結果

問題 No.3315 FPS Game
コンテスト
ユーザー 👑 potato167
提出日時 2025-10-24 22:15:47
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 195 ms / 3,250 ms
コード長 10,332 bytes
コンパイル時間 4,584 ms
コンパイル使用メモリ 254,828 KB
実行使用メモリ 36,488 KB
最終ジャッジ日時 2025-10-24 22:15:57
合計ジャッジ時間 8,232 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 25
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 # 

#line 1 "f.cpp"
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
const ll ILL=2167167167167167167;
const int INF=2100000000;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}

#line 3 "/Users/Shared/po167_library/fps/FPS_Product_Sequence.hpp"
#include <atcoder/convolution>

namespace po167{
template<class T>
std::vector<T> FPS_Product_Sequence(std::vector<std::vector<T>> f){
    if (f.empty()) return {1};
    auto op = [&](auto self,int l, int r) -> std::vector<T> {
        if (l + 1 == r) return f[l];
        int m = (l + r) / 2;
        return atcoder::convolution(self(self, l, m), self(self, m, r));
    };
    return op(op, 0, f.size());
}
}
#line 26 "f.cpp"
using mint = atcoder::modint998244353;
#line 4 "/Users/Shared/po167_library/ds/Sparse_table.hpp"
namespace po167{
template<class T, T(*op)(T, T)>
struct Sparse_table{
    int n;
    int depth;
    std::vector<std::vector<T>> val;
    void init(std::vector<T> &v){
        depth = 1;
        n = v.size();
        while ((1 << depth) <= n) depth++;
        val.resize(depth);
        val[0] = v;
        for (int i = 1; i < depth; i++){
            val[i].resize(n);
            for (int j = 0; j <= n - (1 << i); j++){
                val[i][j] = op(val[i - 1][j], val[i - 1][j + (1 << (i - 1))]);
            }
        }
    }
    Sparse_table(std::vector<T> v){
        init(v);
    }
    Sparse_table(){}
    // 0 <= l < r <= n
    // if l == r : assert
    T prod(int l, int r){
        assert(0 <= l && l < r && r <= n);
        int z=31-__builtin_clz(r-l);
        return op(val[z][l], val[z][r - (1 << z)]);
    }
};
}
#line 6 "/Users/Shared/po167_library/graph/tree/LCA.hpp"
namespace po167{
int op(int a, int b){
    return std::min(a, b);
}
struct LCA{
    Sparse_table<int, op> table;
    std::vector<int> depth;
    std::vector<int> E;
    std::vector<int> order;
    int var_num;
    void init(std::vector<std::vector<int>> &g, int root = 0){
        var_num = g.size();
        assert(0 <= root && root < var_num);
        std::vector<int> val;
        depth.assign(var_num, -1);
        depth[root] = 0;
        E.resize(var_num);
        std::vector<int> tmp;
        order.clear();
        tmp.reserve(var_num);
        order.reserve(var_num);
        int c = 0;
        auto dfs = [&](auto self, int var, int pare) -> void {
            E[var] = c++;
            if (var != root) tmp.push_back(E[pare]);
            order.push_back(var);
            for (auto x : g[var]) if (depth[x] == -1){
                depth[x] = depth[var] + 1;
                self(self, x, var);
            }
        };
        dfs(dfs, root, -1);
        assert(c == var_num);
        table.init(tmp);
    }
    void init(std::vector<int> &pare){
        int root = -1;
        int n = pare.size();
        std::vector<std::vector<int>> g(n);
        for (int i = 0; i < n; i++){
            if (pare[i] < 0){
                assert(root == -1);
                root = i;
            }
            else{
                assert(0 <= pare[i] && pare[i] < n);
                g[pare[i]].push_back(i);
            }
        }
        assert(root != -1);
        init(g, root);
    }
    LCA (std::vector<std::vector<int>> g, int root = 0){
        init(g, root);
    }
    LCA (std::vector<int> pare){
        init(pare);
    }
    LCA(){
        
    }
    int lca(int a, int b){
        assert(0 <= std::min(a, b) && std::max(a, b) < var_num);
        if (a == b) return a;
        if (E[a] > E[b]) std::swap(a, b);
        return order[table.prod(E[a], E[b])];
    }
    int dist(int a, int b){
        assert(0 <= std::min(a, b) && std::max(a, b) < var_num);
        return depth[a] + depth[b] - 2 * depth[lca(a, b)];
    }
    int back(int var, int len){
        assert(len <= depth[var]);
        if (len == 0) return var;
        int l = 0, r = E[var];
        while (r - l > 1){
            int m = (l + r) / 2;
            if (depth[var] - depth[order[table.prod(m, E[var])]] < len){
                r = m;
            }
            else l = m;
        }
        return order[table.prod(l, E[var])];
    }
    // a -> b
    int jump(int a, int b, int len){
        int c = lca(a, b);
        if (len <= depth[a] - depth[c]) return back(a, len);
        len -= depth[a] - depth[c];
        if (len <= depth[b] - depth[c]) return back(b, depth[b] - depth[c] - len);
        return -1;
    }
};

}
#line 2 "/Users/Shared/po167_library/math/Binomial.hpp"

#line 5 "/Users/Shared/po167_library/math/Binomial.hpp"

namespace po167{
template<class T>
struct Binomial{
    std::vector<T> fact_vec, fact_inv_vec;
    void extend(int m = -1){
        int n = fact_vec.size();
        if (m == -1) m = n * 2;
        if (n >= m) return;
        fact_vec.resize(m);
        fact_inv_vec.resize(m);
        for (int i = n; i < m; i++){
            fact_vec[i] = fact_vec[i - 1] * T(i);
        }
        fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];
        for (int i = m - 1; i > n; i--){
            fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);
        }
    }
    Binomial(int MAX = 0){
        fact_vec.resize(1, T(1));
        fact_inv_vec.resize(1, T(1));
        extend(MAX + 1);
    }

    T fact(int i){
        if (i < 0) return 0;
        while (int(fact_vec.size()) <= i) extend();
        return fact_vec[i];
    }
    T invfact(int i){
        if (i < 0) return 0;
        while (int(fact_inv_vec.size()) <= i) extend();
        return fact_inv_vec[i];
    }
    T C(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(b) * invfact(a - b);
    }
    T invC(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(b) * fact(a - b) *invfact(a);
    }
    T P(int a, int b){
        if (a < b || b < 0) return 0;
        return fact(a) * invfact(a - b);
    }
    T inv(int a){
        if (a < 0) return inv(-a) * T(-1);
        if (a == 0) return 1;
        return fact(a - 1) * invfact(a);
    }
    T Catalan(int n){
        if (n < 0) return 0;
        return fact(2 * n) * invfact(n + 1) * invfact(n);
    }
    T narayana(int n, int k){
        if (n <= 0 || n < k || k < 1) return 0;
        return C(n, k) *  C(n, k - 1) * inv(n);
    }
    T Catalan_pow(int n,int d){
        if (n < 0 || d < 0) return 0;
        if (d == 0){
            if (n == 0) return 1;
            return 0;
        }
        return T(d) * inv(d + n) * C(2 * n + d - 1, n);
    }
    // retrun [x^a] 1/(1-x)^b
    T ruiseki(int a,int b){
        if (a < 0 || b < 0) return 0;
        if (a == 0){
            return 1;
        }
        return C(a + b - 1, b - 1);
    }
    // (a, b) -> (c, d)
    // always x + e >= y
    T mirror(int a, int b, int c, int d, int e = 0){
        if (a + e < b || c + e < d) return 0;
        if (a > c || b > d) return 0;
        a += e;
        c += e;
        return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1); 
    }
    // return sum_{i = 0, ... , a} sum_{j = 0, ... , b} C(i + j, i)
    // return C(a + b + 2, a + 1) - 1;
    T gird_sum(int a, int b){
        if (a < 0 || b < 0) return 0;
        return C(a + b + 2, a + 1) - 1;
    }
    // return sum_{i = a, ..., b - 1} sum_{j = c, ... , d - 1} C(i + j, i)
    // AGC 018 E
    T gird_sum_2(int a, int b, int c, int d){
        if (a >= b || c >= d) return 0;
        a--, b--, c--, d--;
        return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);
    }

    // the number of diagonal dissections of a convex n-gon into k+1 regions.
    // OEIS A033282
    // AGC065D
    T diagonal(int n, int k){
        if (n <= 2 || n - 3 < k || k < 0) return 0;
        return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
    }
};
}
#line 29 "f.cpp"

void solve();
// POP'N ROLL MUSIC / TOMOO
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    // cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    int N, S, T;
    cin >> N >> S >> T;
    S--, T--;
    vector<int> A(N - 1), B(N - 1);
    vector<vector<int>> G(N);
    rep(i, 0, N - 1){
        cin >> A[i] >> B[i];
        A[i]--, B[i]--;
        G[A[i]].push_back(B[i]);
        G[B[i]].push_back(A[i]);
    }
    po167::LCA L(G);
    vector<vector<mint>> f = {};
    if (L.dist(A[T], A[S]) > L.dist(A[T], B[S])) swap(A[S], B[S]);
    if (L.dist(A[T], A[S]) > L.dist(B[T], A[S])) swap(A[T], B[T]);
    int len = L.dist(A[S], A[T]);
    po167::Binomial<mint> table;
    rep(i, 0, len + 1){
        int var = L.jump(A[S], A[T], i);
        int X = G[var].size();
        X--;
        vector<mint> tmp = {0};
        rep(j, 0, X){
            tmp.push_back(table.P(X- 1, j));
        }
        f.push_back(tmp);
    }
    auto ans = po167::FPS_Product_Sequence(f);
    rep(i, 0, N){
        if (i) cout << " ";
        cout << (i < (int)ans.size() ? ans[i].val() : 0);
    }
    cout << "\n";
}
/*
 * S, T を入力で与える意味ありますか？
 */
0