt(uint x) { return __builtin_popcount(x); }
int popcnt(ull x) { return __builtin_popcountll(x); }
int bsr(uint x) { return 31 - __builtin_clz(x); }
int bsr(ull x) { return 63 - __builtin_clzll(x); }
int bsf(uint x) { return __builtin_ctz(x); }
int bsf(ull x) { return __builtin_ctzll(x); }

//binary gcd
ll gcd(ll _a, ll _b) {
    ull a = abs(_a), b = abs(_b);
    if (a == 0) return b;
    if (b == 0) return a;
    int shift = bsf(a|b);
    a >>= bsf(a);
    do {
        b >>= bsf(b);
        if (a > b) swap(a, b);
        b -= a;
    } while (b);
    return (a << shift);
}

/// g:gcd(a, b), ax+by=g
struct EG { ll g, x, y; };
EG ext_gcd(ll a, ll b) {
    if (b == 0) {
        if (a >= 0) return EG{a, 1, 0};
        else return EG{-a, -1, 0};
    } else {
        auto e = ext_gcd(b, a % b);
        return EG{e.g, e.y, e.x - a / b * e.y};
    }
}


ll inv_mod(ll x, ll md) {
    auto z = ext_gcd(x, md).x;
    return (z % md + md) % md;
}

template<class T, class U>
T pow_mod(T x, U n, T md) {
    T r = 1 % md;
    x %= md;
    while (n) {
        if (n & 1) r = (r * x) % md;
        x = (x * x) % md;
        n >>= 1;
    }
    return r;
}

// (rem, mod)
pair<ll, ll> crt(const V<ll>& b, const V<ll>& c) {
    int n = int(b.size());
    ll r = 0, m = 1;
    for (int i = 0; i < n; i++) {
        auto eg = ext_gcd(m, c[i]);
        ll g = eg.g, im = eg.x;
        if ((b[i] - r) % g) return {0, -1};
        ll tmp = (b[i] - r) / g * im % (c[i] / g);
        r += m * tmp;
        m *= c[i] / g;
    }
    return {(r % m + m) % m, m};
}




template <class Mint> void nft(bool type, V<Mint>& a) {
    int n = int(a.size()), s = 0;
    while ((1 << s) < n) s++;
    assert(1 << s == n);

    static V<Mint> ep, iep;
    while (int(ep.size()) <= s) {
        ep.push_back(Mint::G.pow(Mint(-1).v / (1 << ep.size())));
        iep.push_back(ep.back().inv());
    }
    V<Mint> b(n);
    for (int i = 1; i <= s; i++) {
        int w = 1 << (s - i);
        Mint base = type ? iep[i] : ep[i], now = 1;
        for (int y = 0; y < n / 2; y += w) {
            for (int x = 0; x < w; x++) {
                auto l = a[y << 1 | x];
                auto r = now * a[y << 1 | x | w];
                b[y | x] = l + r;
                b[y | x | n >> 1] = l - r;
            }
            now *= base;
        }
        swap(a, b);
    }
}

template <class Mint> V<Mint> multiply_nft(const V<Mint>& a, const V<Mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (min(n, m) <= 8) {
        V<Mint> ans(n + m - 1);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
        return ans;
    }
    int lg = 0;
    while ((1 << lg) < n + m - 1) lg++;
    int z = 1 << lg;
    auto a2 = a, b2 = b;
    a2.resize(z);
    b2.resize(z);
    nft(false, a2);
    nft(false, b2);
    for (int i = 0; i < z; i++) a2[i] *= b2[i];
    nft(true, a2);
    a2.resize(n + m - 1);
    Mint iz = Mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;
    return a2;
}

// Cooley-Tukey: input -> butterfly -> bit reversing -> output から
// bit reversingを抜いたもの 直接使うな
template <class Mint> void butterfly(bool type, V<Mint>& a) {
    int n = int(a.size()), h = 0;
    while ((1 << h) < n) h++;
    assert(1 << h == n);
    if (n == 1) return;

    static V<Mint> snow, sinow;
    if (snow.empty()) {
        Mint sep = Mint(1), siep = Mint(1);
        uint mod = Mint(-1).v;
        uint di = 4;
        while (mod % di == 0) {
            Mint ep = Mint::G.pow(mod / di);
            Mint iep = ep.inv();
            snow.push_back(siep * ep);
            sinow.push_back(sep * iep);
            sep *= ep;
            siep *= iep;
            di *= 2;
        }
    }

    if (!type) {
        // fft
        for (int ph = 1; ph <= h; ph++) {
            // phase ph: size w -> 2w の FFT, p 並列
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            Mint now = Mint(1);
            for (int s = 0; s < w; s++) {
                int offset = s << (h - ph + 1);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * now;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                int u = bsf(~uint(s));
                now *= snow[u];
            }
        }
    } else {
        // ifft
        for (int ph = h; ph >= 1; ph--) {
            int w = 1 << (ph - 1), p = 1 << (h - ph);
            Mint inow = Mint(1);
            for (int s = 0; s < w; s++) {
                int offset = s << (h - ph + 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] = (l - r) * inow;
                }
                int u = bsf(~uint(s));
                inow *= sinow[u];
            }
        }
    }
}

template <class Mint> V<Mint> multiply(const V<Mint>& a, const V<Mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (min(n, m) < 8) {
        V<Mint> ans(n + m - 1);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++) ans[i + j] += a[i] * b[j];
        return ans;
    }
    int lg = 0;
    while ((1 << lg) < n + m - 1) lg++;
    int z = 1 << lg;
    auto a2 = a;
    a2.resize(z);
    butterfly(false, a2);
    if (a == b) {
        for (int i = 0; i < z; i++) a2[i] *= a2[i];
    } else {
        auto b2 = b;
        b2.resize(z);
        butterfly(false, b2);
        for (int i = 0; i < z; i++) a2[i] *= b2[i];
    }
    butterfly(true, a2);
    a2.resize(n + m - 1);
    Mint iz = Mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a2[i] *= iz;
    return a2;
}
using mint = ModInt<998244353>;
template<> const mint mint::G = mint(3);

Scanner sc = Scanner(stdin);
Printer pr = Printer(stdout);

int main() {
    int x, y; ll t; int a, b, c, d;
    sc.read(x, y, t, a, b, c, d);
    a--; b--; c--; d--;

    bool sig = t % 2;
    t -= t % 2;

    auto but2 = [&](bool type, VV<mint>& a) {
        int h = int(a.size());
        int w = int(a[0].size());
        for (auto& x : a) {
            butterfly(type, x);
        }
        V<mint> buf(h);
        for (int i = 0; i < w; i++) {
            for (int j = 0; j < h; j++) {
                buf[j] = a[j][i];
            }
            butterfly(type, buf);
            for (int j = 0; j < h; j++) {
                a[j][i] = buf[j];
            }
        }
    };
    auto mul = [&](VV<mint> a, VV<mint> b) {
        int h = int(a.size());
        int w = int(a[0].size());

        but2(false, a);
        but2(false, b);

        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                a[i][j] *= b[i][j];
            }
        }
        but2(true, a);
        mint in = (mint(h) * w).inv();
        for (auto& v: a) for (auto& x: v) x *= in;

        return a;
    };

    int h = 2 << x;
    int w = 2 << y;
    VV<mint> f(h, V<mint>(w));
    {
        f[0][0] += mint(1);
        f[0][1] += mint(1);
        f[1][0] += mint(1);
        f[0][w-1] += mint(1);
        f[h-1][0] += mint(1);

        but2(false, f);
        for (int i = 0; i < h; i++) {
            for (int j = 0; j < w; j++) {
                f[i][j] = f[i][j].pow(t);
            }
        }
        but2(true, f);
        mint in = (mint(h) * w).inv();
        for (auto& v: f) for (auto& z: v) z *= in;


        VV<mint> g(h, V<mint>(w));
        g[a][b] = 1;

        f = mul(f, g);

/*        auto t2 = t;
        while (t2) {
            if (t2 & 1) {
                g = mul(f, g);
            }
            f = mul(f, f);
            t2 >>= 1;
        }
        f = g;*/
    }

    auto solve = [&](int tx, int ty) {
        mint ans = 0;
        ans += f[tx][ty];
        ans -= f[h - 2 - tx][ty];
        ans -= f[tx][w - 2 - ty];
        ans += f[h - 2 - tx][w - 2 - ty];
                        ;
        return ans;
    };

    mint ans = solve(c, d);
    if (sig) {
        ans = solve(c, d);
        if (c) ans += solve(c - 1, d);
        if (d) ans += solve(c, d - 1);
        if (c + 1 < ((1 << x) - 1)) ans += solve(c + 1, d);
        if (d + 1 < ((1 << y) - 1)) ans += solve(c, d + 1);
    }

    pr.writeln(ans.v);

    return 0;
}

yukicoder

結果

テストケース

ソースコード