#919260 (C++17) No.1907 DETERMINATION

提出ソース

結果

問題	No.1907 DETERMINATION
ユーザー	Forested
提出日時	2023-10-09 17:46:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	657 ms / 4,000 ms
コード長	10,800 bytes
コンパイル時間	1,648 ms
コンパイル使用メモリ	142,556 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-26 18:37:28
合計ジャッジ時間	24,125 ms
ジャッジサーバーID （参考情報）	judge5 / 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 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	181 ms 6,944 KB
testcase_08	AC	70 ms 6,940 KB
testcase_09	AC	120 ms 6,940 KB
testcase_10	AC	452 ms 6,944 KB
testcase_11	AC	190 ms 6,944 KB
testcase_12	AC	427 ms 6,940 KB
testcase_13	AC	400 ms 6,940 KB
testcase_14	AC	365 ms 6,944 KB
testcase_15	AC	79 ms 6,940 KB
testcase_16	AC	26 ms 6,944 KB
testcase_17	AC	410 ms 6,940 KB
testcase_18	AC	281 ms 6,944 KB
testcase_19	AC	8 ms 6,944 KB
testcase_20	AC	403 ms 6,940 KB
testcase_21	AC	37 ms 6,940 KB
testcase_22	AC	387 ms 6,944 KB
testcase_23	AC	479 ms 6,940 KB
testcase_24	AC	128 ms 6,940 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	425 ms 6,940 KB
testcase_27	AC	533 ms 6,944 KB
testcase_28	AC	535 ms 6,940 KB
testcase_29	AC	525 ms 6,944 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	435 ms 6,940 KB
testcase_32	AC	422 ms 6,944 KB
testcase_33	AC	424 ms 6,944 KB
testcase_34	AC	425 ms 6,940 KB
testcase_35	AC	2 ms 6,940 KB
testcase_36	AC	2 ms 6,940 KB
testcase_37	AC	2 ms 6,940 KB
testcase_38	AC	426 ms 6,944 KB
testcase_39	AC	427 ms 6,944 KB
testcase_40	AC	654 ms 6,940 KB
testcase_41	AC	429 ms 6,940 KB
testcase_42	AC	656 ms 6,940 KB
testcase_43	AC	657 ms 6,940 KB
testcase_44	AC	494 ms 6,944 KB
testcase_45	AC	531 ms 6,940 KB
testcase_46	AC	422 ms 6,944 KB
testcase_47	AC	421 ms 6,940 KB
testcase_48	AC	427 ms 6,944 KB
testcase_49	AC	457 ms 6,944 KB
testcase_50	AC	426 ms 6,940 KB
testcase_51	AC	424 ms 6,940 KB
testcase_52	AC	2 ms 6,940 KB
testcase_53	AC	477 ms 6,940 KB
testcase_54	AC	487 ms 6,940 KB
testcase_55	AC	2 ms 6,940 KB
testcase_56	AC	474 ms 6,944 KB
testcase_57	AC	474 ms 6,944 KB
testcase_58	AC	368 ms 6,944 KB
testcase_59	AC	268 ms 6,944 KB
testcase_60	AC	274 ms 6,940 KB
testcase_61	AC	353 ms 6,940 KB
testcase_62	AC	276 ms 6,940 KB
testcase_63	AC	423 ms 6,940 KB
testcase_64	AC	2 ms 6,944 KB
testcase_65	AC	2 ms 6,944 KB
testcase_66	AC	2 ms 6,944 KB

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ソースコード

raw source code

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

#ifdef INT128

using u128 = __uint128_t;
using i128 = __int128_t;

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}

#endif

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif

// ============

#include <cassert>
#include <iostream>
#include <type_traits>

// ============

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        val -= rhs.val;
        if (val >= mod)
            val += mod;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ============
// ============
#include <cassert>
#include <vector>

template <typename T>
std::vector<T> characteristic_polynomial(std::vector<std::vector<T>> a) {
    int n = (int)a.size();
    for (int i = 0; i < n; ++i) {
        assert((int)a[i].size() == n);
    }
    for (int i = 0; i < n - 2; ++i) {
        int idx = -1;
        for (int j = i + 2; j < n; ++j) {
            if (a[j][i] != T()) {
                idx = j;
                break;
            }
        }
        if (idx == -1) {
            continue;
        }
        std::swap(a[i + 1], a[idx]);
        for (int j = 0; j < n; ++j) {
            std::swap(a[j][i + 1], a[j][idx]);
        }
        T inv = a[i + 1][i].inv();
        for (int j = i + 2; j < n; ++j) {
            T mul = a[j][i] * inv;
            for (int k = i; k < n; ++k) {
                a[j][k] -= a[i + 1][k] * mul;
            }
            for (int k = 0; k < n; ++k) {
                a[k][i + 1] += a[k][j] * mul;
            }
        }
    }
    std::vector<std::vector<T>> pol(n + 1);
    pol[0].resize(1, T(1));
    for (int i = 0; i < n; ++i) {
        pol[i + 1].resize(i + 2, T());
        for (int j = 0; j < i + 1; ++j) {
            pol[i + 1][j + 1] += pol[i][j];
            pol[i + 1][j] -= pol[i][j] * a[i][i];
        }
        T prod(1);
        for (int j = i - 1; j >= 0; --j) {
            prod *= a[j + 1][j];
            T coeff = prod * -a[j][i];
            for (int k = 0; k < j + 1; ++k) {
                pol[i + 1][k] += pol[j][k] * coeff;
            }
        }
    }
    return pol[n];
}
// ============
using M = ModInt<mod998244353>;

int main() {
    i32 n;
    cin >> n;
    Vec<Vec<M>> a(n, Vec<M>(n)), b(n, Vec<M>(n));
    REP(i, n) REP(j, n) {
        cin >> a[i][j];
    }
    REP(i, n) REP(j, n) {
        cin >> b[i][j];
    }
    i32 mulx = 0;
    M fin(1);
    REP(i, n) {
        i32 idx = -1;
        REP(j, i, n) {
            if (b[j][i].get_val()) {
                idx = j;
                break;
            }
        }
        while (idx == -1 && mulx < n) {
            REP(j, i) {
                M mul = exchange(b[j][i], M());
                REP(k, n) {
                    a[k][i] -= a[k][j] * mul;
                }
            }
            ++mulx;
            REP(j, n) {
                swap(a[j][i], b[j][i]);
            }
            REP(j, i, n) {
                if (b[j][i].get_val()) {
                    idx = j;
                    break;
                }
            }
        }
        if (idx == -1) {
            REP(i, n + 1) {
                cout << 0 << '\n';
            }
            exit(0);
        }
        if (idx != i) {
            swap(a[idx], a[i]);
            swap(b[idx], b[i]);
            fin = -fin;
        }
        fin *= b[i][i];
        M inv = b[i][i].inv();
        REP(j, i, n) {
            b[i][j] *= inv;
        }
        REP(j, n) {
            a[i][j] *= inv;
        }
        REP(j, n) {
            if (j == i) {
                continue;
            }
            M mul = b[j][i];
            REP(k, i, n) {
                b[j][k] -= b[i][k] * mul;
            }
            REP(k, n) {
                a[j][k] -= a[i][k] * mul;
            }
        }
    }
    REP(i, n) REP(j, n) {
        a[i][j] = -a[i][j];
    }
    Vec<M> ans = characteristic_polynomial(a);
    REP(i, mulx, n + 1) {
        cout << ans[i] * fin << '\n';
    }
    REP(i, mulx) {
        cout << 0 << '\n';
    }
}

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結果

テストケース

ソースコード