graph/tree/euler-tour-on-nodes.hpp

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

Depends on

• Lazy Segment Tree (data-structure/lazy-segment-tree.hpp)
• data-structure/sparse-table.hpp
• template/alias.hpp
• template/debug.hpp
• template/func.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Verified with

• test/AOJ/2667.test.cpp

Code

#pragma once
#include "../../data-structure/lazy-segment-tree.hpp"
#include "../../data-structure/sparse-table.hpp"
#include "../../template/template.hpp"

struct EulerTour {
    using Graph = vector<vector<int>>;
    using Node = pair<long long, int>;
    const function<Node(Node, Node)> fm = [](Node a, Node b) { return Node(a.first + b.first, a.second + b.second); };
    const function<void(Node &, long long)> fa = [](Node &a, long long d) { a.first += d * a.second; };
    const function<void(long long &, long long)> fl = [](long long &d, long long e) { d += e; };

    // main results
    Graph tree;
    vector<int> depth;
    vector<int> node;    // the node-number of i-th element of Euler-tour
    vector<int> vf, ve;  // the index of Euler-tour of node v
    vector<int> eid;     // the index of edge e (i*2 + (0: dir to leaf, 1: dir to root))

    // sub results
    SparseTable<pair<int, int>> st;  // depth (to find LCA)

    // segtree
    Lazy_SegTree<Node, long long> seg;

    // initialization
    EulerTour(const Graph &tree_) { init(tree_); }
    void init(const Graph &tree_) {
        tree = tree_;
        int V = (int)tree.size();
        depth.resize(V * 2 - 1);
        node.resize(V * 2 - 1);
        vf.resize(V);
        ve.resize(V);
        eid.resize((V - 1) * 2);
        seg.init((V - 1) * 2, fm, fa, fl, Node(0, 0), 0);
        int k = 0;
        dfs(0, -1, 0, k);
        vector<pair<int, int>> tmp(int(depth.size()));
        for (int i = 0; i < int(depth.size()); i++) {
            tmp[i] = {depth[i], i};
        }
        st.init(tmp);
        seg.build();
    }

    void dfs(int v, int par, int dep, int &ord) {
        node[ord] = v;
        depth[ord] = dep;
        vf[v] = ve[v] = ord;
        ++ord;
        for (auto e : tree[v]) {
            if (e == par) continue;
            seg.set(ord - 1, Node(0, 1));
            dfs(e, v, dep + 1, ord);
            node[ord] = v;
            depth[ord] = dep;
            ve[v] = ord;
            seg.set(ord - 1, Node(0, -1));
            ++ord;
        }
    }

    inline int LCA(int u, int v) {
        int a = vf[u], b = vf[v];
        if (a > b) swap(a, b);
        return node[st.get(a, b + 1).second];
    }

    inline void update(int v, long long x) {
        seg.update(vf[v], ve[v], x);
    }

    inline long long get(int v) {
        return seg.get(0, vf[v]).first;
    }

    inline long long get(int u, int v) {
        int lca = LCA(u, v);
        return get(u) + get(v) - get(lca) * 2;
    }
};

#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 "data-structure/lazy-segment-tree.hpp"

template <class Monoid, class Action>
struct Lazy_SegTree {
    using FuncMonoid = function<Monoid(Monoid, Monoid)>;
    using FuncAction = function<void(Monoid&, Action)>;
    using FuncComposition = function<void(Action&, Action)>;
    FuncMonoid FM;
    FuncAction FA;
    FuncComposition FC;
    Monoid IDENTITY_MONOID;
    Action IDENTITY_LAZY;
    int N, SIZE, HEIGHT;
    vector<Monoid> dat;
    vector<Action> lazy;

    Lazy_SegTree() {}
    Lazy_SegTree(int n, const FuncMonoid fm, const FuncAction fa,
                 const FuncComposition fc,
                 const Monoid& identity_monoid, const Action& identity_lazy)
        : FM(fm), FA(fa), FC(fc), IDENTITY_MONOID(identity_monoid), IDENTITY_LAZY(identity_lazy), N(n) {
        SIZE = 1, HEIGHT = 0;
        while (SIZE < n) SIZE <<= 1, ++HEIGHT;
        dat.assign(SIZE * 2, IDENTITY_MONOID);
        lazy.assign(SIZE * 2, IDENTITY_LAZY);
    }
    void init(int n, const FuncMonoid fm, const FuncAction fa,
              const FuncComposition fc,
              const Monoid& identity_monoid, const Action& identity_lazy) {
        FM = fm, FA = fa, FC = fc;
        IDENTITY_MONOID = identity_monoid, IDENTITY_LAZY = identity_lazy;
        SIZE = 1, HEIGHT = 0;
        while (SIZE < n) SIZE <<= 1, ++HEIGHT;
        dat.assign(SIZE * 2, IDENTITY_MONOID);
        lazy.assign(SIZE * 2, IDENTITY_LAZY);
    }

    void set(int a, const Monoid& v) { dat[a + SIZE] = v; }
    void build() {
        for (int k = SIZE - 1; k > 0; --k)
            dat[k] = FM(dat[k * 2], dat[k * 2 + 1]);
    }

    inline void evaluate(int k) {
        if (lazy[k] == IDENTITY_LAZY) return;
        if (k < SIZE) FC(lazy[k * 2], lazy[k]), FC(lazy[k * 2 + 1], lazy[k]);
        FA(dat[k], lazy[k]);
        lazy[k] = IDENTITY_LAZY;
    }
    inline void update(int a, int b, const Action& v, int k, int l, int r) {
        evaluate(k);
        if (a <= l && r <= b)
            FC(lazy[k], v), evaluate(k);
        else if (a < r && l < b) {
            update(a, b, v, k * 2, l, (l + r) >> 1);
            update(a, b, v, k * 2 + 1, (l + r) >> 1, r);
            dat[k] = FM(dat[k * 2], dat[k * 2 + 1]);
        }
    }
    inline void update(int a, int b, const Action& v) {
        update(a, b, v, 1, 0, SIZE);
    }

    inline Monoid get(int a, int b, int k, int l, int r) {
        evaluate(k);
        if (a <= l && r <= b)
            return dat[k];
        else if (a < r && l < b)
            return FM(get(a, b, k * 2, l, (l + r) >> 1),
                      get(a, b, k * 2 + 1, (l + r) >> 1, r));
        else
            return IDENTITY_MONOID;
    }
    inline Monoid get(int a, int b) {
        return get(a, b, 1, 0, SIZE);
    }
    inline Monoid operator[](int a) {
        return get(a, a + 1);
    }

    friend ostream& operator<<(ostream& os, Lazy_SegTree seg) {
        os << "[ ";
        for (int i = 0; i < seg.N; i++) {
            os << seg.get(i, i + 1) << " ";
        }
        os << ']';
        return os;
    }
};
#line 3 "data-structure/sparse-table.hpp"

template <class T>
struct SparseTable {
    vector<vector<T>> dat;
    vector<int> height;
    using Func = function<T(T, T)>;
    Func F;

    SparseTable() {}
    explicit SparseTable(
        const vector<T> &vec,
        const Func f = [](T a, T b) { return min(a, b); }) {
        init(vec, f);
    }
    void init(
        const vector<T> &vec,
        const Func f = [](T a, T b) { return min(a, b); }) {
        F = f;
        int n = (int)vec.size(), h = 32 - __builtin_clz(n);
        dat.assign(h, vector<T>(1 << h));
        height.assign(n + 1, 0);
        for (int i = 2; i <= n; i++) height[i] = height[i >> 1] + 1;
        for (int i = 0; i < n; ++i) dat[0][i] = vec[i];
        for (int i = 1; i < h; ++i)
            for (int j = 0; j < n; ++j)
                dat[i][j] = F(dat[i - 1][j],
                              dat[i - 1][min(j + (1 << (i - 1)), n - 1)]);
    }

    T get(int a, int b) {
        return F(dat[height[b - a]][a],
                 dat[height[b - a]][b - (1 << height[b - a])]);
    }
};
#line 5 "graph/tree/euler-tour-on-nodes.hpp"

struct EulerTour {
    using Graph = vector<vector<int>>;
    using Node = pair<long long, int>;
    const function<Node(Node, Node)> fm = [](Node a, Node b) { return Node(a.first + b.first, a.second + b.second); };
    const function<void(Node &, long long)> fa = [](Node &a, long long d) { a.first += d * a.second; };
    const function<void(long long &, long long)> fl = [](long long &d, long long e) { d += e; };

    // main results
    Graph tree;
    vector<int> depth;
    vector<int> node;    // the node-number of i-th element of Euler-tour
    vector<int> vf, ve;  // the index of Euler-tour of node v
    vector<int> eid;     // the index of edge e (i*2 + (0: dir to leaf, 1: dir to root))

    // sub results
    SparseTable<pair<int, int>> st;  // depth (to find LCA)

    // segtree
    Lazy_SegTree<Node, long long> seg;

    // initialization
    EulerTour(const Graph &tree_) { init(tree_); }
    void init(const Graph &tree_) {
        tree = tree_;
        int V = (int)tree.size();
        depth.resize(V * 2 - 1);
        node.resize(V * 2 - 1);
        vf.resize(V);
        ve.resize(V);
        eid.resize((V - 1) * 2);
        seg.init((V - 1) * 2, fm, fa, fl, Node(0, 0), 0);
        int k = 0;
        dfs(0, -1, 0, k);
        vector<pair<int, int>> tmp(int(depth.size()));
        for (int i = 0; i < int(depth.size()); i++) {
            tmp[i] = {depth[i], i};
        }
        st.init(tmp);
        seg.build();
    }

    void dfs(int v, int par, int dep, int &ord) {
        node[ord] = v;
        depth[ord] = dep;
        vf[v] = ve[v] = ord;
        ++ord;
        for (auto e : tree[v]) {
            if (e == par) continue;
            seg.set(ord - 1, Node(0, 1));
            dfs(e, v, dep + 1, ord);
            node[ord] = v;
            depth[ord] = dep;
            ve[v] = ord;
            seg.set(ord - 1, Node(0, -1));
            ++ord;
        }
    }

    inline int LCA(int u, int v) {
        int a = vf[u], b = vf[v];
        if (a > b) swap(a, b);
        return node[st.get(a, b + 1).second];
    }

    inline void update(int v, long long x) {
        seg.update(vf[v], ve[v], x);
    }

    inline long long get(int v) {
        return seg.get(0, vf[v]).first;
    }

    inline long long get(int u, int v) {
        int lca = LCA(u, v);
        return get(u) + get(v) - get(lca) * 2;
    }
};

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