結果

問題 No.1776 Love Triangle 2 (Hard)
ユーザー hitonanodehitonanode
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
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testcase_03 AC 32 ms
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testcase_04 AC 88 ms
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testcase_05 AC 89 ms
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testcase_06 AC 88 ms
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testcase_07 AC 88 ms
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testcase_08 AC 88 ms
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testcase_09 AC 177 ms
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testcase_10 AC 213 ms
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testcase_11 AC 112 ms
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testcase_12 AC 95 ms
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testcase_13 AC 73 ms
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testcase_14 AC 63 ms
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testcase_15 AC 55 ms
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testcase_16 AC 51 ms
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testcase_17 AC 47 ms
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testcase_18 AC 46 ms
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testcase_19 AC 158 ms
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testcase_20 AC 148 ms
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testcase_21 AC 113 ms
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testcase_22 AC 92 ms
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testcase_23 AC 71 ms
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testcase_24 AC 111 ms
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testcase_25 AC 90 ms
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testcase_26 AC 73 ms
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testcase_27 AC 91 ms
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testcase_28 AC 68 ms
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testcase_29 AC 46 ms
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testcase_30 AC 75 ms
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testcase_31 AC 187 ms
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testcase_32 AC 365 ms
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testcase_33 AC 658 ms
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testcase_34 AC 658 ms
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testcase_35 AC 908 ms
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testcase_36 AC 1,238 ms
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testcase_37 AC 1,612 ms
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testcase_38 AC 2,106 ms
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testcase_39 AC 58 ms
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testcase_40 AC 123 ms
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testcase_41 AC 212 ms
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testcase_42 AC 251 ms
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testcase_43 AC 262 ms
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testcase_44 AC 148 ms
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testcase_45 AC 805 ms
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testcase_46 AC 310 ms
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testcase_47 AC 83 ms
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testcase_48 AC 421 ms
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testcase_49 AC 44 ms
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testcase_50 AC 75 ms
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testcase_51 AC 190 ms
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testcase_52 AC 366 ms
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testcase_53 AC 647 ms
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testcase_54 AC 645 ms
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testcase_55 AC 883 ms
5,376 KB
testcase_56 AC 1,246 ms
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testcase_57 AC 1,588 ms
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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
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testcase_64 AC 179 ms
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testcase_65 AC 71 ms
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testcase_66 AC 163 ms
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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 -- -
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testcase_148 -- -
testcase_149 -- -
testcase_150 -- -
testcase_151 -- -
testcase_152 -- -
testcase_153 -- -
testcase_154 -- -
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testcase_156 -- -
testcase_157 -- -
testcase_158 -- -
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testcase_160 -- -
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testcase_171 -- -
testcase_172 -- -
testcase_173 -- -
testcase_174 -- -
testcase_175 -- -
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ソースコード

diff #

#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';
}
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