test/library-checker/Tree/LowestCommonAncestor.test.cpp

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• Last update: 2025-11-24 18:49:07+09:00
• Problem: https://judge.yosupo.jp/problem/lca

Depends on

• build/pch/stdc++.hpp
• library/graph/Graph.hpp
• library/tree/HLD.hpp
• library/tree/Tree.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include <bits/stdc++.h>

#include "library/tree/HLD.hpp"
#include "library/tree/Tree.hpp"

int main() {
    int n, q;
    std::cin >> n >> q;
    Tree t(n);
    t.scan_root(0);
    HLD hld(t);
    hld.build();
    while (q--) {
        int u, v;
        std::cin >> u >> v;
        std::cout << hld.lca(u, v) << "\n";
    }
}

#line 1 "test/library-checker/Tree/LowestCommonAncestor.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lca"
#include <bits/stdc++.h>

#line 2 "library/tree/HLD.hpp"
template <typename TREE> struct HLD {
    int n;
    TREE T;
    std::vector<int> sz, head, id, id2, rev_id;
    bool prepared;
    HLD(TREE T_)
        : T(T_), n(T_.n), sz(n), head(n), id(n), id2(n), rev_id(n), prepared(false) {}
    HLD() = default;

  private:
    void dfs_sz(int v) {
        sz[v] = 1;
        for (auto &e : T.son(v)) {
            dfs_sz(e.to);
            sz[v] += sz[e.to];
            if (sz[e.to] > sz[T.son(v)[0].to])
                std::swap(e, T.son(v)[0]);
        }
    }
    void dfs_hld(int v, int &k) {
        id[v] = k++;
        rev_id[id[v]] = v;
        for (int i = 0; i < T.son(v).size(); i++) {
            int to = T.son(v)[i];
            head[to] = (i ? to : head[v]);
            dfs_hld(to, k);
        }
        id2[v] = k;
    }

  public:
    std::vector<int> build(int r = 0) {
        assert(!prepared);
        prepared = true;
        if (~T.root)
            assert(T.root == r);
        else
            T.build(r);
        head[r] = r;
        dfs_sz(r);
        int k = 0;
        dfs_hld(r, k);
        return id;
    }

    int lca(int u, int v) const {
        assert(prepared);
        while (head[u] != head[v])
            if (T.depth[head[u]] > T.depth[head[v]])
                u = T.parent(head[u]);
            else
                v = T.parent(head[v]);
        return (T.depth[u] < T.depth[v] ? u : v);
    }
    int distance(int u, int v) const {
        int w = lca(u, v);
        return T.depth[u] + T.depth[v] - T.depth[w] * 2;
    }

    // v の k 個上の頂点を返す
    int kth_parent(int v, int k) const {
        assert(prepared);
        if(T.depth[v] < k)
            return -1;
        while(T.depth[v] - T.depth[head[v]] < k){
            k -= T.depth[v] - T.depth[head[v]] + 1;
            v = T.parent(head[v]);
        }
        return rev_id[id[v] - k];
    }

    // u から v へ k 回移動した頂点を返す
    int jump(int u, int v, int k) const {
        assert(prepared);
        int w = lca(u, v);
        if(T.depth[u] + T.depth[v] - T.depth[w] * 2 < k)
            return -1;
        if(T.depth[u] - T.depth[w] >= k)
            return kth_parent(u, k);
        return kth_parent(v, T.depth[u] + T.depth[v] - T.depth[w] * 2 - k);
    }

    // l=lca(u,v) とした時、[u,l] パスと [v,l] パス を閉区間の組みで返す
    using path_t = std::vector<std::pair<int, int>>;
    std::pair<path_t, path_t> path(int u, int v) const {
        assert(prepared);
        path_t path_u, path_v;
        while (u != v) {
            if (head[u] == head[v]) {
                if (T.depth[u] < T.depth[v])
                    path_v.emplace_back(id[v], id[u]);
                else
                    path_u.emplace_back(id[u], id[v]);
                break;
            }
            if (T.depth[head[u]] < T.depth[head[v]]) {
                path_v.emplace_back(id[v], id[head[v]]);
                v = T.parent(head[v]);
            } else {
                path_u.emplace_back(id[u], id[head[u]]);
                u = T.parent(head[u]);
            }
        }
        if (u == v)
            path_u.emplace_back(id[u], id[u]);
        return {path_u, path_v};
    }

    // [l,r) が v の部分木
    std::pair<int, int> subtree(int v) const {
        assert(prepared);
        return {id[v], id2[v]};
    }
};
#line 2 "library/graph/Graph.hpp"

#line 6 "library/graph/Graph.hpp"

struct Edge {
    int from, to;
    Edge() = default;
    Edge(int from, int to) : from(from), to(to) {}
    operator int() const { return to; }
};

struct Graph {
    int n;
    using edge_type = Edge;
    std::vector<edge_type> edges;

  protected:
    std::vector<int> in_deg;
    bool prepared;
    class OutgoingEdges {
        Graph *g;
        int l, r;

      public:
        OutgoingEdges(Graph *g, int l, int r) : g(g), l(l), r(r) {}
        edge_type *begin() { return &(g->edges[l]); }
        edge_type *end() { return &(g->edges[r]); }
        edge_type &operator[](int i) { return g->edges[l + i]; }
        int size() const { return r - l; }
    };
    class ConstOutgoingEdges {
        const Graph *g;
        int l, r;

      public:
        ConstOutgoingEdges(const Graph *g, int l, int r) : g(g), l(l), r(r) {}
        const edge_type *begin() const { return &(g->edges[l]); }
        const edge_type *end() const { return &(g->edges[r]); }
        const edge_type &operator[](int i) const { return g->edges[l + i]; }
        int size() const { return r - l; }
    };

  public:
    OutgoingEdges operator[](int v) {
        assert(prepared);
        return {this, in_deg[v], in_deg[v + 1]};
    }
    const ConstOutgoingEdges operator[](int v) const {
        assert(prepared);
        return {this, in_deg[v], in_deg[v + 1]};
    }

    bool is_prepared() const { return prepared; }

    Graph() : n(0), in_deg(1, 0), prepared(false) {}
    Graph(int n) : n(n), in_deg(n + 1, 0), prepared(false) {}
    Graph(int n, int m, bool directed = false, int indexed = 1)
        : n(n), in_deg(n + 1, 0), prepared(false) {
        scan(m, directed, indexed);
    }

    void resize(int n) { n = n; }

    void add_arc(int from, int to) {
        assert(!prepared);
        assert(0 <= from and from < n and 0 <= to and to < n);
        edges.emplace_back(from, to);
        in_deg[from + 1]++;
    }
    void add_edge(int u, int v) {
        add_arc(u, v);
        add_arc(v, u);
    }
    void add_arc(const edge_type &e) { add_arc(e.from, e.to); }
    void add_edge(const edge_type &e) { add_edge(e.from, e.to); }

    void scan(int m, bool directed = false, int indexed = 1) {
        edges.reserve(directed ? m : 2 * m);
        while (m--) {
            int u, v;
            std::cin >> u >> v;
            u -= indexed;
            v -= indexed;
            if (directed)
                add_arc(u, v);
            else
                add_edge(u, v);
        }
        build();
    }

    void build() {
        assert(!prepared);
        prepared = true;
        for (int v = 0; v < n; v++)
            in_deg[v + 1] += in_deg[v];
        std::vector<edge_type> new_edges(in_deg.back());
        auto counter = in_deg;
        for (auto &&e : edges)
            new_edges[counter[e.from]++] = e;
        edges = new_edges;
    }

    void graph_debug() const {
#ifndef __LOCAL
        return;
#endif
        assert(prepared);
        for (int from = 0; from < n; from++) {
            std::cerr << from << ";";
            for (int i = in_deg[from]; i < in_deg[from + 1]; i++)
                std::cerr << edges[i].to << " ";
            std::cerr << "\n";
        }
    }
};
#line 3 "library/tree/Tree.hpp"
struct Tree : Graph {
    using Graph::Graph;
    Tree() = default;
    int root = -1;
    std::vector<int> DFS, BFS, depth;

    void scan_root(int indexed = 1) {
        for (int i = 1; i < n; i++) {
            int p;
            std::cin >> p;
            add_edge(p - indexed, i);
        }
        build();
    }
    void scan(int indexed = 1) {
        Graph::scan(n - 1, false, indexed);
        build();
    }

    edge_type &parent(int v) {
        assert(~root and root != v);
        return (*this)[v][0];
    }
    const edge_type &parent(int v) const {
        assert(~root and root != v);
        return (*this)[v][0];
    }

    OutgoingEdges son(int v) {
        assert(~root);
        if (v == root)
            return {this, in_deg[v], in_deg[v + 1]};
        return {this, in_deg[v] + 1, in_deg[v + 1]};
    }

  private:
    void dfs(int v, int pre = -1) {
        for (auto &e : (*this)[v]) {
            if (e.to == pre)
                std::swap((*this)[v][0], e);
            else {
                depth[e.to] = depth[v] + 1;
                dfs(e.to, v);
            }
        }
        DFS.push_back(v);
    }

  public:
    void build(int r = 0) {
        if (!is_prepared())
            Graph::build();
        if (~root) {
            assert(r == root);
            return;
        }
        root = r;
        depth = std::vector<int>(n, 0);
        DFS.reserve(n);
        BFS.reserve(n);
        dfs(root);
        std::queue<int> que;
        que.push(root);
        while (que.size()) {
            int p = que.front();
            que.pop();
            BFS.push_back(p);
            for (const auto &e : son(p))
                que.push(e.to);
        }
    }
};
#line 6 "test/library-checker/Tree/LowestCommonAncestor.test.cpp"

int main() {
    int n, q;
    std::cin >> n >> q;
    Tree t(n);
    t.scan_root(0);
    HLD hld(t);
    hld.build();
    while (q--) {
        int u, v;
        std::cin >> u >> v;
        std::cout << hld.lca(u, v) << "\n";
    }
}

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