Fu_L's Library

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:heavy_check_mark: verify/library_checker/tree/tree_path_composite_sum.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#include "../../../src/template/template.hpp"
#include "../../../src/graph/graph_template.hpp"
#include "../../../src/tree/rerooting.hpp"
#include "../../../src/template/static_modint.hpp"
using mint = modint998244353;
int main(void) {
    int n;
    cin >> n;
    vector<mint> a(n);
    rep(i, 0, n) cin >> a[i];
    Graph<int> g(n);
    map<pair<int, int>, pair<mint, mint>> mp;
    rep(i, 0, n - 1) {
        int u, v, b, c;
        cin >> u >> v >> b >> c;
        g.add_edge(u, v);
        mp[minmax(u, v)] = {b, c};
    }
    using DP = pair<mint, int>;
    auto f1 = [&](const DP& x, const DP& y) -> DP {
        return {x.first + y.first, x.second + y.second};
    };
    auto f2 = [&](const DP& x, const int child, const int parent) -> DP {
        auto [b, c] = mp[minmax(child, parent)];
        return {(x.first + a[child]) * b + c * (x.second + 1), x.second + 1};
    };
    const DP id = {0, 0};
    vector<DP> dp = rerooting(g, f1, f2, id);
    rep(i, 0, n) {
        cout << dp[i].first + a[i] << " \n"[i + 1 == n];
    }
}
#line 1 "verify/library_checker/tree/tree_path_composite_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/tree_path_composite_sum"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/tree/rerooting.hpp"
template <typename DP, typename T, typename F1, typename F2>
vector<DP> rerooting(const Graph<T>& g, const F1& f1, const F2& f2, const DP& id) {
    const int n = g.size();
    vector<DP> memo(n, id), dp(n, id);
    auto dfs = [&](const auto& dfs, const int cur, const int par) -> void {
        for(const Edge<T>& e : g[cur]) {
            if(e.to == par) continue;
            dfs(dfs, e.to, cur);
            memo[cur] = f1(memo[cur], f2(memo[e.to], e.to, cur));
        }
    };
    auto efs = [&](const auto& efs, const int cur, const int par, const DP& pval) -> void {
        vector<DP> buf;
        for(const Edge<T>& e : g[cur]) {
            if(e.to == par) continue;
            buf.emplace_back(f2(memo[e.to], e.to, cur));
        }
        vector<DP> head(buf.size() + 1), tail(buf.size() + 1);
        head[0] = tail[buf.size()] = id;
        for(int i = 0; i < (int)buf.size(); ++i) head[i + 1] = f1(head[i], buf[i]);
        for(int i = (int)buf.size() - 1; i >= 0; --i) {
            tail[i] = f1(tail[i + 1], buf[i]);
        }
        dp[cur] = par == -1 ? head.back() : f1(pval, head.back());
        int idx = 0;
        for(const Edge<T>& e : g[cur]) {
            if(e.to == par) continue;
            efs(efs, e.to, cur, f2(f1(pval, f1(head[idx], tail[idx + 1])), cur, e));
            ++idx;
        }
    };
    dfs(dfs, 0, -1);
    efs(efs, 0, -1, id);
    return dp;
}
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 6 "verify/library_checker/tree/tree_path_composite_sum.test.cpp"
using mint = modint998244353;
int main(void) {
    int n;
    cin >> n;
    vector<mint> a(n);
    rep(i, 0, n) cin >> a[i];
    Graph<int> g(n);
    map<pair<int, int>, pair<mint, mint>> mp;
    rep(i, 0, n - 1) {
        int u, v, b, c;
        cin >> u >> v >> b >> c;
        g.add_edge(u, v);
        mp[minmax(u, v)] = {b, c};
    }
    using DP = pair<mint, int>;
    auto f1 = [&](const DP& x, const DP& y) -> DP {
        return {x.first + y.first, x.second + y.second};
    };
    auto f2 = [&](const DP& x, const int child, const int parent) -> DP {
        auto [b, c] = mp[minmax(child, parent)];
        return {(x.first + a[child]) * b + c * (x.second + 1), x.second + 1};
    };
    const DP id = {0, 0};
    vector<DP> dp = rerooting(g, f1, f2, id);
    rep(i, 0, n) {
        cout << dp[i].first + a[i] << " \n"[i + 1 == n];
    }
}
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