結果

問題 No.2277 Honest or Dishonest ?
ユーザー 👑 eoeoeoeo
提出日時 2023-05-05 01:06:22
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 35 ms / 2,000 ms
コード長 8,851 bytes
コンパイル時間 3,078 ms
コンパイル使用メモリ 258,648 KB
実行使用メモリ 7,936 KB
最終ジャッジ日時 2024-11-22 14:20:49
合計ジャッジ時間 6,975 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 50
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 # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#ifdef MY_DEBUG
#define dbg(...) debug_out(__VA_ARGS__)
#define dbgn(var) debug_out(#var, "=", var)
#else
#define dbg(...)
#define dbgn(...)
#endif
void debug_out();
template <class Head, class... Tail> void debug_out(Head, Tail...);
template <class T> bool chmax(T&, const T&);
template <class T> bool chmin(T&, const T&);
template <class T> T pwr(T, ll);
template <class T> T squ(T x) { return x * x; }
ll fact(ll);
ll comb(ll, ll);
ll ctoll(char);
char lltoc(ll);
bool flg(ll b, ll i) { return ((b) >> (i)) & 1LL; }  // flg(0b010, 1LL) -> true
const ll LINF = (ll)1e18 + 7;
const double EPS = 1e-9;
const int MAX_DUBUG_SIZE = 10;

// 重み付きUnionFind
struct weighted_union_find {
    vector<ll> par, rank, siz;  // par: parent, rank: depth, siz: size of group
    vector<bool> diff_weight;
    ll group_num;  // 連結成分の個数

    weighted_union_find(ll n) : par(n, -1), rank(n, 0), siz(n, 1), diff_weight(n, false), group_num(n) {}

    ll root(ll x) {
        if (par[x] == -1) {
            return x;
        }
        else {
            ll root_id = root(par[x]);
            diff_weight[x] = (diff_weight[x] ^ diff_weight[par[x]]);
            par[x] = root_id;  // 経路圧縮，帰りがけに根に直接つなぐ
            return par[x];
        }
    }

    bool is_same(ll x, ll y) { return root(x) == root(y); }

    bool weight(ll x) {
        root(x);
        return diff_weight[x];
    }

    // unite by rank, x の根の下に y の根をつなぐ
    // w = weight(y) ^ weight(x) を満たすように
    // 同じ <-> w = false
    bool unite(ll x, ll y, bool w) {
        w = (w ^ weight(x));
        w = (w ^ weight(y));

        ll rx = root(x), ry = root(y);
        if (rx == ry) {
            return false;
        }

        if (rank[rx] < rank[ry]) {
            swap(rx, ry);
        }

        if (rank[rx] == rank[ry]) {
            rank[rx]++;
        }

        par[ry] = rx;
        siz[rx] += siz[ry];
        siz[ry] = 0;
        diff_weight[ry] = w;
        group_num--;
        return true;
    }

    ll size(ll x) { return siz[root(x)]; }

    bool diff(ll x, ll y) { return weight(y) ^ weight(x); }
};

#include <atcoder/math>
#include <atcoder/modint>
using namespace atcoder;

// const int MOD = 1e9 + 7;
// using mint = modint1000000007;

const int MOD = 998244353;
using mint = modint998244353;

// using mint = modint; // main の最初で mint::setmod(/* 任意のMOD */);

ostream& operator<<(ostream& os, const mint& N) { return os << N.val(); }

// // xz = y mod MOD を満たす既約分数 y/x を求める
// string mint_to_ratio(mint z) {
//     string res = "NaN";
//     if (z == 0) {
//         res = "0/1";
//         return res;
//     }
//     const ll MAX = 1000;
//     for (ll x = 1; x <= MAX; x++) {
//         for (ll y = 1; y <= MAX; y++) {
//             mint tmp = x * z - y;
//             if (tmp == 0) {
//                 res = to_string(y) + "/" + to_string(x);
//                 return res;
//             }
//         }
//     }
//     return res;
// }

void solve([[maybe_unused]] int test) {
    ll n, q;
    cin >> n >> q;
    vector<ll> a(q), b(q), c(q);
    for (ll i = 0; i < q; i++) {
        cin >> a[i] >> b[i] >> c[i];
        a[i]--, b[i]--;  // 0-indexed
    }                    // Aren't they one line?

    weighted_union_find wuf(n);
    for (ll i = 0; i < q; i++) {
        if (wuf.is_same(a[i], b[i])) {
            if (wuf.diff(a[i], b[i]) != c[i]) {
                cout << 0 << endl;
                return;
            }
        }
        else {
            wuf.unite(a[i], b[i], c[i]);
        }
    }

    // for (ll i = 0; i < q; i++) {
    //     if ((wuf.weight(a[i]) ^ wuf.weight(b[i])) != c[i]) {
    //         cout << 0 << endl;
    //         return;
    //     }
    // }

    dbg(wuf.diff_weight);
    for (ll i = 0; i < n; i++) {
        dbg(wuf.weight(i));
    }

    mint ans = mint(2).pow(wuf.group_num);

    cout << ans << endl;
}

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(12);

    int testcase_size = 1;
    // cin >> testcase_size;

    for (int _t = 0; _t < testcase_size; _t++) {
        solve(_t);
    }
}

/*



























-----------------------------------MY_FUNCTIONS------------------------------------ */
template <class First, class Second> ostream& operator<<(ostream& os, const pair<First, Second>& pp) {
    return os << "{" << pp.first << "," << pp.second << "}";
}

template <class T> ostream& operator<<(ostream& os, const vector<T>& V) {
    if (V.empty()) return os << "[]";
    os << "[";
    for (ll i = 0; i < (ll)V.size(); i++) {
        os << V[i] << (i == int(V.size() - 1) ? "]" : ",");
    }
    return os;
}

template <class T> ostream& operator<<(ostream& os, const vector<vector<T>>& VV) {
    if (VV.empty()) return os << "[[]]";
    os << "[\n";
    for (auto&& V : VV) {
        os << V << "\n";
    }
    os << "]";
    return os;
}

template <class T> ostream& operator<<(ostream& os, const vector<vector<vector<T>>>& VVV) {
    if (VVV.empty()) return os << "[[[]]]";
    os << "["
       << "\n";
    int cnt = 0;
    for (auto&& VV : VVV) {
        os << cnt++ << VV << "\n\n";
    }
    os << "]";
    return os;
}

template <class T> ostream& operator<<(ostream& os, const set<T>& SS) {
    if (SS.empty()) return os << "[]";
    os << "[";
    auto ii = SS.begin();
    for (; ii != SS.end(); ii++) os << *ii << (ii == prev(SS.end()) ? "]" : ",");
    return os;
}

template <class Key, class Tp> ostream& operator<<(ostream& os, const map<Key, Tp>& MM) {
    if (MM.empty()) return os << "[{:}]";
    os << "[";
    auto ii = MM.begin();
    for (; ii != MM.end(); ii++)
        os << "{" << ii->first << ":" << ii->second << "}" << (ii == prev(MM.end()) ? "]" : ",");
    return os;
}

void debug_out() { cerr << endl; }

void debug_out_vl(vector<ll> V) {
    const int MAX_SIZE = min((int)V.size(), MAX_DUBUG_SIZE);

    cerr << "\033[33m";
    if (V.empty()) {
        cerr << "[]" << endl;
        return;
    }
    cerr << "[";
    for (int i = 0; i < MAX_SIZE; i++) {
        if (V[i] == LINF)
            cerr << "INF";
        else
            cerr << V[i];

        if (i == (int)V.size() - 1)
            cerr << "]\n";
        else if (i == MAX_DUBUG_SIZE - 1)
            cerr << ",...\n";
        else
            cerr << ",";
    }
    return;
}

void debug_out_vvl(vector<vector<ll>> VV) {
    cerr << "\033[33m";
    if (VV.empty()) {
        cerr << "[[]]" << endl;
        return;
    }
    cerr << "[\n";

    int MAX_ROW = min((int)VV.size(), MAX_DUBUG_SIZE);
    for (int i = 0; i < MAX_ROW; i++) {
        const int MAX_COLUMN = min((int)VV[i].size(), MAX_DUBUG_SIZE);
        if (VV[i].empty()) {
            cerr << "[]" << endl;
            continue;
        }
        cerr << "[";
        for (int j = 0; j < MAX_COLUMN; j++) {
            if (VV[i][j] == LINF)
                cerr << "INF";
            else
                cerr << VV[i][j];

            if (j == (int)VV[i].size() - 1)
                cerr << "]\n";
            else if (j == MAX_DUBUG_SIZE - 1)
                cerr << ",...\n";
            else
                cerr << ",";
        }

        if (i != (int)VV.size() - 1 and i == MAX_DUBUG_SIZE - 1) {
            cerr << ":\n:\033[m\n";
            return;
        }
    }

    cerr << "]\033[m\n";
    return;
}

template <class Head, class... Tail> void debug_out(Head H, Tail... T) {
    if constexpr (std::is_same_v<Head, vector<ll>>) {
        debug_out_vl(H);
    }
    else if constexpr (std::is_same_v<Head, vector<vector<ll>>>) {
        debug_out_vvl(H);
    }
    else {
        cerr << "\033[33m" << H << "\033[m ";
    }

    debug_out(T...);
}

template <class T> bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T pwr(T x, ll n) {
    T res = 1;
    for (int i = 0; i < n; i++) {
        res *= x;
    }
    return res;
}

ll fact(ll n) {
    ll res = 1;
    for (ll i = 1; i <= n; i++) res *= i;
    return res;
}

ll comb(ll n, ll r) {  // comb(60, 30)までオーバーフローなし
    ll res = 1;
    for (int i = 1; i <= r; i++) {
        res *= n--;
        res /= i;
    }
    return res;
}

ll ctoll(char c) {
    if (c < '0' or '9' < c) {
        cerr << "\n\033[33m ctoll に '0'~'9' 以外の文字が入りました．\033[m\n" << endl;
    }
    return ll(c - '0');
}

char lltoc(ll n) {
    if (n < 0 or 9 < n) {
        cerr << "\n\033[33m lltoc に 0 ~ 9 以外の数字が入りました．\033[m\n" << endl;
    }
    return char(n + '0');
}
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