test/tree/Tree_Path_Composite_Sum.test.cpp

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Last update: 2023-11-14 18:27:43+09:00
Problem: https://judge.yosupo.jp/problem/tree_path_composite_sum

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"

#include "../../template/template.hpp"
#include "../../tree/RerootingDP.hpp"
#include "../../utility/modint.hpp"

using namespace lib;
using mint = modint998244353;
using pmm = pair<mint, mint>;

pmm merge(pmm a, pmm b) {
    return pmm(a.first + b.first, a.second + b.second);
}
pmm e() {
    return pmm(0, 0);
}

vector<mint> a, b, c;
pmm pute(pmm x, int e) {
    return pmm(b[e] * x.first + c[e] * x.second, x.second);
}
pmm putv(pmm x, int v) {
    return pmm(x.first + a[v], x.second + 1);
}

int main() {
    int n;
    cin >> n;
    a.resize(n), b.resize(n - 1), c.resize(n - 1);
    rep(i, 0, n) {
        ll x;
        cin >> x;
        a[i] = x;
    }
    RerootingDP<pmm, pmm, merge, e, pute, putv> g(n);
    rep(i, 0, n - 1) {
        int u, v;
        cin >> u >> v;
        g.add_edge(u, v, i, i);
        ll y, z;
        cin >> y >> z;
        b[i] = y, c[i] = z;
    }
    g.build();
    auto ans = g.reroot();
    rep(i, 0, n) cout << ans[i].first.val() << " \n"[i == n - 1];
}

#line 1 "test/tree/Tree_Path_Composite_Sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

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

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 2 "tree/RerootingDP.hpp"

#line 4 "tree/RerootingDP.hpp"

namespace lib {

template <class E, class V, E (*merge)(E, E), E (*e)(), E (*put_edge)(V, int),
          V (*put_vertex)(E, int)>
struct RerootingDP {
    struct edge {
        int to, idx, xdi;
    };
    RerootingDP(int _n = 0) : n(_n) {
        es.resize(n);
    }
    void add_edge(int u, int v, int idx1, int idx2) {
        es[u].push_back({v, idx1, idx2});
        es[v].push_back({u, idx2, idx1});
    }
    vector<V> build(int v = 0) {
        root = v;
        outs.resize(n);
        subdp.resize(n);
        in.resize(n), up.resize(n);
        int tnow = 0;
        dfs(root, -1, tnow);
        return subdp;
    }
    vector<V> reroot() {
        reverse_edge.resize(n);
        reverse_edge[root] = e();
        reverse_dp.resize(n);
        answers.resize(n);
        bfs(root);
        return answers;
    }
    V get(int r, int v) {
        if (r == v) return answers[r];
        if (!(in[v] < in[r] && up[r] <= up[v])) return subdp[v];
        int le = 0, ri = outs[v].size();
        while (ri - le > 1) {
            int md = (le + ri) / 2;
            if (in[es[v][md].to] <= in[r])
                le = md;
            else
                ri = md;
        }
        return reverse_dp[es[v][le].to];
    }
    const vector<edge> &operator[](int idx) const {
        return es[idx];
    }

  private:
    int n, root;
    vector<vector<edge>> es;
    vector<vector<E>> outs;
    vector<E> reverse_edge;
    vector<V> subdp, reverse_dp, answers;
    vector<int> in, up;
    void dfs(int v, int p, int &t) {
        E val = e();
        in[v] = t++;
        for (auto &u : es[v]) {
            if (u.to == p && u.to != es[v].back().to) swap(u, es[v].back());
            if (u.to == p) continue;
            dfs(u.to, v, t);
            E nval = put_edge(subdp[u.to], u.idx);
            outs[v].emplace_back(nval);
            val = merge(val, nval);
        }
        subdp[v] = put_vertex(val, v);
        up[v] = t;
    }
    void bfs(int v) {
        int siz = outs[v].size();
        vector<E> lui(siz + 1), rui(siz + 1);
        lui[0] = e(), rui[siz] = e();
        for (int i = 0; i < siz; i++) lui[i + 1] = merge(lui[i], outs[v][i]);
        for (int i = siz - 1; i >= 0; i--)
            rui[i] = merge(outs[v][i], rui[i + 1]);
        for (int i = 0; i < siz; i++) {
            reverse_dp[es[v][i].to] = put_vertex(
                merge(merge(lui[i], rui[i + 1]), reverse_edge[v]), v);
            reverse_edge[es[v][i].to] =
                put_edge(reverse_dp[es[v][i].to], es[v][i].xdi);
            bfs(es[v][i].to);
        }
        answers[v] = put_vertex(merge(lui[siz], reverse_edge[v]), v);
    }
};

}  // namespace lib
#line 2 "utility/modint.hpp"

#line 4 "utility/modint.hpp"

namespace lib {

template <ll m> struct modint {
    using mint = modint;
    ll a;

    modint(ll x = 0) : a((x % m + m) % m) {}
    static constexpr ll mod() {
        return m;
    }
    ll val() const {
        return a;
    }
    ll& val() {
        return a;
    }
    mint pow(ll n) const {
        mint res = 1;
        mint x = a;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    mint inv() const {
        return pow(m - 2);
    }
    mint& operator+=(const mint rhs) {
        a += rhs.a;
        if (a >= m) a -= m;
        return *this;
    }
    mint& operator-=(const mint rhs) {
        if (a < rhs.a) a += m;
        a -= rhs.a;
        return *this;
    }
    mint& operator*=(const mint rhs) {
        a = a * rhs.a % m;
        return *this;
    }
    mint& operator/=(mint rhs) {
        *this *= rhs.inv();
        return *this;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.a == rhs.a;
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1'000'000'007>;

}  // namespace lib
#line 6 "test/tree/Tree_Path_Composite_Sum.test.cpp"

using namespace lib;
using mint = modint998244353;
using pmm = pair<mint, mint>;

pmm merge(pmm a, pmm b) {
    return pmm(a.first + b.first, a.second + b.second);
}
pmm e() {
    return pmm(0, 0);
}

vector<mint> a, b, c;
pmm pute(pmm x, int e) {
    return pmm(b[e] * x.first + c[e] * x.second, x.second);
}
pmm putv(pmm x, int v) {
    return pmm(x.first + a[v], x.second + 1);
}

int main() {
    int n;
    cin >> n;
    a.resize(n), b.resize(n - 1), c.resize(n - 1);
    rep(i, 0, n) {
        ll x;
        cin >> x;
        a[i] = x;
    }
    RerootingDP<pmm, pmm, merge, e, pute, putv> g(n);
    rep(i, 0, n - 1) {
        int u, v;
        cin >> u >> v;
        g.add_edge(u, v, i, i);
        ll y, z;
        cin >> y >> z;
        b[i] = y, c[i] = z;
    }
    g.build();
    auto ans = g.reroot();
    rep(i, 0, n) cout << ans[i].first.val() << " \n"[i == n - 1];
}