#718298 (C++17) No.1776 Love Triangle 2 (Hard)

提出ソース

結果

問題	No.1776 Love Triangle 2 (Hard)
ユーザー	hitonanode
提出日時	2021-11-20 00:54:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE (最新) AC (最初)
実行時間	-
コード長	8,173 bytes
コンパイル時間	2,550 ms
コンパイル使用メモリ	145,516 KB
実行使用メモリ	6,016 KB
最終ジャッジ日時	2024-07-02 12:05:51
合計ジャッジ時間	67,767 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	32 ms 5,248 KB
testcase_01	AC	32 ms 5,376 KB
testcase_02	AC	32 ms 5,376 KB
testcase_03	AC	32 ms 5,376 KB
testcase_04	AC	88 ms 5,376 KB
testcase_05	AC	89 ms 5,376 KB
testcase_06	AC	88 ms 5,376 KB
testcase_07	AC	88 ms 5,376 KB
testcase_08	AC	88 ms 5,376 KB
testcase_09	AC	177 ms 5,376 KB
testcase_10	AC	213 ms 5,376 KB
testcase_11	AC	112 ms 5,376 KB
testcase_12	AC	95 ms 5,376 KB
testcase_13	AC	73 ms 5,376 KB
testcase_14	AC	63 ms 5,376 KB
testcase_15	AC	55 ms 5,376 KB
testcase_16	AC	51 ms 5,376 KB
testcase_17	AC	47 ms 5,376 KB
testcase_18	AC	46 ms 5,376 KB
testcase_19	AC	158 ms 5,376 KB
testcase_20	AC	148 ms 5,376 KB
testcase_21	AC	113 ms 5,376 KB
testcase_22	AC	92 ms 5,376 KB
testcase_23	AC	71 ms 5,376 KB
testcase_24	AC	111 ms 5,376 KB
testcase_25	AC	90 ms 5,376 KB
testcase_26	AC	73 ms 5,376 KB
testcase_27	AC	91 ms 5,376 KB
testcase_28	AC	68 ms 5,376 KB
testcase_29	AC	46 ms 5,376 KB
testcase_30	AC	75 ms 5,376 KB
testcase_31	AC	187 ms 5,376 KB
testcase_32	AC	365 ms 5,376 KB
testcase_33	AC	658 ms 5,376 KB
testcase_34	AC	658 ms 5,376 KB
testcase_35	AC	908 ms 5,376 KB
testcase_36	AC	1,238 ms 5,376 KB
testcase_37	AC	1,612 ms 5,376 KB
testcase_38	AC	2,106 ms 5,376 KB
testcase_39	AC	58 ms 5,376 KB
testcase_40	AC	123 ms 5,376 KB
testcase_41	AC	212 ms 5,376 KB
testcase_42	AC	251 ms 5,376 KB
testcase_43	AC	262 ms 5,376 KB
testcase_44	AC	148 ms 5,376 KB
testcase_45	AC	805 ms 5,376 KB
testcase_46	AC	310 ms 5,376 KB
testcase_47	AC	83 ms 5,376 KB
testcase_48	AC	421 ms 5,376 KB
testcase_49	AC	44 ms 5,376 KB
testcase_50	AC	75 ms 5,376 KB
testcase_51	AC	190 ms 5,376 KB
testcase_52	AC	366 ms 5,376 KB
testcase_53	AC	647 ms 5,376 KB
testcase_54	AC	645 ms 5,376 KB
testcase_55	AC	883 ms 5,376 KB
testcase_56	AC	1,246 ms 5,376 KB
testcase_57	AC	1,588 ms 5,376 KB
testcase_58	AC	2,213 ms 5,376 KB
testcase_59	AC	63 ms 5,376 KB
testcase_60	AC	97 ms 5,376 KB
testcase_61	AC	149 ms 5,376 KB
testcase_62	AC	85 ms 5,376 KB
testcase_63	AC	118 ms 5,376 KB
testcase_64	AC	179 ms 5,376 KB
testcase_65	AC	71 ms 5,376 KB
testcase_66	AC	163 ms 5,376 KB
testcase_67	AC	290 ms 5,376 KB
testcase_68	AC	111 ms 5,376 KB
testcase_69	AC	236 ms 6,004 KB
testcase_70	AC	237 ms 6,000 KB
testcase_71	AC	238 ms 6,000 KB
testcase_72	AC	239 ms 5,888 KB
testcase_73	AC	239 ms 5,876 KB
testcase_74	AC	463 ms 5,760 KB
testcase_75	AC	302 ms 5,888 KB
testcase_76	AC	235 ms 6,008 KB
testcase_77	AC	196 ms 5,888 KB
testcase_78	AC	133 ms 5,888 KB
testcase_79	AC	106 ms 5,888 KB
testcase_80	AC	97 ms 5,888 KB
testcase_81	AC	77 ms 5,888 KB
testcase_82	AC	71 ms 5,872 KB
testcase_83	AC	67 ms 5,888 KB
testcase_84	AC	387 ms 5,888 KB
testcase_85	AC	292 ms 5,888 KB
testcase_86	AC	254 ms 5,872 KB
testcase_87	AC	160 ms 6,004 KB
testcase_88	AC	132 ms 5,888 KB
testcase_89	AC	235 ms 6,008 KB
testcase_90	AC	161 ms 5,888 KB
testcase_91	AC	130 ms 5,760 KB
testcase_92	AC	179 ms 5,888 KB
testcase_93	AC	120 ms 5,888 KB
testcase_94	AC	62 ms 5,888 KB
testcase_95	AC	193 ms 5,888 KB
testcase_96	AC	630 ms 5,880 KB
testcase_97	AC	1,614 ms 5,888 KB
testcase_98	AC	3,459 ms 5,876 KB
testcase_99	AC	3,454 ms 6,008 KB
testcase_100	AC	5,852 ms 5,888 KB
testcase_101	AC	8,207 ms 5,888 KB
testcase_102	TLE	-
testcase_103	TLE	-
testcase_104	--	-
testcase_105	--	-
testcase_106	--	-
testcase_107	--	-
testcase_108	--	-
testcase_109	--	-
testcase_110	--	-
testcase_111	--	-
testcase_112	--	-
testcase_113	--	-
testcase_114	--	-
testcase_115	--	-
testcase_116	--	-
testcase_117	--	-
testcase_118	--	-
testcase_119	--	-
testcase_120	--	-
testcase_121	--	-
testcase_122	--	-
testcase_123	--	-
testcase_124	--	-
testcase_125	--	-
testcase_126	--	-
testcase_127	--	-
testcase_128	--	-
testcase_129	--	-
testcase_130	--	-
testcase_131	--	-
testcase_132	--	-
testcase_133	--	-
testcase_134	--	-
testcase_135	--	-
testcase_136	--	-
testcase_137	--	-
testcase_138	--	-
testcase_139	--	-
testcase_140	--	-
testcase_141	--	-
testcase_142	--	-
testcase_143	--	-
testcase_144	--	-
testcase_145	--	-
testcase_146	--	-
testcase_147	--	-
testcase_148	--	-
testcase_149	--	-
testcase_150	--	-
testcase_151	--	-
testcase_152	--	-
testcase_153	--	-
testcase_154	--	-
testcase_155	--	-
testcase_156	--	-
testcase_157	--	-
testcase_158	--	-
testcase_159	--	-
testcase_160	--	-
testcase_161	--	-
testcase_162	--	-
testcase_163	--	-
testcase_164	--	-
testcase_165	--	-
testcase_166	--	-
testcase_167	--	-
testcase_168	--	-
testcase_169	--	-
testcase_170	--	-
testcase_171	--	-
testcase_172	--	-
testcase_173	--	-
testcase_174	--	-
testcase_175	--	-

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ソースコード

raw source code

#include <array>
#include <chrono>
#include <iostream>
#include <random>
#include <vector>
using namespace std;
// https://epubs.siam.org/doi/10.1137/1.9781611973099.139

// Nimber (64 bit)
// Reference:
// - https://en.wikipedia.org/wiki/Nimber
// - https://kyopro-friends.hatenablog.com/entry/2020/04/07/195850
// - https://judge.yosupo.jp/submission/4542 (implementation idea)
struct Nimber {
    using ull = unsigned long long;
    ull v;
    const static std::array<std::array<unsigned, 256>, 256> small_table;
    const static std::array<std::array<std::array<ull, 256>, 8>, 8> precalc;

    explicit operator bool() const { return v != 0; }
    Nimber(ull val = 0) : v(val) {}
    Nimber operator+(const Nimber &x) const { return Nimber(v ^ x.v); }
    Nimber operator-(const Nimber &x) const { return Nimber(v ^ x.v); }
    Nimber operator-() const { return *this; }
    Nimber &operator+=(const Nimber &x) { return *this = *this + x; }
    Nimber &operator-=(const Nimber &x) { return *this = *this + x; }
    template <class IStream> friend IStream &operator>>(IStream &is, Nimber &x) {
        ull v;
        return is >> v, x = Nimber(v), is;
    }
    template <class OStream> friend OStream &operator<<(OStream &os, const Nimber &x) {
        return os << x.v;
    }
    bool operator==(const Nimber &x) const { return v == x.v; }
    bool operator!=(const Nimber &x) const { return v != x.v; }
    bool operator<(const Nimber &x) const { return v < x.v; }

    static ull _rec(ull x, ull y) {
        if (x == 0 or y == 0) return 0;
        if (x < y) x ^= y, y ^= x, x ^= y; // Make x >= y
        if (y == 1) return x;
        for (int shift = 64 / 2;; shift >>= 1) {
            ull mask = (1ULL << shift) - 1;
            if (y >> shift) {
                ull v00 = _rec(x & mask, y & mask);
                ull v01 = _rec(x & mask, y >> shift);
                ull v10 = _rec(x >> shift, y & mask);
                ull v11 = _rec(x >> shift, y >> shift);
                return v00 ^ ((v01 ^ v10 ^ v11) << shift) ^ _rec(v11, 1ULL << (shift - 1));
            } else if (x >> shift) {
                return (_rec(x >> shift, y) << shift) ^ _rec(x & mask, y);
            }
        }
    }
    Nimber operator*(const Nimber &x) const {
        if (this->v < 256 and x.v < 256) return small_table[this->v][x.v];
        ull ret = 0;
        for (int d = 0; d < 2; ++d) {  // 16 bit
            for (int e = 0; e < 2; ++e) {  // 16 bit
                ret ^= precalc[d][e][small_table[(v >> (d * 8)) & 255][(x.v >> (e * 8)) & 255]];
            }
        }
        return Nimber(ret);
    }
    Nimber &operator*=(const Nimber &x) { return *this = *this * x; }
};

const std::array<std::array<unsigned, 256>, 256> Nimber::small_table = []() {
    std::array<std::array<unsigned, 256>, 256> ret;
    for (int i = 0; i < 256; ++i) {
        for (int j = 0; j < 256; ++j) ret[i][j] = _rec(i, j);
    }
    return ret;
}();
const std::array<std::array<std::array<unsigned long long, 256>, 8>, 8> Nimber::precalc = []() {
    std::array<std::array<std::array<unsigned long long, 256>, 8>, 8> ret;
    for (int d = 0; d < 8; ++d) {
        for (int e = 0; e < 8; ++e) {
            ull p = _rec(1ULL << (8 * d), 1ULL << (8 * e));
            for (int i = 0; i < 256; ++i) ret[d][e][i] = _rec(p, i);
        }
    }
    return ret;
}();

struct rand_int_ {
    using lint = long long;
    mt19937 mt;
    rand_int_() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
    lint operator()(lint x) { return this->operator()(0, x); } // [0, x)
    lint operator()(lint l, lint r) {
        uniform_int_distribution<lint> d(l, r - 1);
        return d(mt);
    }
} rnd;

template <class Fq>
int can_reach(const vector<vector<Fq>> &w, int x, int y, int z, int dlim) {
    // x を始点に y, z を経由し N に到達する長さ dlim 以下のパスがあるかを判定
    int N = w.size() - 1;
    // dp[visited y][visited z][current v][previous v]
    vector dp(2, vector(2, vector(N + 1, vector<Fq>(N + 1, 0))));
    dp[0][0][N][N] = 1;
    for (int d = 1; d <= dlim; ++d) {
        vector dpnxt(2, vector(2, vector(N + 1, vector<Fq>(N + 1, 0))));
        for (int visy = 0; visy < 2; ++visy) {
            for (int visz = 0; visz < 2; ++visz) {
                for (int now = 0; now <= N; ++now) {
                    Fq sum = 0;
                    for (int prv = 0; prv <= N; ++prv) sum += dp[visy][visz][now][prv];
                    for (int nxt = 0; nxt <= N; ++nxt) {
                        if (visy and (nxt == y)) continue;
                        if (visz and (nxt == z)) continue;
                        Nimber wadd = sum - ((now == y or now == z) ? dp[visy][visz][now][nxt] : 0);
                        dpnxt[visy | (nxt == y)][visz | (nxt == z)][nxt][now] += wadd * w[now][nxt];
                    }
                }
            }
        }
        dp = dpnxt;
        for (int i = 0; i < N; ++i) {
            if (dp[1][1][x][i] != 0) return d;
        }
    }
    return 0;  // not found
}

template <class Fq>
int next_step(const vector<vector<Fq>> &w, int h, int vy, int vz, int y, int z, int D) {
    // h を始点に y, z を経由し N に到達する長さ D のパスの次の一歩
    int N = w.size() - 1;
    // dp[visited y][visited z][current v][previous v]
    vector dp(2, vector(2, vector(N + 1, vector<Fq>(N + 1, 0))));
    dp[0][0][N][N] = 1;
    for (int d = 1; d < D; ++d) {
        vector dpnxt(2, vector(2, vector(N + 1, vector<Fq>(N + 1, 0))));
        for (int visy = 0; visy < 2; ++visy) {
            for (int visz = 0; visz < 2; ++visz) {
                for (int now = 0; now <= N; ++now) {
                    Fq sum = 0;
                    for (int prv = 0; prv <= N; ++prv) sum += dp[visy][visz][now][prv];
                    for (int nxt = 0; nxt <= N; ++nxt) {
                        if (visy and (nxt == y)) continue;
                        if (visz and (nxt == z)) continue;
                        // Nimber wadd = sum - ((now == y or now == z) ? dp[visy][visz][now][nxt] : 0);
                        Nimber wadd = sum - dp[visy][visz][now][nxt];
                        if (nxt == h) continue;
                        dpnxt[visy | (nxt == y)][visz | (nxt == z)][nxt][now] += wadd * w[now][nxt];
                    }
                }
            }
        }
        dp = dpnxt;
    }
    for (int i = 0; i < N; ++i) {
        if (!w[i][h]) continue;
        Nimber sum = 0;
        for (int j = 0; j <= N; ++j) sum += dp[vy][vz][i][j];
        if (!sum) continue;
        return i;
    }
    throw;
}

int main() {
    int N, M;
    cin >> N >> M;
    int x, y, z;
    cin >> x >> y >> z;

    --x, --y, --z;
    vector weight(N + 1, vector<Nimber>(N + 1));
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < i; ++j) {
            Nimber w = rnd(1LL << 16);
            Nimber wn = rnd(1LL << 16);
            if (j != x) {
                weight[j][i] = w;
            } else {
                weight[N][i] = wn;
            }
            if (i != x) {
                weight[i][j] = w;
            } else {
                weight[N][j] = wn;
            }
        }
    }

    while (M--) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        weight[a][b] = weight[b][a] = 0;
        if (a == x) weight[N][b] = 0;
        if (b == x) weight[N][a] = 0;
    }
    int len = can_reach(weight, x, y, z, N);
    if (!len) {
        puts("-1");
        return 0;
    }
    cout << len << '\n';

    vector<int> path{x};
    int vy = 1, vz = 1;
    for (int l = 1; l < len; ++l) {
        int cur = path.back();
        if (y == cur) vy = 0;
        if (z == cur) vz = 0;
        int ok = next_step(weight, cur, vy, vz, y, z, len - l + 1);
        path.push_back(ok);

        for (int i = 0; i <= N; ++i) weight[cur][i] = weight[i][cur] = 0;
    }

    path.push_back(x);

    for (auto x : path) cout << x + 1 << ' ';
    cout << '\n';
}

yukicoder

結果

テストケース

ソースコード