結果

問題 No.1907 DETERMINATION
ユーザー rniyarniya
提出日時 2022-04-16 17:50:44
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 700 ms / 4,000 ms
コード長 9,333 bytes
コンパイル時間 2,711 ms
コンパイル使用メモリ 217,300 KB
実行使用メモリ 7,040 KB
最終ジャッジ日時 2024-06-07 15:31:03
合計ジャッジ時間 29,230 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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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 3 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 199 ms
5,632 KB
testcase_08 AC 78 ms
5,376 KB
testcase_09 AC 135 ms
5,376 KB
testcase_10 AC 494 ms
6,912 KB
testcase_11 AC 198 ms
5,760 KB
testcase_12 AC 473 ms
6,784 KB
testcase_13 AC 443 ms
6,784 KB
testcase_14 AC 414 ms
6,912 KB
testcase_15 AC 90 ms
5,376 KB
testcase_16 AC 30 ms
5,376 KB
testcase_17 AC 456 ms
6,784 KB
testcase_18 AC 317 ms
6,016 KB
testcase_19 AC 10 ms
5,376 KB
testcase_20 AC 454 ms
6,912 KB
testcase_21 AC 41 ms
5,376 KB
testcase_22 AC 431 ms
5,632 KB
testcase_23 AC 531 ms
6,912 KB
testcase_24 AC 144 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 477 ms
7,040 KB
testcase_27 AC 586 ms
6,912 KB
testcase_28 AC 586 ms
6,912 KB
testcase_29 AC 581 ms
7,040 KB
testcase_30 AC 2 ms
5,376 KB
testcase_31 AC 490 ms
6,944 KB
testcase_32 AC 474 ms
6,912 KB
testcase_33 AC 475 ms
6,912 KB
testcase_34 AC 474 ms
7,040 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
testcase_38 AC 474 ms
6,912 KB
testcase_39 AC 475 ms
7,040 KB
testcase_40 AC 698 ms
6,912 KB
testcase_41 AC 475 ms
7,040 KB
testcase_42 AC 696 ms
6,912 KB
testcase_43 AC 700 ms
6,912 KB
testcase_44 AC 542 ms
7,040 KB
testcase_45 AC 583 ms
6,940 KB
testcase_46 AC 474 ms
6,784 KB
testcase_47 AC 472 ms
6,912 KB
testcase_48 AC 476 ms
6,944 KB
testcase_49 AC 505 ms
7,040 KB
testcase_50 AC 474 ms
6,912 KB
testcase_51 AC 475 ms
7,040 KB
testcase_52 AC 2 ms
5,376 KB
testcase_53 AC 521 ms
5,760 KB
testcase_54 AC 520 ms
5,760 KB
testcase_55 AC 2 ms
5,376 KB
testcase_56 AC 520 ms
5,760 KB
testcase_57 AC 519 ms
5,888 KB
testcase_58 AC 418 ms
6,912 KB
testcase_59 AC 319 ms
7,040 KB
testcase_60 AC 322 ms
6,944 KB
testcase_61 AC 402 ms
6,940 KB
testcase_62 AC 321 ms
6,948 KB
testcase_63 AC 475 ms
6,912 KB
testcase_64 AC 2 ms
5,376 KB
testcase_65 AC 2 ms
5,376 KB
testcase_66 AC 2 ms
5,376 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

diff # 

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
    for (size_t i = 0; i < N; i++) {
        os << v[i] << (i + 1 == N ? "" : " ");
    }
    return os;
}

template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}

void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion

#include <iostream>
#include "atcoder/modint"

namespace atcoder {

template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
    int64_t v;
    x = static_modint<MOD>{(is >> v, v)};
    return is;
}

template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }

template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }

}  // namespace atcoder

#include <algorithm>
#include <cassert>
#include <vector>

template <typename T> std::vector<T> characteristic_polynomial(std::vector<std::vector<T>> M) {
    assert(M.empty() or M.size() == M[0].size());
    int n = M.size();
    // reduce M to upper Hessenberg form
    for (int j = 0; j < n - 2; j++) {
        for (int i = j + 2; i < n; i++) {
            if (M[i][j] != 0) {
                std::swap(M[j + 1], M[i]);
                for (int k = 0; k < n; k++) std::swap(M[k][j + 1], M[k][i]);
                break;
            }
        }
        if (M[j + 1][j] == 0) continue;
        auto inv = T(1) / M[j + 1][j];
        for (int i = j + 2; i < n; i++) {
            auto coef = M[i][j] * inv;
            for (int k = j; k < n; k++) M[i][k] -= coef * M[j + 1][k];
            for (int k = 0; k < n; k++) M[k][j + 1] += coef * M[k][i];
        }
    }

    // compute the characteristic polynomial of upper Hessenberg matrix M
    std::vector<std::vector<T>> p(n + 1);
    p[0] = {T(1)};
    for (int i = 0; i < n; i++) {
        p[i + 1].resize(i + 2);
        for (int j = 0; j <= i; j++) {
            p[i + 1][j + 1] += p[i][j];
            p[i + 1][j] -= p[i][j] * M[i][i];
        }
        T betas = 1;
        for (int j = i - 1; j >= 0; j--) {
            betas *= M[j + 1][j];
            T coef = -betas * M[j][i];
            for (int k = 0; k <= j; k++) p[i + 1][k] += coef * p[j][k];
        }
    }
    return p[n];
}

template <typename T>
std::vector<T> determinant_polynomial(std::vector<std::vector<T>> M0, std::vector<std::vector<T>> M1) {
    assert(M0.size() == M1.size());
    assert(M0.size() == M0[0].size());
    assert(M1.size() == M1[0].size());
    int n = M0.size(), off = 0;
    T prod = 1;

    for (int p = 0; p < n; p++) {
        int pivot = -1;
        for (int i = p; i < n; i++) {
            if (M1[i][p] != 0) {
                pivot = i;
                break;
            }
        }
        if (pivot == -1) {
            if (++off > n) return std::vector<T>(n + 1, 0);
            for (int i = 0; i < p; i++) {
                for (int k = 0; k < n; k++) M0[k][p] -= M1[i][p] * M0[k][i];
                M1[i][p] = 0;
            }
            for (int i = 0; i < n; i++) std::swap(M0[i][p], M1[i][p]);
            p--;
            continue;
        }
        if (pivot != p) {
            std::swap(M0[p], M0[pivot]);
            std::swap(M1[p], M1[pivot]);
            prod *= -1;
        }
        prod *= M1[p][p];
        auto inv = T(1) / M1[p][p];
        for (int j = 0; j < n; j++) {
            M0[p][j] *= inv;
            M1[p][j] *= inv;
        }
        for (int i = 0; i < n; i++) {
            if (i == p) continue;
            auto coef = M1[i][p];
            for (int j = 0; j < n; j++) {
                M0[i][j] -= M0[p][j] * coef;
                M1[i][j] -= M1[p][j] * coef;
            }
        }
    }

    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            M0[i][j] *= -1;
        }
    }
    auto poly = characteristic_polynomial(M0);
    std::vector<T> res(n + 1, 0);
    for (int i = 0; i + off <= n; i++) res[i] = prod * poly[i + off];
    return res;
}

const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;

using mint = atcoder::modint998244353;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<vector<mint>> M0(N, vector<mint>(N)), M1(N, vector<mint>(N));
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cin >> M0[i][j];
        }
    }
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cin >> M1[i][j];
        }
    }

    auto ans = determinant_polynomial(M0, M1);
    for (auto& x : ans) cout << x << '\n';
    return 0;
}
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