結果

問題 No.2531 Coloring Vertices on Namori
ユーザー tokusakuraitokusakurai
提出日時 2023-11-03 22:01:08
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 111 ms / 2,000 ms
コード長 8,399 bytes
コンパイル時間 2,131 ms
コンパイル使用メモリ 213,908 KB
実行使用メモリ 24,156 KB
最終ジャッジ日時 2024-09-25 20:18:02
合計ジャッジ時間 5,692 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 69 ms
24,028 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 70 ms
24,156 KB
testcase_08 AC 92 ms
24,156 KB
testcase_09 AC 106 ms
24,032 KB
testcase_10 AC 101 ms
24,156 KB
testcase_11 AC 48 ms
16,456 KB
testcase_12 AC 48 ms
16,580 KB
testcase_13 AC 51 ms
16,584 KB
testcase_14 AC 111 ms
24,156 KB
testcase_15 AC 96 ms
24,156 KB
testcase_16 AC 97 ms
24,028 KB
testcase_17 AC 2 ms
5,376 KB
testcase_18 AC 2 ms
5,376 KB
testcase_19 AC 2 ms
5,376 KB
testcase_20 AC 84 ms
15,976 KB
testcase_21 AC 74 ms
16,000 KB
testcase_22 AC 86 ms
16,128 KB
testcase_23 AC 83 ms
16,000 KB
testcase_24 AC 91 ms
16,000 KB
testcase_25 AC 86 ms
16,000 KB
testcase_26 AC 91 ms
15,996 KB
testcase_27 AC 92 ms
15,972 KB
testcase_28 AC 92 ms
15,872 KB
testcase_29 AC 87 ms
15,984 KB
testcase_30 AC 85 ms
16,000 KB
testcase_31 AC 81 ms
16,128 KB
testcase_32 AC 83 ms
16,000 KB
testcase_33 AC 84 ms
15,976 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

diff # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

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

template <typename T>
using maxheap = priority_queue<T>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(15);
    }
} io_setup;

constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

struct Graph {
    struct edge {
        int to, id;
        edge(int to, int id) : to(to), id(id) {}
    };

    vector<vector<edge>> es;
    const int n;
    int m;

    vector<int> used;

    Graph(int n) : es(n), n(n), m(0), used(n) {}

    void add_edge(int from, int to) {
        es[from].emplace_back(to, m);
        es[to].emplace_back(from, m);
        m++;
    }

    bool detect_path(int now, int t, vector<int> &ret, bool use_id = false) {
        used[now] = true;
        if (now == t) {
            if (!use_id) ret.push_back(now);
            return true;
        }
        for (auto &e : es[now]) {
            if (used[e.to]) continue;
            if (detect_path(e.to, t, ret, use_id)) {
                ret.push_back(use_id ? e.id : now);
                return true;
            }
        }
        return false;
    }

    // 点素な s-t パスを 1 つ検出
    vector<int> find_path(int s, int t, bool use_id = false) {
        vector<int> ret;
        fill(begin(used), end(used), 0);
        detect_path(s, t, ret, use_id);
        reverse(begin(ret), end(ret));
        return ret;
    }

    int detect_cycle(int now, vector<int> &ret, int pre = -1, bool use_id = false) {
        if (used[now]++) return 1;
        for (auto &e : es[now]) {
            if (e.id == pre) continue;
            int k = detect_cycle(e.to, ret, e.id, use_id);
            if (k == 2) return 2;
            if (k == 1) {
                ret.push_back(use_id ? e.id : now);
                return used[now];
            }
        }
        return 0;
    }

    // 辺素な閉路を 1 つ検出
    vector<int> find_cycle(bool use_id = false) {
        vector<int> ret;
        fill(begin(used), end(used), 0);
        for (int i = 0; i < n; i++) {
            if (used[i]) continue;
            detect_cycle(i, ret, -1, use_id);
            if (!ret.empty()) {
                reverse(begin(ret), end(ret));
                return ret;
            }
        }
        return {};
    }
};

void solve() {
    int N, K;
    cin >> N >> K;

    Graph G(N);
    rep(i, N) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        G.add_edge(u, v);
    }

    auto C = G.find_cycle();

    int L = sz(C);

    vector<mint> dp(2, 0);
    dp[1] = K;

    rep(i, L - 1) {
        vector<mint> ndp(2, 0);
        ndp[1] += dp[0];
        ndp[0] += dp[1] * (K - 1);
        ndp[0] += dp[0] * (K - 2);
        swap(dp, ndp);
    }

    cout << dp[0] * mint(K - 1).pow(N - L) << '\n';
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
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