Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub ebi-fly13/Library

:heavy_check_mark: test/tree/Tree_Path_Composite_Sum.test.cpp

Depends on

Code

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

#include <iostream>
#include <vector>

#include "../../graph/base.hpp"
#include "../../modint/modint.hpp"
#include "../../tree/rerooting.hpp"

using mint = ebi::modint998244353;

std::vector<mint> a;

struct S {
    mint sum;
    mint sz;
};

S e() {
    return {0, 0};
}

S merge(S lhs, S rhs) {
    return {lhs.sum + rhs.sum, lhs.sz + rhs.sz};
}

S put_edge(std::pair<mint, mint> e, S x) {
    auto [b, c] = e;
    return {b * x.sum + c * x.sz, x.sz};
}

S put_root(int idx, S x) {
    return {a[idx] + x.sum, x.sz + 1};
}

int main() {
    int n;
    std::cin >> n;
    for (int i = 0; i < n; i++) {
        int val;
        std::cin >> val;
        a.emplace_back(val);
    }
    ebi::Graph<std::pair<mint, mint>> g(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v, b, c;
        std::cin >> u >> v >> b >> c;
        g.add_edge(u, v, {b, c});
        g.add_edge(v, u, {b, c});
    }
    g.build();
    ebi::rerooting<std::pair<mint, mint>, S, S, e, merge, put_edge, put_root>
        dp(n, g);
    for (int i = 0; i < n; i++) {
        std::cout << dp.get(i).sum.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"

#include <iostream>
#include <vector>

#line 2 "graph/base.hpp"

#include <cassert>
#line 5 "graph/base.hpp"
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        return edges;
    }

    const auto operator[](int i) const {
        return csr[i];
    }
    auto operator[](int i) {
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int,edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 2 "modint/modint.hpp"

#line 5 "modint/modint.hpp"

#line 2 "modint/base.hpp"

#include <concepts>
#line 6 "modint/base.hpp"

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 7 "modint/modint.hpp"

namespace ebi {

template <int m> struct static_modint {
  private:
    using modint = static_modint;

  public:
    static constexpr int mod() {
        return m;
    }

    static constexpr modint raw(int v) {
        modint x;
        x._v = v;
        return x;
    }

    constexpr static_modint() : _v(0) {}

    constexpr static_modint(long long v) {
        v %= (long long)umod();
        if (v < 0) v += (long long)umod();
        _v = (unsigned int)v;
    }

    constexpr unsigned int val() const {
        return _v;
    }

    constexpr unsigned int value() const {
        return val();
    }

    constexpr modint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr modint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }

    constexpr modint operator++(int) {
        modint res = *this;
        ++*this;
        return res;
    }
    constexpr modint operator--(int) {
        modint res = *this;
        --*this;
        return res;
    }

    constexpr modint &operator+=(const modint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr modint &operator*=(const modint &rhs) {
        unsigned long long x = _v;
        x *= rhs._v;
        _v = (unsigned int)(x % (unsigned long long)umod());
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) {
        return *this = *this * rhs.inv();
    }

    constexpr modint operator+() const {
        return *this;
    }
    constexpr modint operator-() const {
        return modint() - *this;
    }

    constexpr modint pow(long long n) const {
        assert(0 <= n);
        modint x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const {
        assert(_v);
        return pow(umod() - 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 == rhs);
    }

  private:
    unsigned int _v = 0;

    static constexpr unsigned int umod() {
        return m;
    }
};

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;

}  // namespace ebi
#line 2 "tree/rerooting.hpp"

#line 6 "tree/rerooting.hpp"

#line 8 "tree/rerooting.hpp"

namespace ebi {

template <class T, class V, class E, E (*e)(), E (*merge)(E, E),
          E (*put_edge)(T, V), V (*put_root)(int, E)>
struct rerooting {
  private:
    V dfs_sub(int v, int par = -1) {
        E ret = e();
        for (auto &edge : g[v]) {
            if (edge.to == par && g[v].back().to != par)
                std::swap(g[v].back(), edge);
            if (edge.to == par) continue;
            E val = put_edge(edge.cost, dfs_sub(edge.to, v));
            outs[v].emplace_back(val);
            ret = merge(ret, val);
        }
        sub[v] = put_root(v, ret);
        return sub[v];
    }

    void dfs_all(int v, int par = -1, E rev = e()) {
        int sz = outs[v].size();
        std::vector<E> lcum(sz + 1, e()), rcum(sz + 1, e());
        for (int i = 0; i < sz; i++) {
            lcum[i + 1] = merge(lcum[i], outs[v][i]);
            rcum[sz - i - 1] = merge(rcum[sz - i], outs[v][sz - i - 1]);
        }
        for (int i = 0; i < sz; i++) {
            auto edge = g[v][i];
            E ret =
                put_edge(edge.cost,
                         put_root(v, merge(merge(lcum[i], rcum[i + 1]), rev)));
            dfs_all(edge.to, v, ret);
        }
        dp[v] = put_root(v, merge(lcum[sz], rev));
    }

  public:
    rerooting(int n, const Graph<T> &g_) : n(n), g(g_), sub(n), dp(n), outs(n) {
        dfs_sub(0);
        dfs_all(0);
    }

    V get(int v) const {
        return dp[v];
    }

  private:
    int n;
    Graph<T> g;
    std::vector<V> sub;
    std::vector<V> dp;
    std::vector<std::vector<E>> outs;
};

}  // namespace ebi
#line 9 "test/tree/Tree_Path_Composite_Sum.test.cpp"

using mint = ebi::modint998244353;

std::vector<mint> a;

struct S {
    mint sum;
    mint sz;
};

S e() {
    return {0, 0};
}

S merge(S lhs, S rhs) {
    return {lhs.sum + rhs.sum, lhs.sz + rhs.sz};
}

S put_edge(std::pair<mint, mint> e, S x) {
    auto [b, c] = e;
    return {b * x.sum + c * x.sz, x.sz};
}

S put_root(int idx, S x) {
    return {a[idx] + x.sum, x.sz + 1};
}

int main() {
    int n;
    std::cin >> n;
    for (int i = 0; i < n; i++) {
        int val;
        std::cin >> val;
        a.emplace_back(val);
    }
    ebi::Graph<std::pair<mint, mint>> g(n);
    for (int i = 0; i < n - 1; i++) {
        int u, v, b, c;
        std::cin >> u >> v >> b >> c;
        g.add_edge(u, v, {b, c});
        g.add_edge(v, u, {b, c});
    }
    g.build();
    ebi::rerooting<std::pair<mint, mint>, S, S, e, merge, put_edge, put_root>
        dp(n, g);
    for (int i = 0; i < n; i++) {
        std::cout << dp.get(i).sum.val() << " \n"[i == n - 1];
    }
}
Back to top page