#pragma once
#include <algorithm>
#include <vector>
#include "Mylib/Graph/GraphUtils/strongly_connected_components.cpp"
#include "Mylib/Graph/Template/graph.cpp"
namespace haar_lib {
namespace chu_liu_edmonds_impl {
template <typename T>
graph<T> rec(graph<T> g, int r) {
const int N = g.size();
graph<T> in_edges(N);
for (int i = 0; i < N; ++i) {
if (i != r) {
auto e = *std::min_element(
g[i].begin(), g[i].end(),
[](const auto &a, const auto &b) {
return a.cost < b.cost;
});
in_edges[i].push_back(e);
}
}
const auto [s, m] = strongly_connected_components(in_edges);
std::vector<std::vector<int>> v(m);
for (int i = 0; i < N; ++i) {
v[s[i]].push_back(i);
}
int count_cycle = 0;
for (int i = 0; i < m; ++i) {
if (v[i].size() > 1) {
for (int j : v[i]) {
auto c =
*std::min_element(
g[j].begin(), g[j].end(),
[](const auto &a, const auto &b) { return a.cost < b.cost; });
for (auto &e : g[j]) {
e.cost -= c.cost;
}
}
++count_cycle;
}
}
if (count_cycle == 0) {
return in_edges;
}
graph<T> G(m);
const int R = s[r];
for (int i = 0; i < N; ++i) {
for (auto &e : g[i]) {
if (s[e.from] == s[e.to]) continue;
G.add_edge(s[e.from], s[e.to], e.cost);
}
}
auto res = rec(G, R);
for (int i = 0; i < m; ++i) {
if (i == R) continue;
int j = res[i][0].to;
std::vector<edge<T>> c;
for (int x : v[i]) {
for (auto &e : g[x]) {
if (s[e.to] == j) {
c.push_back(e);
}
}
}
auto e =
*std::min_element(
c.begin(), c.end(),
[](const auto &a, const auto &b) { return a.cost < b.cost; });
in_edges[e.from][0] = e;
}
return in_edges;
}
} // namespace chu_liu_edmonds_impl
template <typename T>
auto chu_liu_edmonds(graph<T> g, int r) {
std::vector<edge<T>> ret;
const int N = g.size();
graph<T> rg(N);
for (int i = 0; i < N; ++i) {
for (auto &e : g[i]) {
rg.add_edge(e.to, e.from, e.cost);
}
}
auto res = chu_liu_edmonds_impl::rec(rg, r);
for (int i = 0; i < N; ++i) {
if (i != r) {
std::vector<T> c;
for (auto &e : rg[i]) {
if (e.to == res[i][0].to) {
c.push_back(e.cost);
}
}
ret.emplace_back(res[i][0].to, i, *std::min_element(c.begin(), c.end()));
}
}
return ret;
}
} // namespace haar_lib
#line 2 "Mylib/Graph/MinimumSpanningTree/chu_liu_edmonds.cpp"
#include <algorithm>
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"
namespace haar_lib {
template <typename T>
struct edge {
int from, to;
T cost;
int index = -1;
edge() {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
};
template <typename T>
struct graph {
using weight_type = T;
using edge_type = edge<T>;
std::vector<std::vector<edge<T>>> data;
auto& operator[](size_t i) { return data[i]; }
const auto& operator[](size_t i) const { return data[i]; }
auto begin() const { return data.begin(); }
auto end() const { return data.end(); }
graph() {}
graph(int N) : data(N) {}
bool empty() const { return data.empty(); }
int size() const { return data.size(); }
void add_edge(int i, int j, T w, int index = -1) {
data[i].emplace_back(i, j, w, index);
}
void add_undirected(int i, int j, T w, int index = -1) {
add_edge(i, j, w, index);
add_edge(j, i, w, index);
}
template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
void read(int M) {
for (int i = 0; i < M; ++i) {
int u, v;
std::cin >> u >> v;
u -= I;
v -= I;
T w = 1;
if (WEIGHTED) std::cin >> w;
if (DIRECTED)
add_edge(u, v, w, i);
else
add_undirected(u, v, w, i);
}
}
};
template <typename T>
using tree = graph<T>;
} // namespace haar_lib
#line 5 "Mylib/Graph/GraphUtils/strongly_connected_components.cpp"
namespace haar_lib {
template <typename T>
auto strongly_connected_components(const graph<T> &g) {
const int n = g.size();
std::vector<int> ret(n), low(n, -1), ord(n, -1), S;
std::vector<bool> check(n);
S.reserve(n);
int t = 0;
int k = 0;
auto dfs =
[&](auto &dfs, int cur) -> void {
low[cur] = ord[cur] = t++;
S.push_back(cur);
check[cur] = true;
for (auto &e : g[cur]) {
if (ord[e.to] == -1) {
dfs(dfs, e.to);
low[cur] = std::min(low[cur], low[e.to]);
} else if (check[e.to]) {
low[cur] = std::min(low[cur], low[e.to]);
}
}
if (low[cur] == ord[cur]) {
while (true) {
int u = S.back();
S.pop_back();
check[u] = false;
ret[u] = k;
if (cur == u) break;
}
++k;
}
};
for (int i = 0; i < n; ++i) {
if (ord[i] == -1) {
t = 0;
dfs(dfs, i);
}
}
for (auto &x : ret) x = k - 1 - x;
return std::make_pair(ret, k);
}
} // namespace haar_lib
#line 6 "Mylib/Graph/MinimumSpanningTree/chu_liu_edmonds.cpp"
namespace haar_lib {
namespace chu_liu_edmonds_impl {
template <typename T>
graph<T> rec(graph<T> g, int r) {
const int N = g.size();
graph<T> in_edges(N);
for (int i = 0; i < N; ++i) {
if (i != r) {
auto e = *std::min_element(
g[i].begin(), g[i].end(),
[](const auto &a, const auto &b) {
return a.cost < b.cost;
});
in_edges[i].push_back(e);
}
}
const auto [s, m] = strongly_connected_components(in_edges);
std::vector<std::vector<int>> v(m);
for (int i = 0; i < N; ++i) {
v[s[i]].push_back(i);
}
int count_cycle = 0;
for (int i = 0; i < m; ++i) {
if (v[i].size() > 1) {
for (int j : v[i]) {
auto c =
*std::min_element(
g[j].begin(), g[j].end(),
[](const auto &a, const auto &b) { return a.cost < b.cost; });
for (auto &e : g[j]) {
e.cost -= c.cost;
}
}
++count_cycle;
}
}
if (count_cycle == 0) {
return in_edges;
}
graph<T> G(m);
const int R = s[r];
for (int i = 0; i < N; ++i) {
for (auto &e : g[i]) {
if (s[e.from] == s[e.to]) continue;
G.add_edge(s[e.from], s[e.to], e.cost);
}
}
auto res = rec(G, R);
for (int i = 0; i < m; ++i) {
if (i == R) continue;
int j = res[i][0].to;
std::vector<edge<T>> c;
for (int x : v[i]) {
for (auto &e : g[x]) {
if (s[e.to] == j) {
c.push_back(e);
}
}
}
auto e =
*std::min_element(
c.begin(), c.end(),
[](const auto &a, const auto &b) { return a.cost < b.cost; });
in_edges[e.from][0] = e;
}
return in_edges;
}
} // namespace chu_liu_edmonds_impl
template <typename T>
auto chu_liu_edmonds(graph<T> g, int r) {
std::vector<edge<T>> ret;
const int N = g.size();
graph<T> rg(N);
for (int i = 0; i < N; ++i) {
for (auto &e : g[i]) {
rg.add_edge(e.to, e.from, e.cost);
}
}
auto res = chu_liu_edmonds_impl::rec(rg, r);
for (int i = 0; i < N; ++i) {
if (i != r) {
std::vector<T> c;
for (auto &e : rg[i]) {
if (e.to == res[i][0].to) {
c.push_back(e.cost);
}
}
ret.emplace_back(res[i][0].to, i, *std::min_element(c.begin(), c.end()));
}
}
return ret;
}
} // namespace haar_lib
Chu-Liu/Edmonds algorithm
Basic graph
(Mylib/Graph/Template/graph.cpp)