centroid
(src/tree/centroid.hpp)

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• Last update: 2024-11-09 01:34:39+09:00
• Include: #include "src/tree/centroid.hpp"

centroid

vector<int> centroid(Graph<T> g)

$n$ 頂点の木 g の重心を全て返します．

頂点 $v$ が $n$ 頂点の木 g の重心であるとは，頂点 $v$ を取り除いたときにできる連結成分の大きさの最大値が $n / 2$ 以下であることを指します．
任意の木には重心が $1$ つ，または $2$ つ存在します．

制約

• g は木である

計算量

• $O(n)$

Depends on

• Graph (src/graph/graph_template.hpp)
• template (src/template/template.hpp)

Verified with

• verify/unit_test/tree/centroid.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "../graph/graph_template.hpp"
template <typename T>
vector<int> centroid(const Graph<T>& g) {
    const int n = g.size();
    stack<pair<int, int>> st;
    st.emplace(0, -1);
    vector<int> sz(n), par(n);
    while(!st.empty()) {
        const pair<int, int> p = st.top();
        if(sz[p.first] == 0) {
            sz[p.first] = 1;
            for(const Edge<T>& e : g[p.first]) {
                if(e.to != p.second) {
                    st.emplace(e.to, p.first);
                }
            }
        } else {
            for(const Edge<T>& e : g[p.first]) {
                if(e.to != p.second) {
                    sz[p.first] += sz[e.to];
                }
            }
            par[p.first] = p.second;
            st.pop();
        }
    }
    vector<int> ret;
    int size = n;
    for(int i = 0; i < n; ++i) {
        int val = n - sz[i];
        for(const Edge<T>& e : g[i]) {
            if(e.to != par[i]) {
                val = max(val, sz[e.to]);
            }
        }
        if(val < size) size = val, ret.clear();
        if(val == size) ret.emplace_back(i);
    }
    return ret;
}

#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/tree/centroid.hpp"
template <typename T>
vector<int> centroid(const Graph<T>& g) {
    const int n = g.size();
    stack<pair<int, int>> st;
    st.emplace(0, -1);
    vector<int> sz(n), par(n);
    while(!st.empty()) {
        const pair<int, int> p = st.top();
        if(sz[p.first] == 0) {
            sz[p.first] = 1;
            for(const Edge<T>& e : g[p.first]) {
                if(e.to != p.second) {
                    st.emplace(e.to, p.first);
                }
            }
        } else {
            for(const Edge<T>& e : g[p.first]) {
                if(e.to != p.second) {
                    sz[p.first] += sz[e.to];
                }
            }
            par[p.first] = p.second;
            st.pop();
        }
    }
    vector<int> ret;
    int size = n;
    for(int i = 0; i < n; ++i) {
        int val = n - sz[i];
        for(const Edge<T>& e : g[i]) {
            if(e.to != par[i]) {
                val = max(val, sz[e.to]);
            }
        }
        if(val < size) size = val, ret.clear();
        if(val == size) ret.emplace_back(i);
    }
    return ret;
}

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