#870624 (C++17) No.2305 [Cherry 5th Tune N] Until That Day...

提出ソース

結果

問題	No.2305 [Cherry 5th Tune N] Until That Day...
ユーザー	tokusakurai
提出日時	2023-05-19 22:51:16
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,377 ms / 10,000 ms
コード長	11,324 bytes
コンパイル時間	3,075 ms
コンパイル使用メモリ	221,080 KB
実行使用メモリ	6,824 KB
最終ジャッジ日時	2024-12-20 01:23:59
合計ジャッジ時間	8,169 ms
ジャッジサーバーID （参考情報）	judge2 / 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 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	3 ms 6,820 KB
testcase_03	AC	3 ms 6,816 KB
testcase_04	AC	3 ms 6,816 KB
testcase_05	AC	3 ms 6,820 KB
testcase_06	AC	3 ms 6,820 KB
testcase_07	AC	7 ms 6,820 KB
testcase_08	AC	8 ms 6,816 KB
testcase_09	AC	7 ms 6,820 KB
testcase_10	AC	7 ms 6,820 KB
testcase_11	AC	1,377 ms 6,820 KB
testcase_12	AC	1,348 ms 6,816 KB
testcase_13	AC	143 ms 6,820 KB
testcase_14	AC	145 ms 6,816 KB
testcase_15	AC	4 ms 6,816 KB
testcase_16	AC	4 ms 6,816 KB
testcase_17	AC	2 ms 6,816 KB
testcase_18	AC	1,371 ms 6,816 KB
testcase_19	AC	4 ms 6,824 KB
testcase_20	AC	4 ms 6,816 KB

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ソースコード

raw source code

#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 popcount(int x) { return __builtin_popcount(x); }
int popcount(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);
    }
} 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>;

template <typename T>
struct Number_Theoretic_Transform {
    static int max_base;
    static T root;
    static vector<T> r, ir;

    Number_Theoretic_Transform() {}

    static void init() {
        if (!r.empty()) return;
        int mod = T::get_mod();
        int tmp = mod - 1;
        root = 2;
        while (root.pow(tmp >> 1) == 1) root++;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        r.resize(max_base), ir.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]  := 1 の 2^(i+2) 乗根
            ir[i] = r[i].inverse();                 // ir[i] := 1/r[i]
        }
    }

    static void ntt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = n; k >>= 1;) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = w * a[j];
                    a[i] = x + y, a[j] = x - y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }

    static void intt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = 1; k < n; k <<= 1) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = a[j];
                    a[i] = x + y, a[j] = w * (x - y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for (auto &e : a) e *= inv;
    }

    static vector<T> convolve(vector<T> a, vector<T> b) {
        if (a.empty() || b.empty()) return {};
        if (min(a.size(), b.size()) < 40) {
            int n = a.size(), m = b.size();
            vector<T> c(n + m - 1, 0);
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j];
            }
            return c;
        }
        int k = (int)a.size() + (int)b.size() - 1, n = 1;
        while (n < k) n <<= 1;
        a.resize(n, 0), b.resize(n, 0);
        ntt(a), ntt(b);
        for (int i = 0; i < n; i++) a[i] *= b[i];
        intt(a), a.resize(k);
        return a;
    }
};

template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;

template <typename T>
T Number_Theoretic_Transform<T>::root = T();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();

using NTT = Number_Theoretic_Transform<mint>;

// [x^k](P(x)/Q(x))
template <typename T>
T Bostan_Mori(vector<T> P, vector<T> Q, long long k) {
    using NTT_ = Number_Theoretic_Transform<T>;
    int n = max((int)P.size(), (int)Q.size());
    P.resize(n, 0), Q.resize(n, 0);
    assert(n > 0 && Q[0] != 0);
    int t = 1;
    while (t < 2 * n - 1) t <<= 1;
    for (; k > 0; k >>= 1) {
        vector<T> R = Q;
        for (int i = 1; i < n; i += 2) R[i] = -R[i];
        P.resize(t, 0), NTT_::ntt(P);
        Q.resize(t, 0), NTT_::ntt(Q);
        R.resize(t, 0), NTT_::ntt(R);
        vector<T> A(t), B(t);
        for (int i = 0; i < t; i++) {
            A[i] = P[i] * R[i];
            B[i] = Q[i] * R[i];
        }
        NTT_::intt(A), NTT_::intt(B);
        Q.resize(n);
        for (int i = 0; i < n; i++) Q[i] = B[2 * i];
        P.resize(n);
        if (k & 1) {
            for (int i = 0; i < n - 1; i++) P[i] = A[2 * i + 1];
            P[n - 1] = 0;
        } else {
            for (int i = 0; i < n; i++) P[i] = A[2 * i];
        }
    }
    return P[0] / Q[0];
}

// d 項間線形漸化式 a[n] = c[1]*a[n-1]+c[2]*a[n-2]+...+c[d]*a[n-d] の第 k 項 (0-indexed)
template <typename T>
T linear_recurrence(const vector<T> &a, const vector<T> &c, long long k) {
    using NTT_ = Number_Theoretic_Transform<T>;
    int d = a.size();
    vector<T> Q(d + 1, 0);
    Q[0] = 1;
    for (int i = 1; i <= d; i++) Q[i] = -c[i];
    vector<T> P = NTT_::convolve(a, Q);
    P.resize(d);
    return Bostan_Mori(P, Q, k);
}

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

    N++;

    vector<vector<int>> es(N);
    rep2(i, 1, N) {
        int p;
        cin >> p;
        es[p].eb(i);
    }

    vector<mint> w(N);
    rep2(i, 1, N) cin >> w[i];

    vector<mint> P(N, 0);
    vector<int> d(N, 0);
    P[0] = 1, d[0] = 0;

    auto dfs = [&](auto &&dfs, int now) -> void {
        if (empty(es[now])) return;
        mint S = 0;
        each(e, es[now]) S += w[e];
        each(e, es[now]) {
            P[e] += P[now] * w[e] / S;
            d[e] = d[now] + 1;
            dfs(dfs, e);
        }
    };
    dfs(dfs, 0);
    // print(P), print(d);

    vector<mint> f = {1, -1};
    vector<mint> g(N + 1, 0);
    g[0] = 1;
    rep(i, N) {
        if (empty(es[i])) g[d[i] + 1] -= P[i];
    }

    vector<mint> a = {1};
    vector<mint> b = NTT::convolve(f, g);
    while (b.back() == 0) b.pop_back();

    int Q;
    cin >> Q;

    while (Q--) {
        int v, k;
        cin >> v >> k;

        if (k < d[v]) {
            cout << "0\n";
            continue;
        }

        mint E = Bostan_Mori(a, b, k - d[v]);
        E *= P[v];
        if (v == 0) E--;
        cout << E << '\n';
    }
}

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

yukicoder

結果

テストケース

ソースコード