test/aoj0452.test.cpp

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Last update: 2021-06-21 15:24:20+09:00
Problem: https://onlinejudge.u-aizu.ac.jp/problems/0452

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Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0452"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#include "../tree/centroid_decomposition.cpp"

#include "../math/ntt.cpp"

class Factorial {
    vector<mint> facts, factinv;
public:
    explicit Factorial(int n) : facts(n+1), factinv(n+1) {
        facts[0] = 1;
        for (int i = 1; i < n+1; ++i) facts[i] = facts[i-1] * mint(i);
        factinv[n] = facts[n].inv();
        for (int i = n-1; i >= 0; --i) factinv[i] = factinv[i+1] * mint(i+1);
    }
    mint fact(int k) const {
        if(k >= 0) return facts[k]; else return factinv[-k];
    }
    mint operator[](const int &k) const {
        if(k >= 0) return facts[k]; else return factinv[-k];
    }
    mint C(int p, int q) const {
        if(q < 0 || p < q) return 0;
        return facts[p] * factinv[q] * factinv[p-q];
    }
    mint P(int p, int q) const {
        if(q < 0 || p < q) return 0;
        return facts[p] * factinv[p-q];
    }
    mint H(int p, int q) const {
        if(p < 0 || q < 0) return 0;
        return q == 0 ? 1 : C(p+q-1, q);
    }
};


int main() {
    int n;
    cin >> n;
    CentroidDecomposition G(n);
    for (int i = 0; i < n-1; ++i) {
        int u, v;
        scanf("%d %d", &u, &v);
        u--; v--;
        G.add_edge(u, v);
    }
    int root = G.get(0);
    vector<int> bad(n);
    poly val;
    auto dfs = [&](int centroid, auto &&f) -> void {
        bad[centroid] = 1;
        poly all(1);
        all[0] = 1;
        for (auto &&i : G.G[centroid]) {
            if(bad[i]) continue;
            poly a;
            queue<tuple<int, int, int>> Q;
            Q.emplace(i, centroid, 1);
            while(!Q.empty()){
                auto [x, par, dep] = Q.front(); Q.pop();
                while(a.size() <= dep) a.v.emplace_back();
                while(all.size() <= dep) all.v.emplace_back();
                a[dep]++; all[dep]++;
                for (auto &&y : G.G[x]) {
                    if(y != par && !bad[y]) Q.emplace(y, x, dep+1);
                }
            }
            val -= a * a;
        }
        val += all * all;
        for (auto &&i : G.out[centroid]) f(i, f);
    };
    dfs(root, dfs);
    Factorial f(n);
    for (int i = 1; i < val.size(); ++i) {
        val[i-1] = val[i]*mint(499122177)*f[i-1];
    }
    val.v.pop_back();
    poly fact(n);
    for (int i = 0; i < n; ++i) {
        fact[i] = f[-(n-1-i)];
    }
    val *= fact;
    for (int i = 0; i < n-1; ++i) {
        if(n+i < val.size()+1) printf("%d\n", (val[n-1+i]*f[-i]).val);
        else printf("%d\n", 0);
    }
    return 0;
}

#line 1 "test/aoj0452.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/0452"
#include <iostream>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <numeric>
#include <bitset>
#include <cmath>

static const int MOD = 1000000007;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using namespace std;

template<class T> constexpr T INF = ::numeric_limits<T>::max() / 32 * 15 + 208;

#line 1 "tree/centroid_decomposition.cpp"
class CentroidDecomposition {
    int dfs(int x, int par){
        sz[x] = 1;
        for (auto &&i : G[x]) {
            if(i == par || v[i]) continue;
            sz[x] += dfs(i, x);
        }
        return sz[x];
    }

    int search_centroid(int x, int p, const int mid){
        for (auto &&i : G[x]) {
            if(i == p || v[i]) continue;
            if(sz[i] > mid) return search_centroid(i, x, mid);
        }
        return x;
    }
public:
    int n;
    vector<vector<int>> G, out;
    vector<int> sz, v;
    CentroidDecomposition(int n) : n(n), G(n), out(n), sz(n), v(n) {}
    void add_edge(int l, int r){
        G[l].emplace_back(r);
        G[r].emplace_back(l);
    }
    int get(int x){
        int centroid = search_centroid(x, -1, dfs(x, -1)/2);
        v[centroid] = true;
        for (auto &&i : G[centroid]) {
            if(!v[i]) out[centroid].emplace_back(get(i));
        }
        v[centroid] = false;
        return centroid;
    }
};
#line 21 "test/aoj0452.test.cpp"

#line 1 "math/ntt.cpp"
constexpr int ntt_mod = 998244353, ntt_root = 3;
// 1012924417 -> 5, 924844033 -> 5
// 998244353  -> 3, 897581057 -> 3
// 645922817  -> 3;
template <uint M>
struct modint {
    uint val;
public:
    static modint raw(int v) { modint x; x.val = v; return x; }
    modint() : val(0) {}
    template <class T>
    modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = uint(x); }
    modint(bool v) { val = ((unsigned int)(v) % M); }
    modint& operator++() { val++; if (val == M) val = 0; return *this; }
    modint& operator--() { if (val == 0) val = M; val--; return *this; }
    modint operator++(int) { modint result = *this; ++*this; return result; }
    modint operator--(int) { modint result = *this; --*this; return result; }
    modint& operator+=(const modint& rhs) { val += rhs.val; if (val >= M) val -= M; return *this; }
    modint& operator-=(const modint& rhs) { val -= rhs.val; if (val >= M) val += M; return *this; }
    modint& operator*=(const modint& rhs) { ull z = val; z *= rhs.val; val = (uint)(z % M); return *this; }
    modint& operator/=(const modint& rhs) { return *this = *this * rhs.inv(); }
    modint operator+() const { return *this; }
    modint operator-() const { return modint() - *this; }
    modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; }
    modint inv() const { return pow(M-2); }
    friend modint operator+(const modint& lhs, const modint& rhs) { return modint(lhs) += rhs; }
    friend modint operator-(const modint& lhs, const modint& rhs) { return modint(lhs) -= rhs; }
    friend modint operator*(const modint& lhs, const modint& rhs) { return modint(lhs) *= rhs; }
    friend modint operator/(const modint& lhs, const modint& rhs) { return modint(lhs) /= rhs; }
    friend bool operator==(const modint& lhs, const modint& rhs) { return lhs.val == rhs.val; }
    friend bool operator!=(const modint& lhs, const modint& rhs) { return lhs.val != rhs.val; }
};
using mint = modint<998244353>;

class NTT {
    static constexpr int max_base = 20, maxN = 1 << max_base; // N <= 524288 * 2
    mint sum_e[30], sum_ie[30];
public:
    mint es[30], ies[30];
    NTT() {
        int cnt2 = __builtin_ctz(ntt_mod-1);
        mint e = mint(ntt_root).pow((ntt_mod-1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 0; i--){
            es[i] = e; ies[i] = ie;
            e *= e; ie *= ie;
        }
        mint now = 1, nowi = 1;
        for (int i = 0; i < cnt2 - 2; i++) {
            sum_e[i] = es[i+2] * now; now *= ies[i+2];
            sum_ie[i] = ies[i+2] * nowi; nowi *= es[i+2];
        }
    }

    void transform(vector<mint> &a, int sign){
        const int n = a.size();
        int h = 0;
        while ((1U << h) < (unsigned int)(n)) h++;
        if(!sign){ // fft
            for (int ph = 1; ph <= h; ph++) {
                int w = 1 << (ph-1), p = 1 << (h-ph);
                mint now = 1;
                for (int s = 0; s < w; s++) {
                    int offset = s << (h-ph+1);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i+offset], r = a[i+offset+p]*now;
                        a[i+offset] = l+r, a[i+offset+p] = l-r;
                    }
                    now *= sum_e[__builtin_ctz(~(unsigned int)(s))];
                }
            }
        }else { // ifft
            for (int ph = h; ph >= 1; ph--) {
                int w = 1 << (ph-1), p = 1 << (h-ph);
                mint inow = 1;
                for (int s = 0; s < w; s++) {
                    int offset = s << (h-ph+1);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i+offset], r = a[i+offset+p];
                        a[i+offset] = l+r, a[i+offset+p] = (l-r)*inow;
                    }
                    inow *= sum_ie[__builtin_ctz(~(unsigned int)(s))];
                }
            }
        }
    }
};

NTT ntt;

struct poly {
    vector<mint> v;
    poly() = default;
    explicit poly(int n) : v(n) {};
    explicit poly(vector<mint> vv) : v(std::move(vv)) {};
    int size() const {return (int)v.size(); }
    poly cut(int len){
        if(len < v.size()) v.resize(static_cast<unsigned long>(len));
        return *this;
    }
    inline mint& operator[] (int i) {return v[i]; }
    poly& operator+=(const poly &a) {
        this->v.resize(max(size(), a.size()));
        for (int i = 0; i < a.size(); ++i) this->v[i] += a.v[i];
        return *this;
    }
    poly& operator-=(const poly &a) {
        this->v.resize(max(size(), a.size()));
        for (int i = 0; i < a.size(); ++i) this->v[i] -= a.v[i];
        return *this;
    }
    poly& operator*=(poly a) {
        int N = size()+a.size()-1;
        int sz = 1;
        while(sz < N) sz <<= 1;
        this->v.resize(sz); a.v.resize(sz);
        ntt.transform(this->v, 0); ntt.transform(a.v, 0);
        for(int i = 0; i < sz; ++i) this->v[i] *= a.v[i];
        ntt.transform(this->v, 1);
        this->v.resize(N);
        mint iz = mint(sz).inv();
        for (int i = 0; i < N; i++) this->v[i] *= iz;
        return *this;
    }
    poly& operator/=(const poly &a){ return (*this *= a.inv()); }
    poly operator+(const poly &a) const { return poly(*this) += a; }
    poly operator-(const poly &a) const { return poly(*this) -= a; }
    poly operator*(const poly &a) const { return poly(*this) *= a; }

    poly inv() const {
        int n = size();
        poly r(1);
        r[0] = (this->v[0]).inv();
        for (int k = 1; k < n; k <<= 1) {
            poly ff(2*k);
            for (int i = 0; i < min(k*2, n); ++i) ff[i] = this->v[i];
            poly nr = (r*r*ff).cut(k*2);
            for (int i = 0; i < k; ++i) {
                nr[i] = (r[i]+r[i]-nr[i]);
                nr[i+k] = -nr[i+k];
            }
            r = nr;
        }
        r.v.resize(n);
        return r;
    }
};
#line 23 "test/aoj0452.test.cpp"

class Factorial {
    vector<mint> facts, factinv;
public:
    explicit Factorial(int n) : facts(n+1), factinv(n+1) {
        facts[0] = 1;
        for (int i = 1; i < n+1; ++i) facts[i] = facts[i-1] * mint(i);
        factinv[n] = facts[n].inv();
        for (int i = n-1; i >= 0; --i) factinv[i] = factinv[i+1] * mint(i+1);
    }
    mint fact(int k) const {
        if(k >= 0) return facts[k]; else return factinv[-k];
    }
    mint operator[](const int &k) const {
        if(k >= 0) return facts[k]; else return factinv[-k];
    }
    mint C(int p, int q) const {
        if(q < 0 || p < q) return 0;
        return facts[p] * factinv[q] * factinv[p-q];
    }
    mint P(int p, int q) const {
        if(q < 0 || p < q) return 0;
        return facts[p] * factinv[p-q];
    }
    mint H(int p, int q) const {
        if(p < 0 || q < 0) return 0;
        return q == 0 ? 1 : C(p+q-1, q);
    }
};


int main() {
    int n;
    cin >> n;
    CentroidDecomposition G(n);
    for (int i = 0; i < n-1; ++i) {
        int u, v;
        scanf("%d %d", &u, &v);
        u--; v--;
        G.add_edge(u, v);
    }
    int root = G.get(0);
    vector<int> bad(n);
    poly val;
    auto dfs = [&](int centroid, auto &&f) -> void {
        bad[centroid] = 1;
        poly all(1);
        all[0] = 1;
        for (auto &&i : G.G[centroid]) {
            if(bad[i]) continue;
            poly a;
            queue<tuple<int, int, int>> Q;
            Q.emplace(i, centroid, 1);
            while(!Q.empty()){
                auto [x, par, dep] = Q.front(); Q.pop();
                while(a.size() <= dep) a.v.emplace_back();
                while(all.size() <= dep) all.v.emplace_back();
                a[dep]++; all[dep]++;
                for (auto &&y : G.G[x]) {
                    if(y != par && !bad[y]) Q.emplace(y, x, dep+1);
                }
            }
            val -= a * a;
        }
        val += all * all;
        for (auto &&i : G.out[centroid]) f(i, f);
    };
    dfs(root, dfs);
    Factorial f(n);
    for (int i = 1; i < val.size(); ++i) {
        val[i-1] = val[i]*mint(499122177)*f[i-1];
    }
    val.v.pop_back();
    poly fact(n);
    for (int i = 0; i < n; ++i) {
        fact[i] = f[-(n-1-i)];
    }
    val *= fact;
    for (int i = 0; i < n-1; ++i) {
        if(n+i < val.size()+1) printf("%d\n", (val[n-1+i]*f[-i]).val);
        else printf("%d\n", 0);
    }
    return 0;
}