test/tree/Jump_on_Tree_HLD.test.cpp

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• Last update: 2024-04-28 15:17:37+09:00
• Problem: https://judge.yosupo.jp/problem/jump_on_tree

Depends on

• Simple CSR (data_structure/simple_csr.hpp)
• Graph (CSR format) (graph/base.hpp)
• Heavy Light Decomposition (tree/heavy_light_decomposition.hpp)

Code

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

#include <iostream>

#include "../../graph/base.hpp"
#include "../../tree/heavy_light_decomposition.hpp"

int main() {
    int n, q;
    std::cin >> n >> q;
    ebi::Graph<int> g(n);
    g.read_tree(0);
    ebi::heavy_light_decomposition hld(g);
    while (q--) {
        int s, t, i;
        std::cin >> s >> t >> i;
        std::cout << hld.jump(s, t, i) << '\n';
    }
}

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

#include <iostream>

#line 2 "graph/base.hpp"

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

#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 "tree/heavy_light_decomposition.hpp"

#include <algorithm>
#line 6 "tree/heavy_light_decomposition.hpp"

#line 8 "tree/heavy_light_decomposition.hpp"

namespace ebi {

template <class T> struct heavy_light_decomposition {
  private:
    void dfs_sz(int v, Graph<T> &g) {
        for (auto &e : g[v]) {
            if (e.to == par[v]) continue;
            par[e.to] = v;
            depth_[e.to] = depth_[v] + 1;
            dist[e.to] = dist[v] + e.cost;
            dfs_sz(e.to, g);
            sz[v] += sz[e.to];
            if (sz[e.to] > sz[g[v][0].to] || g[v][0].to == par[v])
                std::swap(e, g[v][0]);
        }
    }

    void dfs_hld(int v, const Graph<T> &g) {
        in[v] = num++;
        rev[in[v]] = v;
        for (auto e : g[v]) {
            if (e.to == par[v]) continue;
            nxt[e.to] = (e.to == g[v][0].to ? nxt[v] : e.to);
            dfs_hld(e.to, g);
        }
        out[v] = num;
    }

    // [u, v) パスの取得 (v は u の祖先)
    std::vector<std::pair<int, int>> ascend(int u, int v) const {
        std::vector<std::pair<int, int>> res;
        while (nxt[u] != nxt[v]) {
            res.emplace_back(in[u], in[nxt[u]]);
            u = par[nxt[u]];
        }
        if (u != v) res.emplace_back(in[u], in[v] + 1);
        return res;
    }

    // (u, v] パスの取得 (u は v の祖先)
    std::vector<std::pair<int, int>> descend(int u, int v) const {
        if (u == v) return {};
        if (nxt[u] == nxt[v]) return {{in[u] + 1, in[v]}};
        auto res = descend(u, par[nxt[v]]);
        res.emplace_back(in[nxt[v]], in[v]);
        return res;
    }

  public:
    heavy_light_decomposition(Graph<T> gh, int root = 0)
        : n(gh.size()),
          sz(n, 1),
          in(n),
          out(n),
          nxt(n),
          par(n, -1),
          depth_(n, 0),
          rev(n),
          dist(n, 0) {
        nxt[root] = root;
        dfs_sz(root, gh);
        dfs_hld(root, gh);
    }

    int idx(int u) const {
        return in[u];
    }

    int rev_idx(int i) const {
        return rev[i];
    }

    int la(int v, int k) const {
        while (1) {
            int u = nxt[v];
            if (in[u] <= in[v] - k) return rev[in[v] - k];
            k -= in[v] - in[u] + 1;
            v = par[u];
        }
    }

    int lca(int u, int v) const {
        while (nxt[u] != nxt[v]) {
            if (in[u] < in[v]) std::swap(u, v);
            u = par[nxt[u]];
        }
        return depth_[u] < depth_[v] ? u : v;
    }

    int jump(int s, int t, int i) const {
        if (i == 0) return s;
        int l = lca(s, t);
        int d = depth_[s] + depth_[t] - depth_[l] * 2;
        if (d < i) return -1;
        if (depth_[s] - depth_[l] >= i) return la(s, i);
        i = d - i;
        return la(t, i);
    }

    std::vector<int> path(int s, int t) const {
        int l = lca(s, t);
        std::vector<int> a, b;
        for (; s != l; s = par[s]) a.emplace_back(s);
        for (; t != l; t = par[t]) b.emplace_back(t);
        a.emplace_back(l);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    int root_of_heavy_path(int u) const {
        return nxt[u];
    }

    int parent(int u) const {
        return par[u];
    }

    T distance(int u, int v) const {
        return dist[u] + dist[v] - 2 * dist[lca(u, v)];
    }

    T distance_from_root(int v) const {
        return dist[v];
    }

    T depth(int v) const {
        return depth_[v];
    }

    bool at_path(int u, int v, int s) const {
        return distance(u, v) == distance(u, s) + distance(s, v);
    }

    template <class F>
    void path_noncommutative_query(int u, int v, bool vertex,
                                   const F &f) const {
        int l = lca(u, v);
        for (auto [a, b] : ascend(u, l)) f(a + 1, b);
        if (vertex) f(in[l], in[l] + 1);
        for (auto [a, b] : descend(l, v)) f(a, b + 1);
    }

    std::vector<std::pair<int, int>> path_sections(int u, int v,
                                                   bool vertex) const {
        int l = lca(u, v);
        std::vector<std::pair<int, int>> sections;
        for (auto [a, b] : ascend(u, l)) sections.emplace_back(a + 1, b);
        if (vertex) sections.emplace_back(in[l], in[l] + 1);
        for (auto [a, b] : descend(l, v)) sections.emplace_back(a, b + 1);
        return sections;
    }

    template <class F>
    int max_path(int u, int v, bool vertex, F binary_search) const {
        int prev = -1;
        int l = lca(u, v);
        for (auto [a, b] : ascend(u, l)) {
            a++;
            int m = binary_search(a, b);
            if (m == b) {
                prev = rev[b];
            } else {
                return (m == a ? prev : rev[m]);
            }
        }
        if (vertex) {
            int m = binary_search(in[l], in[l] + 1);
            if (m == in[l]) {
                return prev;
            } else {
                prev = l;
            }
        }
        for (auto [a, b] : descend(l, v)) {
            b++;
            int m = binary_search(a, b);
            if (m == b) {
                prev = rev[b - 1];
            } else {
                return m == a ? prev : rev[m - 1];
            }
        }
        return v;
    }

    template <class F> void subtree_query(int u, bool vertex, const F &f) {
        f(in[u] + int(!vertex), out[u]);
    }

    const std::vector<int> &dfs_order() const {
        return rev;
    }

    std::vector<std::pair<int, int>> lca_based_auxiliary_tree_dfs_order(
        std::vector<int> vs) const;

    std::pair<std::vector<int>, Graph<T>> lca_based_auxiliary_tree(
        std::vector<int> vs) const;

  private:
    int n;
    std::vector<int> sz, in, out, nxt, par, depth_, rev;
    std::vector<T> dist;

    int num = 0;
};

}  // namespace ebi
#line 7 "test/tree/Jump_on_Tree_HLD.test.cpp"

int main() {
    int n, q;
    std::cin >> n >> q;
    ebi::Graph<int> g(n);
    g.read_tree(0);
    ebi::heavy_light_decomposition hld(g);
    while (q--) {
        int s, t, i;
        std::cin >> s >> t >> i;
        std::cout << hld.jump(s, t, i) << '\n';
    }
}

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