Rerooting DP
(tree/rerooting.hpp)

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• Last update: 2024-03-13 15:52:21+09:00
• Include: #include "tree/rerooting.hpp"

説明

抽象化全方位木DPライブラリ。各頂点を根としたときの木DPを求める。$O(N)$

コンストラクタ

rerooting<V, E, e, merge, put_edge, put_root> dp(int n, std::vector<std::pair<int,int>> edges);

• DPの値の型 V
• 可換モノイドの型 E
• E の単位元を返す関数 E e()
• E の演算子 E merge(E s, E t)
• 辺 i を根に付与する関数 E put_edge(T edge, V x)
• 頂点 $v$ を根として追加する関数 V put_root(int v, E x)

をテンプレートとして用いている。

Depends on

• Simple CSR (data_structure/simple_csr.hpp)
• Graph (CSR format) (graph/base.hpp)

Verified with

• test/tree/Tree_Path_Composite_Sum.test.cpp

Code

#pragma once

#include <cassert>
#include <utility>
#include <vector>

#include "../graph/base.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 2 "tree/rerooting.hpp"

#include <cassert>
#include <utility>
#include <vector>

#line 2 "graph/base.hpp"

#line 4 "graph/base.hpp"
#include <iostream>
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#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 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

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