結果

問題 No.3229 Liar Game Comibination
コンテスト
ユーザー wasd314
提出日時 2025-08-08 22:45:32
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 195 ms / 2,000 ms
コード長 8,083 bytes
コンパイル時間 6,198 ms
コンパイル使用メモリ 332,952 KB
実行使用メモリ 30,228 KB
最終ジャッジ日時 2025-08-08 22:45:42
合計ジャッジ時間 8,859 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 29
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

diff # 

// https://judge.yosupo.jp/submission/275205
#include <algorithm>
#include <array>
#include <bit>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
// #include <compare>
#include <complex>
// #include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numbers>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <ranges>
#include <set>
#include <span>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <atcoder/all>

// #define int ll
#define INT128_MAX (__int128)(((unsigned __int128)1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define pb push_back
#define eb emplace_back
#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> pr)
{
    return os << pr.first << ' ' << pr.second;
}
template <class T, size_t N>
ostream &operator<<(ostream &os, const array<T, N> &arr)
{
    for (size_t i = 0; T x : arr) {
        os << x;
        if (++i != N) os << ' ';
    }
    return os;
}
template <class T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
    for (size_t i = 0; T x : vec) {
        os << x;
        if (++i != size(vec)) os << ' ';
    }
    return os;
}
template <class T>
ostream &operator<<(ostream &os, const set<T> &s)
{
    for (size_t i = 0; T x : s) {
        os << x;
        if (++i != size(s)) os << ' ';
    }
    return os;
}
template <class T1, class T2>
ostream &operator<<(ostream &os, const map<T1, T2> &m)
{
    for (size_t i = 0; pair<T1, T2> x : m) {
        os << x;
        if (++i != size(m)) os << ' ';
    }
    return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template <typename T>
void _do(T &&x)
{
    cerr << x;
}
template <typename T, typename... S>
void _do(T &&x, S &&...y)
{
    cerr << x << ", ";
    _do(y...);
}
template <typename T>
void _do2(T &&x)
{
    cerr << x << endl;
}
template <typename T, typename... S>
void _do2(T &&x, S &&...y)
{
    cerr << x << ", ";
    _do2(y...);
}
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
// #define double ldb

template <typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using max_heap = priority_queue<T>;

template <ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &&v)
{
    if (!v.empty())
        for (T p = v[0]; T &x : v | views::drop(1))
            x = p = OP()(p, x);
}
template <ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &&v, OP op)
{
    if (!v.empty())
        for (T p = v[0]; T &x : v | views::drop(1))
            x = p = op(p, x);
}

template <ranges::forward_range rng>
void Unique(rng &v)
{
    ranges::sort(v);
    v.resize(unique(v.begin(), v.end()) - v.begin());
}

template <ranges::random_access_range rng>
rng invPerm(rng p)
{
    rng ret = p;
    for (int i = 0; i < ssize(p); i++)
        ret[p[i]] = i;
    return ret;
}

template <ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p)
{
    rng ret = v;
    for (int i = 0; i < ssize(p); i++)
        ret[p[i]] = v[i];
    return ret;
}

template <bool directed>
vector<vector<int>> readGraph(int n, int m, int base)
{
    vector<vector<int>> g(n);
    for (int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        u -= base, v -= base;
        g[u].emplace_back(v);
        if constexpr (!directed)
            g[v].emplace_back(u);
    }
    return g;
}

template <class T>
void setBit(T &msk, int bit, bool x)
{
    msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template <class T>
void flipBit(T &msk, int bit)
{
    msk ^= T(1) << bit;
}
template <class T>
bool getBit(T msk, int bit)
{
    return msk >> bit & T(1);
}

template <class T>
T floorDiv(T a, T b)
{
    if (b < 0) a *= -1, b *= -1;
    return a >= 0 ? a / b : (a - b + 1) / b;
}
template <class T>
T ceilDiv(T a, T b)
{
    if (b < 0) a *= -1, b *= -1;
    return a >= 0 ? (a + b - 1) / b : a / b;
}

template <class T>
bool chmin(T &a, T b)
{
    return a > b ? a = b, 1 : 0;
}
template <class T>
bool chmax(T &a, T b)
{
    return a < b ? a = b, 1 : 0;
}

// rank: size(prs), det: full_rank ? sgn : 0
// inv(LI): L == I ? R : -1
// Ax=b(Ab): b is pivot col ? -1 : x[c] = M[prs[i]].back
// where c is pivot column of row prs[i]
const int mod = 998244353;
auto eliminate(vector<vector<int>> M)
{
    int n = ssize(M), m = M.empty() ? 0 : ssize(M[0]), sgn = 1;
    vector<int> prs;
    for (int r = 0, c = 0; r < n and c < m; c++) {
        int pr = r;
        while (pr < n and M[pr][c] == 0) pr++;
        if (pr == n) continue;
        prs.emplace_back(r);
        if (r != pr)
            M[r].swap(M[pr]), sgn = (mod - sgn) % mod;
        ll inv = 1, b = M[r][c];
        sgn = (ll)sgn * b % mod;
        for (int i = 0; i < 30; i++, b = b * b % mod)
            if ((mod - 2) >> i & 1)
                inv = inv * b % mod;
        for (int i = 0; i < m; i++)
            M[r][i] = M[r][i] * inv % mod;
        for (int i = 0; i < n; i++) {
            if (i == r or M[i][c] == 0) continue;
            ll x = M[i][c];
            for (int j = c; j < m; j++)
                M[i][j] = (M[i][j] + mod - M[r][j] * x % mod) % mod;
        }
        r++;
    }
    return tuple(M, prs, sgn);
}

template <uint32_t m_max = 1>
pair<vector<string>, vector<int>> eliminate(vector<string> M)
{
    if (m_max < size(M[0]))
        return eliminate<min(m_max << 1, 1u << 13)>(std::move(M));
    int n = ssize(M), m = ssize(M[0]);
    vector<bitset<m_max>> N;
    for (auto &s : M) {
        ranges::reverse(s);
        N.emplace_back(s);
    }
    vector<int> prs;
    for (int r = 0, c = 0; r < n and c < m; c++) {
        int pr = r;
        while (pr < n and !N[pr][c]) pr++;
        if (pr == n) continue;
        prs.emplace_back(r);
        if (r != pr) swap(N[r], N[pr]);
        for (int i = 0; i < n; i++)
            if (i != r and N[i][c])
                N[i] ^= N[r];
        r++;
    }
    for (int i = 0; i < n; i++) {
        string s = N[i].to_string().substr(m_max - m);
        ranges::reverse(s);
        M[i] = s;
    }
    return pair(M, prs);
}

signed main()
{
    ios::sync_with_stdio(false), cin.tie(NULL);

    int n, m;
    using lint = long long;
    lint k;
    cin >> m >> n >> k;
    vector<string> a(n);
    for (auto &s : a) cin >> s;
    for (auto &s : a) {
        // char c;
        // cin >> c;
        s += '0';
    }

    auto [M, prs] = eliminate(a);
    string sol(m, '0');
    vector<int> mp(n, -1);
    vector<bool> is_pivot(m, false);
    for (int i : prs) {
        int j = M[i].find('1');
        if (j == m) {
            cout << 0 << '\n';
            return 0;
        }
        if (M[i][m] == '1') sol[j] = '1';
        mp[i] = j, is_pivot[j] = true;
    }
    cout << atcoder::pow_mod(2, m - ssize(prs), k) << "\n";

    // vector<string> basis;
    // for (int c = 0; c < m; c++) {
    //     if (is_pivot[c]) continue;
    //     string s(m, '0');
    //     s[c] = '1';
    //     for (int r = 0; r < n; r++) {
    //         if (M[r][c] == '0') continue;
    //         s[mp[r]] = '1';
    //     }
    //     basis.eb(s);
    // }

    // cout << m - ssize(prs) << '\n';
    // cout << sol << '\n';
    // for (auto &s : basis) cout << s << '\n';

    return 0;
}
0