cp-library
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test/two_edge_connected_components.test.cpp
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- Last update: 2025-11-07 09:14:02+08:00
- Problem: https://judge.yosupo.jp/problem/two_edge_connected_components
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Code
#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"
#include "../weilycoder/graph/tarjan.hpp"
#include <iostream>
using namespace std;
using namespace weilycoder;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin.exceptions(cin.failbit | cin.badbit);
size_t n, m;
cin >> n >> m;
TwoEdgeConnectedComponents graph(n);
for (size_t i = 0; i < m; ++i) {
size_t u, v;
cin >> u >> v;
graph.add_edge(u, v);
}
graph.solve();
cout << graph.eccs.size() << '\n';
for (const auto &ecc : graph.eccs) {
cout << ecc.size();
for (size_t u : ecc)
cout << ' ' << u;
cout << '\n';
}
return 0;
}#line 1 "test/two_edge_connected_components.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"
#line 1 "weilycoder/graph/tarjan.hpp"
/**
* @file tarjan.hpp
* @brief Tarjan's Algorithm for Graph Connected Problems
*/
#include <algorithm>
#include <cstddef>
#include <stack>
#include <utility>
#include <vector>
namespace weilycoder {
/**
* @brief Strongly Connected Components using Tarjan's Algorithm
* @tparam ptr_t Type for representing indices (default: size_t)
*/
template <typename ptr_t = size_t> struct StrongConnectedComponents {
ptr_t dfs_time = 0;
std::vector<bool> in_stack;
std::stack<ptr_t> stk;
std::vector<ptr_t> dfn, low;
std::vector<std::vector<ptr_t>> graph;
std::vector<std::vector<ptr_t>> sccs;
/**
* @brief Constructs a StrongConnectedComponents for n nodes
* @param n Number of nodes
*/
StrongConnectedComponents(ptr_t n)
: in_stack(n, false), dfn(n, 0), low(n, 0), graph(n) {}
/**
* @brief Adds a directed edge from u to v
* @param u Source node
* @param v Destination node
*/
void add_edge(ptr_t u, ptr_t v) { graph[u].push_back(v); }
/**
* @brief Tarjan's DFS to find SCCs
* @param u Current node
*/
void tarjan(ptr_t u) {
dfn[u] = low[u] = ++dfs_time;
stk.push(u), in_stack[u] = true;
for (const auto &v : graph[u]) {
if (!dfn[v])
tarjan(v), low[u] = std::min(low[u], low[v]);
else if (in_stack[v])
low[u] = std::min(low[u], dfn[v]);
}
if (dfn[u] == low[u]) {
sccs.emplace_back();
sccs.back().push_back(u);
in_stack[u] = false;
while (stk.top() != u)
sccs.back().push_back(stk.top()), in_stack[stk.top()] = false,
stk.pop();
stk.pop();
}
}
/**
* @brief Solves for all SCCs in the graph, sorting them in DFS order,
* i.e., if there is an edge from SCC A to SCC B, then A appears before B
*/
void solve() {
for (size_t i = 0; i < graph.size(); ++i)
if (!dfn[i])
tarjan(i);
std::reverse(sccs.begin(), sccs.end());
}
};
/**
* @brief Two-Edge Connected Components using Tarjan's Algorithm
* @tparam ptr_t Type for representing indices (default: size_t)
*/
template <typename ptr_t = size_t> struct TwoEdgeConnectedComponents {
ptr_t dfs_time = 0, edge_time = 1;
std::vector<bool> in_stack;
std::stack<ptr_t> stk;
std::vector<ptr_t> dfn, low;
std::vector<std::vector<std::pair<ptr_t, ptr_t>>> graph;
std::vector<std::vector<ptr_t>> eccs;
/**
* @brief Constructs a TwoEdgeConnectedComponents for n nodes
* @param n Number of nodes
*/
TwoEdgeConnectedComponents(ptr_t n)
: in_stack(n, false), dfn(n, 0), low(n, 0), graph(n) {}
/**
* @brief Adds an undirected edge between u and v
* @param u One endpoint
* @param v Other endpoint
*/
void add_edge(ptr_t u, ptr_t v) {
graph[u].emplace_back(v, edge_time);
graph[v].emplace_back(u, edge_time);
edge_time++;
}
/**
* @brief Tarjan's DFS to find 2-edge connected components
* @param u Current node
* @param parent_edge Edge ID of the edge leading to u
*/
void tarjan(ptr_t u, ptr_t parent_edge) {
dfn[u] = low[u] = ++dfs_time;
stk.push(u), in_stack[u] = true;
for (const auto &[v, edge_id] : graph[u]) {
if (edge_id == parent_edge)
continue;
if (!dfn[v])
tarjan(v, edge_id), low[u] = std::min(low[u], low[v]);
else if (in_stack[v])
low[u] = std::min(low[u], dfn[v]);
}
if (dfn[u] == low[u]) {
eccs.emplace_back();
eccs.back().push_back(u);
in_stack[u] = false;
while (stk.top() != u)
eccs.back().push_back(stk.top()), in_stack[stk.top()] = false,
stk.pop();
stk.pop();
}
}
/**
* @brief Solves for all 2-edge connected components in the graph
*/
void solve() {
for (size_t i = 0; i < graph.size(); ++i)
if (!dfn[i])
tarjan(i, 0);
}
};
/**
* @brief Biconnected Components using Tarjan's Algorithm
* @tparam ptr_t Type for representing indices (default: size_t)
*/
template <typename ptr_t = size_t> struct BiconnectedComponents {
ptr_t dfs_time = 0;
std::stack<ptr_t> stk;
std::vector<ptr_t> dfn, low;
std::vector<std::vector<ptr_t>> graph;
std::vector<bool> is_cut;
std::vector<std::vector<ptr_t>> dccs;
/**
* @brief Constructs a BiconnectedComponents for n nodes
* @param n Number of nodes
*/
BiconnectedComponents(ptr_t n)
: dfn(n, 0), low(n, 0), graph(n), is_cut(n, false) {}
/**
* @brief Adds an undirected edge between u and v
* @param u One endpoint
* @param v Other endpoint
*/
void add_edge(ptr_t u, ptr_t v) {
graph[u].push_back(v);
graph[v].push_back(u);
}
/**
* @brief Tarjan's DFS to find biconnected components
* @param u Current node
* @param is_root Whether u is the root of the DFS tree
*/
void tarjan(ptr_t u, bool is_root) {
dfn[u] = low[u] = ++dfs_time, stk.push(u);
if (is_root && graph[u].empty()) {
dccs.emplace_back();
dccs.back().push_back(u);
return;
}
ptr_t child = 0;
for (const auto &v : graph[u]) {
if (!dfn[v]) {
tarjan(v, false), low[u] = std::min(low[u], low[v]);
if (low[v] >= dfn[u]) {
if (++child > 1 || !is_root)
is_cut[u] = true;
dccs.emplace_back();
do
dccs.back().push_back(stk.top()), stk.pop();
while (dccs.back().back() != v);
dccs.back().push_back(u);
}
} else
low[u] = std::min(low[u], dfn[v]);
}
}
/**
* @brief Solves for all biconnected components in the graph
*/
void solve() {
for (size_t i = 0; i < graph.size(); ++i)
if (!dfn[i])
tarjan(i, true);
}
};
} // namespace weilycoder
#line 4 "test/two_edge_connected_components.test.cpp"
#include <iostream>
using namespace std;
using namespace weilycoder;
int main() {
cin.tie(nullptr)->sync_with_stdio(false);
cin.exceptions(cin.failbit | cin.badbit);
size_t n, m;
cin >> n >> m;
TwoEdgeConnectedComponents graph(n);
for (size_t i = 0; i < m; ++i) {
size_t u, v;
cin >> u >> v;
graph.add_edge(u, v);
}
graph.solve();
cout << graph.eccs.size() << '\n';
for (const auto &ecc : graph.eccs) {
cout << ecc.size();
for (size_t u : ecc)
cout << ' ' << u;
cout << '\n';
}
return 0;
}