#894843 (C++17) No.2267 群の公理

提出ソース

結果

問題	No.2267 群の公理
ユーザー	poyon
提出日時	2023-07-23 16:51:46
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	6,773 bytes
コンパイル時間	2,432 ms
コンパイル使用メモリ	209,988 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-24 18:19:49
合計ジャッジ時間	3,452 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

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 6,812 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,940 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,940 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	1 ms 6,944 KB
testcase_16	AC	2 ms 6,944 KB
testcase_17	AC	1 ms 6,940 KB
testcase_18	AC	2 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	1 ms 6,944 KB
testcase_21	AC	2 ms 6,940 KB
testcase_22	AC	1 ms 6,944 KB
testcase_23	AC	2 ms 6,940 KB
testcase_24	AC	2 ms 6,940 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	1 ms 6,940 KB
testcase_27	AC	1 ms 6,944 KB
testcase_28	AC	1 ms 6,944 KB
testcase_29	AC	2 ms 6,944 KB
testcase_30	AC	1 ms 6,940 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	2 ms 6,940 KB
testcase_33	AC	2 ms 6,940 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	2 ms 6,940 KB
testcase_38	AC	1 ms 6,944 KB
testcase_39	AC	2 ms 6,940 KB
testcase_40	AC	2 ms 6,944 KB
testcase_41	AC	2 ms 6,940 KB
testcase_42	AC	2 ms 6,940 KB
testcase_43	AC	2 ms 6,940 KB
testcase_44	AC	2 ms 6,940 KB
testcase_45	AC	2 ms 6,944 KB
testcase_46	AC	2 ms 6,944 KB
testcase_47	AC	1 ms 6,940 KB
testcase_48	AC	2 ms 6,944 KB
testcase_49	AC	1 ms 6,940 KB

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ソースコード

raw source code

// clang-format off
#ifdef _LOCAL
    #include <pch.hpp>
#else
    #include <bits/stdc++.h>
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(...)
    #define debug2(vv)
    #define debug3(vvv)
#endif

using namespace std;
using ll = long long;
using ld = long double;
using str = string;
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VC = vector<char>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define FORE(e,c) for (auto&& e : c)
#define ALL(c) (c).begin(), (c).end()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort((c).rbegin(), (c).rend())
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define len(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) ((ll)__builtin_popcountll(b))
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) do { SORT(c); (c).erase(unique(ALL(c)), (c).end()); (c).shrink_to_fit(); } while (0)
#define END(...) do { print(__VA_ARGS__); exit(0); } while (0)
constexpr ld EPS = 1e-10;
constexpr ld PI  = acosl(-1.0);
constexpr int inf = (1 << 30) - (1 << 15);   // 1,073,709,056
constexpr ll INF = (1LL << 62) - (1LL << 31);  // 4,611,686,016,279,904,256
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class P1, class P2> void print(const pair<P1, P2>& a) { cout << a.first << " " << a.second << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> void print(const vector<T>& a) { cout_line(a, 0, a.size()); }
template<class S, class T> bool chmin(S& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class S, class T> bool chmax(S& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = false) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
template<class T> string to_binary(T x, int B = 0) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; }
template<class F> ll binary_search(const F& is_ok, ll ok, ll ng) { while (abs(ok - ng) > 1) { ll m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class F> double binary_search_real(const F& is_ok, double ok, double ng, int iter = 90) { for (int i = 0; i < iter; i++) { double m = (ok + ng) / 2; (is_ok(m) ? ok : ng) = m; } return ok; }
template<class T> using PQ_max = priority_queue<T>;
template<class T> using PQ_min = priority_queue<T, vector<T>, greater<T>>;
template<class T> T pick(stack<T>& s) { assert(not s.empty()); T x = s.top(); s.pop(); return x; }
template<class T> T pick(queue<T>& q) { assert(not q.empty()); T x = q.front(); q.pop(); return x; }
template<class T> T pick_front(deque<T>& dq) { assert(not dq.empty()); T x = dq.front(); dq.pop_front(); return x; }
template<class T> T pick_back(deque<T>& dq) { assert(not dq.empty()); T x = dq.back(); dq.pop_back(); return x; }
template<class T> T pick(PQ_min<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(PQ_max<T>& pq) { assert(not pq.empty()); T x = pq.top(); pq.pop(); return x; }
template<class T> T pick(vector<T>& v) { assert(not v.empty()); T x = v.back(); v.pop_back(); return x; }
int to_int(const char c) { if (islower(c)) { return (c - 'a'); } if (isupper(c)) { return (c - 'A'); } if (isdigit(c)) { return (c - '0'); } assert(false); }
char to_a(const int i) { assert(0 <= i && i < 26); return ('a' + i); }
char to_A(const int i) { assert(0 <= i && i < 26); return ('A' + i); }
char to_d(const int i) { assert(0 <= i && i <= 9); return ('0' + i); }
ll min(int a, ll b) { return min((ll)a, b); }
ll min(ll a, int b) { return min(a, (ll)b); }
ll max(int a, ll b) { return max((ll)a, b); }
ll max(ll a, int b) { return max(a, (ll)b); }
ll mod(ll x, ll m) { assert(m > 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digitlen(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll msb(ll b) { return (b <= 0 ? -1 : (63 - __builtin_clzll(b))); }
ll lsb(ll b) { return (b <= 0 ? -1 : __builtin_ctzll(b)); }
// --------------------------------------------------------

// clang-format on
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll N;
    input(N);
    VVLL A(N, VLL(N));
    REP (i, N) {
        REP (j, N) { input(A[i][j]); }
    }

    REP (n0, N) {
        REP (n1, N) {
            REP (n2, N) {
                if (A[A[n0][n1]][n2] != A[n0][A[n1][n2]]) { END("No"); }
            }
        }
    }

    ll e = -1;
    REP (ee, N) {
        bool ok = true;
        REP (n, N) {
            if (A[n][ee] == n && n == A[ee][n]) { continue; }
            ok = false;
            break;
        }
        if (ok) { e = ee; }
    }
    if (e == -1) { END("No"); }

    REP (n, N) {
        bool ok = false;
        REP (i, N) {
            if (A[n][i] == e && e == A[i][n]) {
                ok = true;
                break;
            }
        }
        if (not ok) { END("No"); }
    }
    print("Yes");

    return 0;
}

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結果

テストケース

ソースコード