結果

問題 No.3047 Verification of Sorting Network
ユーザー 👑 Mizar
提出日時 2025-01-31 23:18:05
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 857 ms / 2,000 ms
コード長 4,541 bytes
コンパイル時間 5,035 ms
コンパイル使用メモリ 313,920 KB
実行使用メモリ 8,608 KB
最終ジャッジ日時 2025-03-05 20:33:22
合計ジャッジ時間 38,213 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 61
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ソースコード

diff # 

// O(M*2^n)+4並列64bit高速化解
#pragma GCC optimize ("O3")
#pragma GCC target ("tune=native")
#include <bits/stdc++.h> // all
using namespace std;

#define MAX_T 10000
#define MAX_N 27
#define MAX_COST 1e8
using node_index = uint8_t;

expected<vector<bool>, vector<bool>> is_sorting_network_j64(const size_t n, const vector<pair<node_index, node_index>> cmps) {
    assert(2 <= n && n <= MAX_N && MAX_N <= UINT64_WIDTH && 8 <= MAX_N);
    for (auto [a, b] : cmps) {
        // 0-indexed
        assert(0 <= a && a < b && b < n);
    }
    size_t m = cmps.size();
    vector<bool> unused(m, true), unsorted(n - 1, false);
    array<array<uint64_t, 4>, MAX_N> states;
    const array<uint64_t, 6> lows = {0xaaaaaaaaaaaaaaaa, 0xcccccccccccccccc, 0xf0f0f0f0f0f0f0f0, 0xff00ff00ff00ff00, 0xffff0000ffff0000, 0xffffffff00000000};
    uint64_t limit = 1ULL << (max(n, 8uz) - 8);
    for (uint64_t i = 0; i < limit; ++i) {
        for (size_t j = 0; auto x : lows) {
            states[j++] = { x, x, x, x };
        }
        states[6] = { 0, UINT64_MAX, 0, UINT64_MAX };
        states[7] = { 0, 0, UINT64_MAX, UINT64_MAX };
        for (size_t j = 8; j < n; ++j) {
            uint64_t x = ((i >> (j - 8)) & 1) != 0 ? UINT64_MAX : 0;
            states[j] = { x, x, x, x };
        }
        for (size_t j = 0; auto [a, b] : cmps) {
            uint64_t va0 = states[a][0], va1 = states[a][1], va2 = states[a][2], va3 = states[a][3];
            uint64_t vb0 = states[b][0], vb1 = states[b][1], vb2 = states[b][2], vb3 = states[b][3];
            uint64_t na0 = (va0 & vb0), na1 = (va1 & vb1), na2 = (va2 & vb2), na3 = (va3 & vb3);
            uint64_t nb0 = (va0 | vb0), nb1 = (va1 | vb1), nb2 = (va2 | vb2), nb3 = (va3 | vb3);
            if (na0 != va0 || na1 != va1 || na2 != va2 || na3 != va3) {
                states[a] = { na0, na1, na2, na3 };
                states[b] = { nb0, nb1, nb2, nb3 };
                unused[j] = false;
            }
            ++j;
        }
        for (size_t j = 1; j < n; ++j) {
            if ((states[j - 1][0] & ~states[j][0]) != 0 ||
                (states[j - 1][1] & ~states[j][1]) != 0 ||
                (states[j - 1][2] & ~states[j][2]) != 0 ||
                (states[j - 1][3] & ~states[j][3]) != 0) {
                unsorted[j - 1] = true;
            }
        }
    }
    if (any_of(unsorted.begin(), unsorted.end(), [](bool x) { return x; })) {
        return unexpected(unsorted);
    }
    return unused;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    assert(MAX_N <= numeric_limits<node_index>::max());

    size_t t;
    cin >> t;
    assert(1 <= t && t <= MAX_T);

    // phi = (1 + sqrt(5)) / 2 : golden ratio
    double phi = sqrt(1.25) + 0.5;
    // testcases cost <= 1e8
    double cost = 0.0;

    for (size_t i = 0; i < t; ++i) {
        size_t n, m;
        cin >> n >> m;
        vector<pair<node_index, node_index>> cmps;
        assert(2 <= n && n <= MAX_N && 1 <= m && m <= n * (n - 1) / 2);
        cost += m * pow(phi, n);
        assert(cost <= MAX_COST);
        vector<int> vec_a, vec_b;
        for (int j = 0; j < m; ++j) {
            int a;
            cin >> a;
            vec_a.push_back(a);
        }
        for (int j = 0; j < m; ++j) {
            int b;
            cin >> b;
            vec_b.push_back(b);
        }
        for (int j = 0; j < m; ++j) {
            int a = vec_a[j], b = vec_b[j];
            assert(1 <= a && a < b && b <= n);
            // 1-indexed to 0-indexed
            cmps.emplace_back(a - 1, b - 1);
        }
        auto is_sorting = is_sorting_network_j64(n, cmps);
        if (is_sorting.has_value()) {
            auto unused = is_sorting.value();
            assert(unused.size() == m);
            cout << "Yes\n";
            cout << count(unused.begin(), unused.end(), true) << '\n';
            // 1-indexed
            for (int j = 1; const auto x : unused) {
                if (x) {
                    cout << j << ' ';
                }
                ++j;
            }
            cout << '\n';
        } else {
            auto unsorted = is_sorting.error();
            assert(unsorted.size() == n - 1);
            cout << "No\n";
            cout << count(unsorted.begin(), unsorted.end(), true) << '\n';
            // 1-indexed
            for (int j = 1; const auto x : unsorted) {
                if (x) {
                    cout << j << ' ';
                }
                ++j;
            }
            cout << '\n';
        }
    }

    return 0;
}
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