#718338 (C++17) No.1775 Love Triangle 2

提出ソース

結果

問題	No.1775 Love Triangle 2
ユーザー	hitonanode
提出日時	2021-11-20 02:24:55
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	408 ms / 8,000 ms
コード長	5,768 bytes
コンパイル時間	2,035 ms
コンパイル使用メモリ	140,884 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-03 21:09:00
合計ジャッジ時間	20,126 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

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	29 ms 6,812 KB
testcase_01	AC	29 ms 6,940 KB
testcase_02	AC	30 ms 6,940 KB
testcase_03	AC	31 ms 6,940 KB
testcase_04	AC	396 ms 6,940 KB
testcase_05	AC	391 ms 6,944 KB
testcase_06	AC	400 ms 6,940 KB
testcase_07	AC	408 ms 6,940 KB
testcase_08	AC	396 ms 6,940 KB
testcase_09	AC	123 ms 6,940 KB
testcase_10	AC	133 ms 6,940 KB
testcase_11	AC	95 ms 6,940 KB
testcase_12	AC	89 ms 6,940 KB
testcase_13	AC	76 ms 6,944 KB
testcase_14	AC	70 ms 6,940 KB
testcase_15	AC	60 ms 6,940 KB
testcase_16	AC	56 ms 6,944 KB
testcase_17	AC	54 ms 6,944 KB
testcase_18	AC	52 ms 6,944 KB
testcase_19	AC	115 ms 6,944 KB
testcase_20	AC	110 ms 6,944 KB
testcase_21	AC	100 ms 6,940 KB
testcase_22	AC	87 ms 6,940 KB
testcase_23	AC	75 ms 6,944 KB
testcase_24	AC	95 ms 6,940 KB
testcase_25	AC	91 ms 6,944 KB
testcase_26	AC	79 ms 6,944 KB
testcase_27	AC	87 ms 6,944 KB
testcase_28	AC	72 ms 6,944 KB
testcase_29	AC	52 ms 6,940 KB
testcase_30	AC	77 ms 6,944 KB
testcase_31	AC	118 ms 6,940 KB
testcase_32	AC	166 ms 6,940 KB
testcase_33	AC	212 ms 6,944 KB
testcase_34	AC	213 ms 6,940 KB
testcase_35	AC	253 ms 6,944 KB
testcase_36	AC	294 ms 6,944 KB
testcase_37	AC	342 ms 6,944 KB
testcase_38	AC	387 ms 6,944 KB
testcase_39	AC	63 ms 6,940 KB
testcase_40	AC	95 ms 6,940 KB
testcase_41	AC	127 ms 6,944 KB
testcase_42	AC	134 ms 6,940 KB
testcase_43	AC	144 ms 6,944 KB
testcase_44	AC	108 ms 6,944 KB
testcase_45	AC	246 ms 6,940 KB
testcase_46	AC	162 ms 6,940 KB
testcase_47	AC	85 ms 6,940 KB
testcase_48	AC	175 ms 6,940 KB
testcase_49	AC	52 ms 6,940 KB
testcase_50	AC	73 ms 6,940 KB
testcase_51	AC	113 ms 6,944 KB
testcase_52	AC	158 ms 6,944 KB
testcase_53	AC	206 ms 6,944 KB
testcase_54	AC	210 ms 6,940 KB
testcase_55	AC	251 ms 6,940 KB
testcase_56	AC	302 ms 6,940 KB
testcase_57	AC	353 ms 6,944 KB
testcase_58	AC	399 ms 6,940 KB
testcase_59	AC	65 ms 6,944 KB
testcase_60	AC	86 ms 6,940 KB
testcase_61	AC	108 ms 6,944 KB
testcase_62	AC	80 ms 6,944 KB
testcase_63	AC	96 ms 6,940 KB
testcase_64	AC	119 ms 6,940 KB
testcase_65	AC	73 ms 6,944 KB
testcase_66	AC	115 ms 6,944 KB
testcase_67	AC	149 ms 6,940 KB
testcase_68	AC	98 ms 6,940 KB
testcase_69	AC	165 ms 6,944 KB
testcase_70	AC	302 ms 6,944 KB
testcase_71	AC	350 ms 6,944 KB
testcase_72	AC	386 ms 6,944 KB
testcase_73	AC	378 ms 6,940 KB
testcase_74	AC	394 ms 6,944 KB
testcase_75	AC	402 ms 6,944 KB
testcase_76	AC	352 ms 6,940 KB
testcase_77	AC	395 ms 6,940 KB
testcase_78	AC	397 ms 6,940 KB
testcase_79	AC	137 ms 6,944 KB
testcase_80	AC	154 ms 6,944 KB
testcase_81	AC	206 ms 6,940 KB
testcase_82	AC	184 ms 6,944 KB
testcase_83	AC	223 ms 6,940 KB
testcase_84	AC	170 ms 6,944 KB
testcase_85	AC	211 ms 6,940 KB
testcase_86	AC	146 ms 6,940 KB
testcase_87	AC	206 ms 6,940 KB
testcase_88	AC	305 ms 6,940 KB
testcase_89	AC	269 ms 6,944 KB

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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 {
        ull ret = 0;
        for (int d = 0; d < 8; ++d) {
            for (int e = 0; e < 8; ++e) {
                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 solve(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;
                        Fq 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 -1;  // not found
}

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;
    }
    cout << solve(weight, x, y, z, N) << '\n';
}

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結果

テストケース

ソースコード