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#include "graph/tree/tree-diameter.hpp"
木の直径を求める.
適当な頂点から DFS して最も遠い点 $u$ を求める, $u$ から DFS して最も遠い点 $v$ を見つけると, そのペア $(u, v)$ が直径の端点.
build()
: 木の直径を返す. path
には直径を構成する辺が格納される.$O(V)$
#pragma once
#include "../graph-template.hpp"
/**
* @brief Tree-Diameter(木の直径)
*
*/
template <typename T = int>
struct TreeDiameter : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
vector<Edge<T> > path;
T build() {
to.assign(g.size(), -1);
auto p = dfs(0, -1);
auto q = dfs(p.second, -1);
int now = p.second;
while (now != q.second) {
for (auto &e : g[now]) {
if (to[now] == e.to) {
path.emplace_back(e);
}
}
now = to[now];
}
return q.first;
}
explicit TreeDiameter(const Graph<T> &g) : Graph<T>(g) {}
private:
vector<int> to;
pair<T, int> dfs(int idx, int par) {
pair<T, int> ret(0, idx);
for (auto &e : g[idx]) {
if (e.to == par) continue;
auto cost = dfs(e.to, idx);
cost.first += e.cost;
if (ret < cost) {
ret = cost;
to[idx] = e.to;
}
}
return ret;
}
};
#line 2 "graph/tree/tree-diameter.hpp"
#line 2 "graph/graph-template.hpp"
template <typename T = int>
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template <typename T = int>
struct Graph {
vector<vector<Edge<T> > > g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const { return g.size(); }
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false,
bool directed = false) {
for (int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted) cin >> c;
if (directed)
add_directed_edge(a, b, c);
else
add_edge(a, b, c);
}
}
inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }
inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};
template <typename T = int>
using Edges = vector<Edge<T> >;
#line 4 "graph/tree/tree-diameter.hpp"
/**
* @brief Tree-Diameter(木の直径)
*
*/
template <typename T = int>
struct TreeDiameter : Graph<T> {
public:
using Graph<T>::Graph;
using Graph<T>::g;
vector<Edge<T> > path;
T build() {
to.assign(g.size(), -1);
auto p = dfs(0, -1);
auto q = dfs(p.second, -1);
int now = p.second;
while (now != q.second) {
for (auto &e : g[now]) {
if (to[now] == e.to) {
path.emplace_back(e);
}
}
now = to[now];
}
return q.first;
}
explicit TreeDiameter(const Graph<T> &g) : Graph<T>(g) {}
private:
vector<int> to;
pair<T, int> dfs(int idx, int par) {
pair<T, int> ret(0, idx);
for (auto &e : g[idx]) {
if (e.to == par) continue;
auto cost = dfs(e.to, idx);
cost.first += e.cost;
if (ret < cost) {
ret = cost;
to[idx] = e.to;
}
}
return ret;
}
};