Auxiliary Tree
(graph/tree/auxiliary-tree.hpp)

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• Last update: 2024-08-24 11:50:18+09:00
• Include: #include "graph/tree/auxiliary-tree.hpp"

Depends on

• Lowest Common Ancestor (graph/tree/lca.hpp)
• template/alias.hpp
• template/debug.hpp
• template/func.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#pragma once
#include "../../template/template.hpp"
#include "lca.hpp"

struct AuxiliaryTree : LCA {
    using super = LCA;

    vector<int> idx;
    vector<vector<int>> T;
    explicit AuxiliaryTree(const vector<vector<int>> &G, int r = 0)
        : super(G, r) {
        build(G, r);
    }

    void dfs(const vector<vector<int>> &G, int v, int p, int &pos) {
        idx[v] = pos++;
        for (int u : G[v])
            if (u != p) dfs(G, u, v, pos);
    }

    void build(const vector<vector<int>> &G, int r = 0) {
        int V = (int)G.size();
        idx.assign(V, 0);
        T.assign(V, vector<int>());
        int pos = 0;
        dfs(G, r, -1, pos);
    }

    void add_aux_edge(int u, int v) {
        T[u].emplace_back(v);
        T[v].emplace_back(u);
    }

    using super::get, super::depth;
    void query(vector<int> &vs) {
        assert(!vs.empty());
        sort(vs.begin(), vs.end(),
             [&](int a, int b) { return idx[a] < idx[b]; });
        vs.erase(unique(vs.begin(), vs.end()), vs.end());

        int k = vs.size();
        stack<int> st;
        st.emplace(vs[0]);
        for (int i = 0; i + 1 < k; i++) {
            int w = get(vs[i], vs[i + 1]);
            if (w != vs[i]) {
                int l = st.top();
                st.pop();
                while (!st.empty() and depth[w] < depth[st.top()]) {
                    add_aux_edge(st.top(), l);
                    l = st.top();
                    st.pop();
                }
                if (st.empty() or st.top() != w) {
                    st.emplace(w);
                    vs.emplace_back(w);
                }
                add_aux_edge(w, l);
            }
            st.emplace(vs[i + 1]);
        }

        while (st.size() > 1) {
            int c = st.top();
            st.pop();
            add_aux_edge(st.top(), c);
        }
    }

    void clear(const vector<int> &ws) {
        for (int w : ws) T[w].clear();
    }
};

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#line 3 "template/macro.hpp"

#define overload3(_1, _2, _3, name, ...) name
#define all1(v) std::begin(v), std::end(v)
#define all2(v, a) std::begin(v), std::begin(v) + a
#define all3(v, a, b) std::begin(v) + a, std::begin(v) + b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define rall1(v) std::rbegin(v), std::rend(v)
#define rall2(v, a) std::rbegin(v), std::rbegin(v) + a
#define rall3(v, a, b) std::rbegin(v) + a, std::rbegin(v) + b
#define rall(...) overload3(__VA_ARGS__, rall3, rall2, rall1)(__VA_ARGS__)
#define elif else if
#define updiv(N, X) (((N) + (X) - 1) / (X))
#define sigma(a, b) (((a) + (b)) * ((b) - (a) + 1) / 2)
#define INT(...)     \
    int __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    scan(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    scan(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    scan(__VA_ARGS__)
#define DOU(...)        \
    double __VA_ARGS__; \
    scan(__VA_ARGS__)
#define LD(...)     \
    ld __VA_ARGS__; \
    scan(__VA_ARGS__)
#define pb push_back
#define eb emplace_back
#line 3 "template/alias.hpp"

using ll = long long;
using ld = long double;
using pii = std::pair<int, int>;
using pll = std::pair<ll, ll>;
constexpr int inf = 1 << 30;
constexpr ll INF = 1LL << 60;
constexpr int dx[8] = {1, 0, -1, 0, 1, -1, 1, -1};
constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
constexpr int mod = 998244353;
constexpr int MOD = 1e9 + 7;
#line 3 "template/func.hpp"

template <typename T>
inline bool chmax(T& a, T b) { return ((a < b) ? (a = b, true) : (false)); }
template <typename T>
inline bool chmin(T& a, T b) { return ((a > b) ? (a = b, true) : (false)); }
template <typename T, typename U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (auto it = std::begin(v); it != std::end(v);) {
        os << *it << ((++it) != std::end(v) ? " " : "");
    }
    return os;
}
template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &in : v) {
        is >> in;
    }
    return is;
}
inline void scan() {}
template <class Head, class... Tail>
inline void scan(Head &head, Tail &...tail) {
    std::cin >> head;
    scan(tail...);
}
template <class T>
inline void print(const T &t) { std::cout << t << '\n'; }
template <class Head, class... Tail>
inline void print(const Head &head, const Tail &...tail) {
    std::cout << head << ' ';
    print(tail...);
}
template <class... T>
inline void fin(const T &...a) {
    print(a...);
    exit(0);
}
#line 3 "template/util.hpp"

struct IOSetup {
    IOSetup() {
        std::cin.tie(nullptr);
        std::ios::sync_with_stdio(false);
        std::cout.tie(0);
        std::cout << std::fixed << std::setprecision(12);
        std::cerr << std::fixed << std::setprecision(12);
    }
} IOSetup;
#line 3 "template/debug.hpp"

#ifdef LOCAL
#include <dump.hpp>
#else
#define debug(...)
#endif
#line 8 "template/template.hpp"
using namespace std;
#line 3 "graph/tree/lca.hpp"

struct LCA {
    vector<vector<int>> parent;
    vector<int> depth;
    LCA() {}
    explicit LCA(const vector<vector<int>>& G, int r = 0) { init(G, r); }
    void init(const vector<vector<int>>& G, int r = 0) {
        int V = (int)G.size();
        int h = 1;
        while ((1 << h) < V) ++h;
        parent.assign(h, vector<int>(V, -1));
        depth.assign(V, -1);
        dfs(G, r, -1, 0);
        for (int i = 0; i + 1 < (int)parent.size(); ++i)
            for (int v = 0; v < V; ++v)
                if (parent[i][v] != -1)
                    parent[i + 1][v] = parent[i][parent[i][v]];
    }
    void dfs(const vector<vector<int>>& G, int v, int p, int d) {
        parent[0][v] = p;
        depth[v] = d;
        for (auto e : G[v])
            if (e != p) dfs(G, e, v, d + 1);
    }
    int after(int u, int k) {
        for (int i = 0; i < (int)parent.size(); i++) {
            if (k & (1 << i)) {
                u = parent[i][u];
            }
        }
        return u;
    }
    int get(int u, int v) {
        if (depth[u] > depth[v]) swap(u, v);
        v = after(v, depth[v] - depth[u]);
        if (u == v) return u;
        for (int i = (int)parent.size() - 1; i >= 0; --i) {
            if (parent[i][u] != parent[i][v]) {
                u = parent[i][u];
                v = parent[i][v];
            }
        }
        return parent[0][u];
    }
    int dist(int u, int v) {
        return depth[u] + depth[v] - 2 * depth[get(u, v)];
    }
    bool is_on_path(int u, int v, int a) {
        return dist(u, a) + dist(a, v) == dist(u, v);
    }
};
#line 4 "graph/tree/auxiliary-tree.hpp"

struct AuxiliaryTree : LCA {
    using super = LCA;

    vector<int> idx;
    vector<vector<int>> T;
    explicit AuxiliaryTree(const vector<vector<int>> &G, int r = 0)
        : super(G, r) {
        build(G, r);
    }

    void dfs(const vector<vector<int>> &G, int v, int p, int &pos) {
        idx[v] = pos++;
        for (int u : G[v])
            if (u != p) dfs(G, u, v, pos);
    }

    void build(const vector<vector<int>> &G, int r = 0) {
        int V = (int)G.size();
        idx.assign(V, 0);
        T.assign(V, vector<int>());
        int pos = 0;
        dfs(G, r, -1, pos);
    }

    void add_aux_edge(int u, int v) {
        T[u].emplace_back(v);
        T[v].emplace_back(u);
    }

    using super::get, super::depth;
    void query(vector<int> &vs) {
        assert(!vs.empty());
        sort(vs.begin(), vs.end(),
             [&](int a, int b) { return idx[a] < idx[b]; });
        vs.erase(unique(vs.begin(), vs.end()), vs.end());

        int k = vs.size();
        stack<int> st;
        st.emplace(vs[0]);
        for (int i = 0; i + 1 < k; i++) {
            int w = get(vs[i], vs[i + 1]);
            if (w != vs[i]) {
                int l = st.top();
                st.pop();
                while (!st.empty() and depth[w] < depth[st.top()]) {
                    add_aux_edge(st.top(), l);
                    l = st.top();
                    st.pop();
                }
                if (st.empty() or st.top() != w) {
                    st.emplace(w);
                    vs.emplace_back(w);
                }
                add_aux_edge(w, l);
            }
            st.emplace(vs[i + 1]);
        }

        while (st.size() > 1) {
            int c = st.top();
            st.pop();
            add_aux_edge(st.top(), c);
        }
    }

    void clear(const vector<int> &ws) {
        for (int w : ws) T[w].clear();
    }
};

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