tree_diameter
(src/tree/tree_diameter.hpp)

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• Last update: 2024-11-09 02:42:16+09:00
• Include: #include "src/tree/tree_diameter.hpp"

tree_diameter

pair<T, vector<int>> tree_diameter(Graph<T> g)

$n$ 頂点の木 g を与えると，その木の直径のうち1つを選んで，パス長と，パスの頂点を順に格納した配列を返します．
木の直径になりうるパスが複数あるとき，どのパスが選ばれるかは未定義です．

制約

• T は int / uint / ll / ull / double / long double
• g は木

計算量

• $O(n)$

Depends on

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

Verified with

• verify/aizu_online_judge/grl/diameter_of_a_tree.test.cpp
• verify/library_checker/tree/tree_diameter.test.cpp

Code

#pragma once
#include "../template/template.hpp"
#include "../graph/graph_template.hpp"
template <typename T>
pair<T, vector<int>> tree_diameter(const Graph<T>& g) {
    const int n = g.size();
    vector<T> depth(n);
    vector<int> par(n);
    auto dfs = [&](const auto& dfs, const int v, const int p, const T& d) -> void {
        depth[v] = d;
        par[v] = p;
        for(const Edge<T>& e : g[v]) {
            if(e.to == p) continue;
            dfs(dfs, e.to, v, d + e.cost);
        }
    };
    int s = 0;
    for(int i = 0; i < 2; ++i) {
        dfs(dfs, s, -1, 0);
        T ma = -1;
        for(int j = 0; j < n; ++j) {
            if(depth[j] > ma) {
                ma = depth[j];
                s = j;
            }
        }
    }
    vector<int> path;
    const T diameter = depth[s];
    while(s != -1) {
        path.emplace_back(s);
        s = par[s];
    }
    return {diameter, path};
}

#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/tree_diameter.hpp"
template <typename T>
pair<T, vector<int>> tree_diameter(const Graph<T>& g) {
    const int n = g.size();
    vector<T> depth(n);
    vector<int> par(n);
    auto dfs = [&](const auto& dfs, const int v, const int p, const T& d) -> void {
        depth[v] = d;
        par[v] = p;
        for(const Edge<T>& e : g[v]) {
            if(e.to == p) continue;
            dfs(dfs, e.to, v, d + e.cost);
        }
    };
    int s = 0;
    for(int i = 0; i < 2; ++i) {
        dfs(dfs, s, -1, 0);
        T ma = -1;
        for(int j = 0; j < n; ++j) {
            if(depth[j] > ma) {
                ma = depth[j];
                s = j;
            }
        }
    }
    vector<int> path;
    const T diameter = depth[s];
    while(s != -1) {
        path.emplace_back(s);
        s = par[s];
    }
    return {diameter, path};
}

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