#866420 (C++17) No.2293 無向辺 2-SAT

提出ソース

結果

問題	No.2293 無向辺 2-SAT
ユーザー	haruki_K
提出日時	2023-05-05 22:08:47
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	88 ms / 4,000 ms
コード長	15,644 bytes
コンパイル時間	2,246 ms
コンパイル使用メモリ	216,480 KB
実行使用メモリ	13,196 KB
最終ジャッジ日時	2024-05-02 16:31:21
合計ジャッジ時間	12,304 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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	1 ms 5,248 KB
testcase_01	AC	3 ms 5,248 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	88 ms 13,196 KB
testcase_04	AC	78 ms 5,376 KB
testcase_05	AC	75 ms 5,376 KB
testcase_06	AC	71 ms 5,376 KB
testcase_07	AC	35 ms 5,376 KB
testcase_08	AC	72 ms 5,376 KB
testcase_09	AC	64 ms 5,376 KB
testcase_10	AC	64 ms 5,376 KB
testcase_11	AC	76 ms 5,376 KB
testcase_12	AC	77 ms 5,376 KB
testcase_13	AC	64 ms 5,376 KB
testcase_14	AC	59 ms 5,376 KB
testcase_15	AC	56 ms 5,376 KB
testcase_16	AC	76 ms 5,376 KB
testcase_17	AC	80 ms 5,504 KB
testcase_18	AC	81 ms 5,376 KB
testcase_19	AC	38 ms 5,376 KB
testcase_20	AC	81 ms 5,376 KB
testcase_21	AC	80 ms 5,376 KB
testcase_22	AC	83 ms 5,376 KB
testcase_23	AC	82 ms 5,376 KB
testcase_24	AC	80 ms 5,376 KB
testcase_25	AC	82 ms 5,376 KB
testcase_26	AC	83 ms 5,376 KB
testcase_27	AC	82 ms 5,376 KB
testcase_28	AC	81 ms 5,376 KB
testcase_29	AC	85 ms 5,376 KB
testcase_30	AC	81 ms 5,376 KB
testcase_31	AC	82 ms 5,376 KB
testcase_32	AC	76 ms 5,376 KB
testcase_33	AC	73 ms 5,376 KB
testcase_34	AC	74 ms 5,376 KB
testcase_35	AC	73 ms 5,376 KB
testcase_36	AC	72 ms 5,376 KB
testcase_37	AC	75 ms 5,376 KB
testcase_38	AC	73 ms 5,376 KB
testcase_39	AC	72 ms 5,376 KB
testcase_40	AC	73 ms 5,376 KB
testcase_41	AC	64 ms 5,376 KB
testcase_42	AC	72 ms 5,376 KB
testcase_43	AC	76 ms 5,376 KB
testcase_44	AC	74 ms 5,376 KB
testcase_45	AC	79 ms 5,376 KB
testcase_46	AC	79 ms 5,376 KB
testcase_47	AC	79 ms 5,376 KB
testcase_48	AC	81 ms 5,376 KB
testcase_49	AC	80 ms 5,376 KB
testcase_50	AC	82 ms 5,376 KB
testcase_51	AC	80 ms 5,376 KB
testcase_52	AC	82 ms 5,376 KB
testcase_53	AC	81 ms 5,376 KB
testcase_54	AC	81 ms 5,376 KB
testcase_55	AC	81 ms 6,024 KB

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define rep(i, n) if (const int _rep_n = n; true) for (int i = 0; i < _rep_n; i++)
#define rep1(i, n) if (const int _rep_n = n; true) for (int i = 1; i <= _rep_n; i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif

template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> {
    vector<T> &data() { return this->c; }
    void clear() { this->c.clear(); }
};
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;

template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) {
    bool f = true;
    for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
    return os;
}
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) {
    bool f = true;
    for (auto const& x : a) os << (f ? "" : " ") << x, f = false;
    return os;
}
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) {
    return os << p.first << " " << p.second;
}
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) {
    return is >> p.first >> p.second;
}
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) {
    bool f = true;
    apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t);
    return os;
}
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) {
    apply([&](auto&&... x) { ((is >> x), ...); }, t);
    return is;
}
struct IOSetup {
    IOSetup() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
    }
} iosetup;

template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const {
        return F::operator()(*this, forward<T>(x)...);
    }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const {
        return FixPoint<F>(forward<F>(f));
    }
};
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)

template <class F> struct FixPoint_d : private F {
    const char* const name;
    constexpr FixPoint_d(F&& f, const char* name) : F(forward<F>(f)), name(name) {}
    template <class... T> constexpr auto operator()(T&&... x) const {
        auto ret = F::operator()(*this, forward<T>(x)...);
#ifdef LOCAL
        cerr << name << to_s(tuple(x...)) << " -> " << to_s(ret) << '\n';
#endif
        return ret;
    }
};
struct MakeFixPoint_d {
    const char* const name;
    MakeFixPoint_d(const char* name) : name(name) {}
    template <class F> constexpr auto operator|(F&& f) const {
        return FixPoint_d<F>(forward<F>(f), name);
    }
};
#ifdef LOCAL
#define def_d(name, ...) auto name = MakeFixPoint_d(#name) | [&](auto &&name, __VA_ARGS__)
#else
#define def_d def
#endif

template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) {
        return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...));
    }
};
template <class T> struct vec_impl<T, 0> {
    using type = T;
    static type make_v(T const& x = {}) { return x; }
};
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) {
    return vec_impl<T, d>::make_v(forward<Args>(args)...);
}
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) {
    return x > (T)y ? x = (T)y, true : false;
}
template <class T, class U> constexpr bool chmax(T& x, U const& y) {
    return x < (T)y ? x = (T)y, true : false;
}
template <class It> constexpr auto sumof(It b, It e) {
    return accumulate(b, e, typename iterator_traits<It>::value_type{});
}
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))>
constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T>
int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x) - begin(v); }
template <class C, class T>
int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x) - begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
template <class Comp> vector<int> iota(int n, Comp comp) {
    vector<int> idx(n);
    iota(begin(idx), end(idx), 0);
    stable_sort(begin(idx), end(idx), comp);
    return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class Vec> int sort_unique(Vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class Vec, class Comp> int sort_unique(Vec &v, Comp comp) {
    sort(begin(v), end(v), comp);
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class A, class B>
pair<vector<A>, vector<B>> unzip(vector<pair<A, B>> const& c) {
    vector<A> a;
    vector<B> b;
    for (auto const& [x, y] : c) {
        a.push_back(x);
        b.push_back(y);
    }
    return { a, b };
}
template <class A, class B>
pair<vector<A>, vector<B>> unzip(map<A, B> const& c) {
    vector<A> a;
    vector<B> b;
    for (auto const& [x, y] : c) {
        a.push_back(x);
        b.push_back(y);
    }
    return { a, b };
}
// <<<
// >>> union find (undo)
struct UnionFind {
    int n, sz; // id : 0...n-1
    vector<int32_t> par;
    vector<pair<int32_t, int32_t>> hist;

    UnionFind(int n = 0) : n(n), sz(n), par(n, -1) { }
    void clear() {
        fill(par.begin(), par.end(), -1);
        sz = n;
        hist.clear();
    }
    int root(int x) {
        assert(0 <= x); assert(x < n);
        return par[x] < 0 ? x : root(par[x]);
    }
    bool unite(int x, int y) {
        x = root(x), y = root(y);
        hist.emplace_back(x, par[x]);
        hist.emplace_back(y, par[y]);
        if (par[x] < par[y]) swap(x, y);
        if (x == y) return false;
        sz--;
        par[y] += par[x];
        par[x] = y;
        return true;
    }
    void undo() {
        assert(hist.size());
        bool change = false;
        rep (_, 2) {
            auto [x, par_x] = hist.back(); hist.pop_back();
            change |= par[x] != par_x;
            par[x] = par_x;
        }
        if (change) sz++;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return -par[root(x)]; }
    int size() const { return sz; }
    vector<vector<int>> groups() {
        vector<vector<int>> g(n);
        rep (i, n) if (par[i] < 0) g[i].reserve(-par[i]);
        rep (i, n) g[root(i)].push_back(i);
        vector<vector<int>> grp; grp.reserve(size());
        rep (i, n) if (g[i].size()) grp.emplace_back(move(g[i]));
        return grp;
    }
};
// <<<
constexpr int64_t MOD = 998244353;
//constexpr int64_t MOD = 1e9+7;
// >>> modint, mod table
// >>> modint
template <uint32_t md> class modint {
    static_assert(md < (1u<<31), "");
    using M = modint;
    using i64 = int64_t;
    uint32_t x;
public:
    static constexpr uint32_t mod = md;
    constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }
    constexpr i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    constexpr bool operator==(M r) const { return x == r.x; }
    constexpr bool operator!=(M r) const { return x != r.x; }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { return M()-*this; }
    constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }
    constexpr M& operator/=(M r) { return *this *= r.inv(); }
    constexpr M operator+(M r) const { return M(*this) += r; }
    constexpr M operator-(M r) const { return M(*this) -= r; }
    constexpr M operator*(M r) const { return M(*this) *= r; }
    constexpr M operator/(M r) const { return M(*this) /= r; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }
    constexpr M inv() const { assert(x > 0); return pow(md-2); }
    constexpr M pow(i64 n) const {
//        assert(not (x == 0 and n == 0));
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
#ifdef LOCAL
    friend string to_s(M r) { return to_s(r.val(), mod); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};
// <<<
using mint = modint<MOD>;
mint sign(int n) { return n & 1 ? -1 : +1; }
// >>> mod table
template <uint32_t mod> struct ModTable {
    static_assert(mod > 1, "");
    vector<uint32_t> fact = { 1, 1 }, finv = { 1, 1 }, inv = { 0, 1 };
    ModTable(int n = 0) {
        calc(n);
    }
    void calc(int n) {
        const int now = fact.size();
        if (n < now) return;
        assert(n < int(1e9));
        int nxt = now;
        do nxt <<= 1; while (nxt <= n);
        fact.resize(nxt);
        finv.resize(nxt);
        inv.resize(nxt);
        for (uint32_t i = now; i < nxt; i++) {
            fact[i] = uint64_t(fact[i-1]) * i % mod;
            inv[i] = mod - uint64_t(inv[mod%i]) * (mod/i) % mod;
            finv[i] = uint64_t(finv[i-1]) * inv[i] % mod;
        }
    }
};

ModTable<MOD> mod_tab;

modint<MOD> fact(int n) {
    assert(0 <= n);
    mod_tab.calc(n);
    return mod_tab.fact[n];
}
modint<MOD> finv(int n) {
    assert(0 <= n);
    mod_tab.calc(n);
    return mod_tab.finv[n];
}
modint<MOD> inv(int n) {
    assert(0 <= n);
    mod_tab.calc(n);
    return mod_tab.inv[n];
}
modint<MOD> comb(int n, int k) {
    if (k < 0) {
        return 0;
    } else if (n >= k) {
        mod_tab.calc(n);
        return (uint64_t)mod_tab.finv[k] * mod_tab.finv[n-k] % MOD * mod_tab.fact[n];
    } else if (n < 0) {
        n = -n+k-1;
        mod_tab.calc(n);
        int ans = (uint64_t)mod_tab.finv[k] * mod_tab.finv[n-k] % MOD * mod_tab.fact[n];
        if (k & 1) ans = -ans;
        return ans;
    } else {
        return 0;
    }
}
// <<<
// <<<

int32_t main() {
    int n, q; cin >> n >> q;
    UnionFind uf(2*n);
    bool bad = false;
    while (q--) {
        int t; cin >> t;
        if (t == 1) {
            int x, y; cin >> x >> y; --x, --y;
            uf.unite(x, y);
            uf.unite(n+x, n+y);
            if (uf.same(x, n+x) or uf.same(y, n+y)) bad = true;
        } else if (t == 2) {
            int x, y; cin >> x >> y; --x, --y;
            uf.unite(x, n+y);
            uf.unite(n+x, y);
            if (uf.same(x, n+x) or uf.same(y, n+y)) bad = true;
        } else {
            while (uf.hist.size()) uf.undo();
            bad = false;
        }

        if (bad) {
            cout << 0 << '\n';
        } else {
            int c = uf.size();
            assert(c % 2 == 0);
            cout << mint(2).pow(c/2) << '\n';
        }

    }
}

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結果

テストケース

ソースコード