#626018 (C++17) No.1421 国勢調査 (Hard)

提出ソース

結果

問題	No.1421 国勢調査 (Hard)
ユーザー	👑 hitonanode
提出日時	2021-03-05 22:55:20
言語	C++17 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	23 ms / 2,000 ms
コード長	7,988 bytes
コンパイル時間	3,059 ms
コンパイル使用メモリ	210,420 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-04-16 10:54:25
合計ジャッジ時間	3,934 ms
ジャッジサーバーID （参考情報）	judge3 / judge2

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 6,816 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	2 ms 6,948 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	1 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 6,940 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	2 ms 6,944 KB
testcase_15	AC	2 ms 6,940 KB
testcase_16	AC	2 ms 6,944 KB
testcase_17	AC	2 ms 6,944 KB
testcase_18	AC	2 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	2 ms 6,944 KB
testcase_22	AC	22 ms 6,940 KB
testcase_23	AC	22 ms 6,940 KB
testcase_24	AC	23 ms 6,944 KB
testcase_25	AC	23 ms 6,944 KB
testcase_26	AC	22 ms 6,944 KB
testcase_27	AC	21 ms 6,944 KB
testcase_28	AC	16 ms 6,940 KB
testcase_29	AC	14 ms 6,944 KB
testcase_30	AC	8 ms 6,944 KB
testcase_31	AC	5 ms 6,944 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
constexpr int Wmax = 10 + 1;
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#else
constexpr int Wmax = 50 + 1;
#define dbg(x) (x)
#endif


std::vector<std::bitset<Wmax>> gauss_jordan(int W, std::vector<std::bitset<Wmax>> mtr) {
    int H = mtr.size(), c = 0;
    for (int h = 0; h < H; h++, c++) {
        if (c == W) break;
        int piv = -1;
        for (int j = h; j < H; j++)
            if (mtr[j][c]) {
                piv = j;
                break;
            }
        if (piv == -1) {
            h--;
            continue;
        }
        std::swap(mtr[piv], mtr[h]);
        for (int hh = 0; hh < H; hh++) {
            if (hh != h and mtr[hh][c]) mtr[hh] ^= mtr[h];
        }
    }
    return mtr;
}

int rank_gauss_jordan(int W, const std::vector<std::bitset<Wmax>> &mtr) // Rank of Gauss-Jordan eliminated matrix
{
    for (int h = (int)mtr.size() - 1; h >= 0; h--) {
        if (mtr[h]._Find_first() < W) return h + 1;
    }
    return 0;
}

std::vector<std::bitset<Wmax>> matmul(const std::vector<std::bitset<Wmax>> &A, const std::vector<std::bitset<Wmax>> &B) {
    int H = A.size(), K = B.size();
    std::vector<std::bitset<Wmax>> C(H);
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < K; j++) {
            if (A[i][j]) C[i] ^= B[j];
        }
    }
    return C;
}

std::vector<std::bitset<Wmax>> matpower(std::vector<std::bitset<Wmax>> X, long long n) {
    int D = X.size();
    std::vector<std::bitset<Wmax>> ret(D);
    for (int i = 0; i < D; i++) ret[i][i] = 1;
    while (n) {
        if (n & 1) ret = matmul(ret, X);
        X = matmul(X, X), n >>= 1;
    }
    return ret;
}

// Solve Ax = b on F_2
// - retval: {true, one of the solutions, {freedoms}} (if solution exists)
//           {false, {}, {}} (otherwise)
std::tuple<bool, std::bitset<Wmax>, std::vector<std::bitset<Wmax>>> system_of_linear_equations(std::vector<std::bitset<Wmax>> A, std::bitset<Wmax> b, int W) {
    int H = A.size();
    assert(W + 1 <= Wmax);
    assert(H <= Wmax);

    std::vector<std::bitset<Wmax>> M = A;
    for (int i = 0; i < H; i++) M[i][W] = b[i];
    M = gauss_jordan(W + 1, M);
    std::vector<int> ss(W, -1);
    for (int i = 0; i < H; i++) {
        int j = M[i]._Find_first();
        if (j == W) { return std::make_tuple(false, std::bitset<Wmax>(), std::vector<std::bitset<Wmax>>()); }
        if (j < W) ss[j] = i;
    }
    std::bitset<Wmax> x;
    std::vector<std::bitset<Wmax>> D;
    for (int j = 0; j < W; j++) {
        if (ss[j] == -1) {
            std::bitset<Wmax> d;
            d[j] = 1;
            for (int jj = 0; jj < W; jj++)
                if (ss[jj] != -1) d[jj] = M[ss[jj]][j];
            D.emplace_back(d);
        } else
            x[j] = M[ss[j]][W];
    }
    return std::make_tuple(true, x, D);
}

void bad() {
    puts("-1");
    exit(0);
}

int main() {
    int N, M;
    cin >> N >> M;

    using ull = unsigned long long;
    vector<pair<ull, int>> basis;
    while (M--) {
        int a;
        cin >> a;
        ull mask = 0;
        while (a--) {
            int b;
            cin >> b;
            b--;
            mask += 1ULL << b;
        }
        int y;
        cin >> y;
        for (auto [v, w] : basis) {
            if (chmin(mask, mask ^ v)) y ^= w;
        }
        if (!mask and y) bad();
        if (mask) basis.emplace_back(mask, y);
    }

    vector<int> ret(N);
    REP(d, 30) {
        vector<bitset<Wmax>> A;
        bitset<Wmax> b;
        b.reset();
        REP(i, basis.size()) {
            b[i] = ((basis[i].second >> d) & 1);
            bitset<Wmax> a;
            a.reset();
            REP(j, N) if ((basis[i].first >> j) & 1) a[j] = 1;
            A.emplace_back(a);
        }
        auto [ok, solution, freedoms] = system_of_linear_equations(A, b, N);
        if (!ok) bad();
        REP(i, N) ret[i] += int(solution[i]) << d;
    }
    for (auto x : ret) cout << x << '\n';
}

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結果

テストケース

ソースコード