結果

問題 No.2267 群の公理
ユーザー sten_san
提出日時 2023-04-14 21:29:36
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,531 bytes
コンパイル時間 1,929 ms
コンパイル使用メモリ 198,060 KB
最終ジャッジ日時 2025-02-12 06:20:44
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 50
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 # 

#include <bits/stdc++.h>
using namespace std;

struct iofast_t {
    iofast_t() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} iofast;

struct uns_t {} uns;
template <typename Element, typename Head, typename ...Args>
auto vec(Element init, Head arg, Args ...args) {
    if constexpr (sizeof...(Args) == 0) return vector(arg, init);
    else return vector(arg, vec(init, args...));
}
template <typename Element, typename Head, typename ...Args>
auto vec(uns_t, Head arg, Args ...args) {
    return vec(Element(), arg, args...);
}

template <typename Container>
auto distance(const Container &c, decltype(begin(c)) iter) {
    return distance(begin(c), iter);
}

template <typename RIter, typename Compare = less<typename iterator_traits<RIter>::value_type>>
auto isort(RIter first, RIter last, Compare comp = Compare()) {
    vector<int> i(distance(first, last));
    iota(begin(i), end(i), 0);
    sort(begin(i), end(i), [&](auto x, auto y) {
        return comp(*(first + x), *(first + y));
    });
    return i;
}

template <typename, template <typename> typename, typename = void_t<>>
struct detect : false_type {};
template <typename T, template <typename> typename Check>
struct detect<T, Check, void_t<Check<T>>> : true_type {};
template <typename T, template <typename> typename Check>
constexpr inline bool detect_v = detect<T, Check>::value;

template <typename T>
using has_member_sort = decltype(declval<T>().sort());

template <typename Container, typename Compare = less<typename Container::value_type>>
auto sorted(Container c, Compare comp = Compare()) {
    if constexpr (detect_v<Container, has_member_sort>) {
        c.sort(comp);
        return c;
    }
    else {
        sort(begin(c), end(c), comp);
        return c;
    }
}

template <typename Container, typename Compare = equal_to<typename Container::value_type>>
auto uniqued(Container c, Compare comp = Compare()) {
    c.erase(unique(begin(c), end(c), comp), end(c));
    return c;
}

template <typename T, typename Compare = less<T>>
T &chmin(T &l, T r, Compare &&f = less<T>()) { return l = min(l, r, f); }
template <typename T, typename Compare = less<T>>
T &chmax(T &l, T r, Compare &&f = less<T>()) { return l = max(l, r, f); }

template <typename F>
constexpr auto fix(F &&f) noexcept {
    return [f = std::tuple<F>(std::forward<F>(f))](auto &&...args) mutable {
        return std::get<0>(f)(fix(std::get<0>(f)), std::forward<decltype(args)>(args)...);
    };
}

int main() {
    int n; cin >> n;

    auto f = vec<int>(uns, n, n);
    for (auto &v : f) {
        for (auto &e : v) {
            cin >> e;
        }
    }

    int e = -1;
    for (int i = 0; i < n; ++i) {
        bool g = true;

        for (int j = 0; j < n && g; ++j) {
            g &= (f[i][j] == j);
            g &= (f[j][i] == j);
        }

        if (g) {
            e = i;
        }
    }

    if (e < 0) {
        cout << "No" << endl;
        return 0;
    }

    for (int i = 0; i < n; ++i) {
        bool g = false;
        for (int j = 0; j < n && !g; ++j) {
            g |= (f[i][j] == e) && (f[j][i] == e);
        }

        if (!g) {
            cout << "No" << endl;
            return 0;
        }
    }

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            for (int k = 0; k < n; ++k) {
                if (f[f[i][j]][k] != f[i][f[j][k]]) {
                    cout << "No" << endl;
                    return 0;
                }
            }
        }
    }

    cout << "Yes" << endl;
}
0