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‎index.md‎

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libraryCategories:
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- name: weilycoder/ds
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pages:
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- icon: ':heavy_check_mark:'
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path: weilycoder/ds/group.hpp
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title: Group Definitions
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- icon: ':heavy_check_mark:'
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path: weilycoder/ds/point_add_range_sum.hpp
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title: Point Add Range Sum using Fenwick Tree
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- icon: ':heavy_check_mark:'
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path: weilycoder/ds/static_range_sum.hpp
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title: weilycoder/ds/static_range_sum.hpp
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title: Static Range Sum using Prefix Sums
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- icon: ':heavy_check_mark:'
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path: weilycoder/ds/unionfind.hpp
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title: weilycoder/ds/unionfind.hpp
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title: Union-Find (Disjoint Set Union) Data Structure
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- name: weilycoder
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pages:
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- icon: ':heavy_check_mark:'
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path: weilycoder/fast-io.hpp
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title: weilycoder/fast-io.hpp
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title: Fast Input/Output Utilities
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- name: weilycoder/graph
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pages:
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- icon: ':heavy_check_mark:'
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path: weilycoder/graph/tarjan.hpp
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title: weilycoder/graph/tarjan.hpp
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title: Tarjan's Algorithm for Graph Connected Problems
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verificationCategories:
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- name: test
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pages:
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- icon: ':heavy_check_mark:'
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path: test/many_aplusb_128bit.test.cpp
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title: test/many_aplusb_128bit.test.cpp
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- icon: ':heavy_check_mark:'
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path: test/point_add_range_sum.test.cpp
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title: test/point_add_range_sum.test.cpp
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- icon: ':heavy_check_mark:'
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path: test/static_range_sum.test.cpp
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title: test/static_range_sum.test.cpp

‎test/aplusb.test.cpp.md‎

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‎test/biconnected_components.test.cpp.md‎

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_extendedDependsOn:
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- icon: ':heavy_check_mark:'
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path: weilycoder/graph/tarjan.hpp
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title: weilycoder/graph/tarjan.hpp
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title: Tarjan's Algorithm for Graph Connected Problems
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_extendedRequiredBy: []
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_extendedVerifiedWith: []
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_isVerificationFailed: false
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- https://judge.yosupo.jp/problem/biconnected_components
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bundledCode: "#line 1 \"test/biconnected_components.test.cpp\"\n#define PROBLEM\
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\ \"https://judge.yosupo.jp/problem/biconnected_components\"\n\n#line 1 \"weilycoder/graph/tarjan.hpp\"\
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\n\n\n\n#include <algorithm>\n#include <cstddef>\n#include <stack>\n#include <utility>\n\
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#include <vector>\n\nnamespace weilycoder {\ntemplate <typename ptr_t = size_t>\
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\ struct StrongConnectedComponents {\n ptr_t dfs_time = 0;\n\n std::vector<bool>\
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\n\n\n\n/**\n * @file tarjan.hpp\n * @brief Tarjan's Algorithm for Graph Connected\
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\ Problems\n */\n\n#include <algorithm>\n#include <cstddef>\n#include <stack>\n\
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#include <utility>\n#include <vector>\n\nnamespace weilycoder {\n/**\n * @brief\
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\ Strongly Connected Components using Tarjan's Algorithm\n * @tparam ptr_t Type\
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\ for representing indices (default: size_t)\n */\ntemplate <typename ptr_t =\
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\ size_t> struct StrongConnectedComponents {\n ptr_t dfs_time = 0;\n\n std::vector<bool>\
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\ in_stack;\n std::stack<ptr_t> stk;\n std::vector<ptr_t> dfn, low;\n std::vector<std::vector<ptr_t>>\
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\ graph;\n\n std::vector<std::vector<ptr_t>> sccs;\n\n StrongConnectedComponents(ptr_t\
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\ n)\n : in_stack(n, false), dfn(n, 0), low(n, 0), graph(n) {}\n\n void\
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\ add_edge(ptr_t u, ptr_t v) { graph[u].push_back(v); }\n\n void tarjan(ptr_t\
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\ graph;\n\n std::vector<std::vector<ptr_t>> sccs;\n\n /**\n * @brief Constructs\
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\ a StrongConnectedComponents for n nodes\n * @param n Number of nodes\n */\n\
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\ StrongConnectedComponents(ptr_t n)\n : in_stack(n, false), dfn(n, 0),\
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\ low(n, 0), graph(n) {}\n\n /**\n * @brief Adds a directed edge from u to\
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\ v\n * @param u Source node\n * @param v Destination node\n */\n void\
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\ add_edge(ptr_t u, ptr_t v) { graph[u].push_back(v); }\n\n /**\n * @brief\
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\ Tarjan's DFS to find SCCs\n * @param u Current node\n */\n void tarjan(ptr_t\
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\ u) {\n dfn[u] = low[u] = ++dfs_time;\n stk.push(u), in_stack[u] = true;\n\
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\n for (const auto &v : graph[u]) {\n if (!dfn[v])\n tarjan(v),\
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\ low[u] = std::min(low[u], low[v]);\n else if (in_stack[v])\n low[u]\
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\ = std::min(low[u], dfn[v]);\n }\n\n if (dfn[u] == low[u]) {\n sccs.emplace_back();\n\
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\ sccs.back().push_back(u);\n in_stack[u] = false;\n while (stk.top()\
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\ != u)\n sccs.back().push_back(stk.top()), in_stack[stk.top()] = false,\n\
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\ stk.pop();\n stk.pop();\n }\n\
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\ }\n\n void solve() {\n for (size_t i = 0; i < graph.size(); ++i)\n \
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\ if (!dfn[i])\n tarjan(i);\n std::reverse(sccs.begin(), sccs.end());\n\
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\ }\n};\n\ntemplate <typename ptr_t = size_t> struct TwoEdgeConnectedComponents\
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\ }\n\n /**\n * @brief Solves for all SCCs in the graph, sorting them in DFS\
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\ order,\n * i.e., if there is an edge from SCC A to SCC B, then A appears\
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\ before B\n */\n void solve() {\n for (size_t i = 0; i < graph.size();\
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\ ++i)\n if (!dfn[i])\n tarjan(i);\n std::reverse(sccs.begin(),\
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\ sccs.end());\n }\n};\n\n/**\n * @brief Two-Edge Connected Components using\
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\ Tarjan's Algorithm\n * @tparam ptr_t Type for representing indices (default:\
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\ size_t)\n */\ntemplate <typename ptr_t = size_t> struct TwoEdgeConnectedComponents\
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\ {\n ptr_t dfs_time = 0, edge_time = 1;\n\n std::vector<bool> in_stack;\n \
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\ std::stack<ptr_t> stk;\n std::vector<ptr_t> dfn, low;\n std::vector<std::vector<std::pair<ptr_t,\
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\ ptr_t>>> graph;\n\n std::vector<std::vector<ptr_t>> eccs;\n\n TwoEdgeConnectedComponents(ptr_t\
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\ n)\n : in_stack(n, false), dfn(n, 0), low(n, 0), graph(n) {}\n\n void\
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\ add_edge(ptr_t u, ptr_t v) {\n graph[u].emplace_back(v, edge_time);\n \
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\ graph[v].emplace_back(u, edge_time);\n edge_time++;\n }\n\n void tarjan(ptr_t\
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\ u, ptr_t parent_edge) {\n dfn[u] = low[u] = ++dfs_time;\n stk.push(u),\
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\ in_stack[u] = true;\n\n for (const auto &[v, edge_id] : graph[u]) {\n \
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\ if (edge_id == parent_edge)\n continue;\n if (!dfn[v])\n \
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\ tarjan(v, edge_id), low[u] = std::min(low[u], low[v]);\n else if (in_stack[v])\n\
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\ low[u] = std::min(low[u], dfn[v]);\n }\n\n if (dfn[u] == low[u])\
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\ {\n eccs.emplace_back();\n eccs.back().push_back(u);\n in_stack[u]\
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\ = false;\n while (stk.top() != u)\n eccs.back().push_back(stk.top()),\
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\ ptr_t>>> graph;\n\n std::vector<std::vector<ptr_t>> eccs;\n\n /**\n * @brief\
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\ Constructs a TwoEdgeConnectedComponents for n nodes\n * @param n Number of\
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\ nodes\n */\n TwoEdgeConnectedComponents(ptr_t n)\n : in_stack(n, false),\
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\ dfn(n, 0), low(n, 0), graph(n) {}\n\n /**\n * @brief Adds an undirected edge\
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\ between u and v\n * @param u One endpoint\n * @param v Other endpoint\n\
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\ */\n void add_edge(ptr_t u, ptr_t v) {\n graph[u].emplace_back(v, edge_time);\n\
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\ graph[v].emplace_back(u, edge_time);\n edge_time++;\n }\n\n /**\n \
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\ * @brief Tarjan's DFS to find 2-edge connected components\n * @param u Current\
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\ node\n * @param parent_edge Edge ID of the edge leading to u\n */\n void\
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\ tarjan(ptr_t u, ptr_t parent_edge) {\n dfn[u] = low[u] = ++dfs_time;\n \
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\ stk.push(u), in_stack[u] = true;\n\n for (const auto &[v, edge_id] : graph[u])\
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\ {\n if (edge_id == parent_edge)\n continue;\n if (!dfn[v])\n\
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\ tarjan(v, edge_id), low[u] = std::min(low[u], low[v]);\n else if\
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\ (in_stack[v])\n low[u] = std::min(low[u], dfn[v]);\n }\n\n if (dfn[u]\
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\ == low[u]) {\n eccs.emplace_back();\n eccs.back().push_back(u);\n\
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\ in_stack[u] = false;\n while (stk.top() != u)\n eccs.back().push_back(stk.top()),\
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\ in_stack[stk.top()] = false,\n stk.pop();\n\
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\ stk.pop();\n }\n }\n\n void solve() {\n for (size_t i = 0; i <\
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\ graph.size(); ++i)\n if (!dfn[i])\n tarjan(i, 0);\n }\n};\n\ntemplate\
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\ <typename ptr_t = size_t> struct BiconnectedComponents {\n ptr_t dfs_time =\
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\ 0;\n\n std::stack<ptr_t> stk;\n std::vector<ptr_t> dfn, low;\n std::vector<std::vector<ptr_t>>\
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\ graph;\n\n std::vector<bool> is_cut;\n std::vector<std::vector<ptr_t>> dccs;\n\
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\n BiconnectedComponents(ptr_t n)\n : dfn(n, 0), low(n, 0), graph(n), is_cut(n,\
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\ false) {}\n\n void add_edge(ptr_t u, ptr_t v) {\n graph[u].push_back(v);\n\
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\ graph[v].push_back(u);\n }\n\n void tarjan(ptr_t u, bool is_root) {\n \
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\ dfn[u] = low[u] = ++dfs_time, stk.push(u);\n\n if (is_root && graph[u].empty())\
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\ {\n dccs.emplace_back();\n dccs.back().push_back(u);\n return;\n\
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\ }\n\n ptr_t child = 0;\n for (const auto &v : graph[u]) {\n if\
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\ (!dfn[v]) {\n tarjan(v, false), low[u] = std::min(low[u], low[v]);\n\
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\ if (low[v] >= dfn[u]) {\n if (++child > 1 || !is_root)\n \
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\ is_cut[u] = true;\n dccs.emplace_back();\n do\n \
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\ dccs.back().push_back(stk.top()), stk.pop();\n while (dccs.back().back()\
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\ != v);\n dccs.back().push_back(u);\n }\n } else\n \
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\ low[u] = std::min(low[u], dfn[v]);\n }\n }\n\n void solve() {\n for\
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\ (size_t i = 0; i < graph.size(); ++i)\n if (!dfn[i])\n tarjan(i,\
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\ true);\n }\n};\n} // namespace weilycoder\n\n\n#line 4 \"test/biconnected_components.test.cpp\"\
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\n#include <iostream>\nusing namespace std;\nusing namespace weilycoder;\n\nint\
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\ main() {\n cin.tie(nullptr)->sync_with_stdio(false);\n cin.exceptions(cin.failbit\
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\ | cin.badbit);\n size_t n, m;\n cin >> n >> m;\n\n BiconnectedComponents\
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\ graph(n);\n for (size_t i = 0; i < m; ++i) {\n size_t u, v;\n cin >>\
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\ u >> v;\n graph.add_edge(u, v);\n }\n\n graph.solve();\n\n cout << graph.dccs.size()\
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\ << '\\n';\n for (const auto &dcc : graph.dccs) {\n cout << dcc.size();\n\
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\ for (size_t u : dcc)\n cout << ' ' << u;\n cout << '\\n';\n }\n\
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\ return 0;\n}\n"
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\ stk.pop();\n }\n }\n\n /**\n * @brief Solves for all 2-edge connected\
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\ components in the graph\n */\n void solve() {\n for (size_t i = 0; i <\
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\ graph.size(); ++i)\n if (!dfn[i])\n tarjan(i, 0);\n }\n};\n\n/**\n\
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\ * @brief Biconnected Components using Tarjan's Algorithm\n * @tparam ptr_t Type\
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\ for representing indices (default: size_t)\n */\ntemplate <typename ptr_t =\
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\ size_t> struct BiconnectedComponents {\n ptr_t dfs_time = 0;\n\n std::stack<ptr_t>\
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\ stk;\n std::vector<ptr_t> dfn, low;\n std::vector<std::vector<ptr_t>> graph;\n\
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\n std::vector<bool> is_cut;\n std::vector<std::vector<ptr_t>> dccs;\n\n /**\n\
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\ * @brief Constructs a BiconnectedComponents for n nodes\n * @param n Number\
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\ of nodes\n */\n BiconnectedComponents(ptr_t n)\n : dfn(n, 0), low(n,\
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\ 0), graph(n), is_cut(n, false) {}\n\n /**\n * @brief Adds an undirected edge\
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\ between u and v\n * @param u One endpoint\n * @param v Other endpoint\n\
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\ */\n void add_edge(ptr_t u, ptr_t v) {\n graph[u].push_back(v);\n graph[v].push_back(u);\n\
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\ }\n\n /**\n * @brief Tarjan's DFS to find biconnected components\n * @param\
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\ u Current node\n * @param is_root Whether u is the root of the DFS tree\n\
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\ */\n void tarjan(ptr_t u, bool is_root) {\n dfn[u] = low[u] = ++dfs_time,\
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\ stk.push(u);\n\n if (is_root && graph[u].empty()) {\n dccs.emplace_back();\n\
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\ dccs.back().push_back(u);\n return;\n }\n\n ptr_t child = 0;\n\
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\ for (const auto &v : graph[u]) {\n if (!dfn[v]) {\n tarjan(v,\
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\ false), low[u] = std::min(low[u], low[v]);\n if (low[v] >= dfn[u]) {\n\
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\ if (++child > 1 || !is_root)\n is_cut[u] = true;\n \
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\ dccs.emplace_back();\n do\n dccs.back().push_back(stk.top()),\
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\ stk.pop();\n while (dccs.back().back() != v);\n dccs.back().push_back(u);\n\
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\ }\n } else\n low[u] = std::min(low[u], dfn[v]);\n }\n\
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\ }\n\n /**\n * @brief Solves for all biconnected components in the graph\n\
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\ */\n void solve() {\n for (size_t i = 0; i < graph.size(); ++i)\n \
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\ if (!dfn[i])\n tarjan(i, true);\n }\n};\n} // namespace weilycoder\n\
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\n\n#line 4 \"test/biconnected_components.test.cpp\"\n#include <iostream>\nusing\
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\ namespace std;\nusing namespace weilycoder;\n\nint main() {\n cin.tie(nullptr)->sync_with_stdio(false);\n\
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\ cin.exceptions(cin.failbit | cin.badbit);\n size_t n, m;\n cin >> n >> m;\n\
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\n BiconnectedComponents graph(n);\n for (size_t i = 0; i < m; ++i) {\n size_t\
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\ u, v;\n cin >> u >> v;\n graph.add_edge(u, v);\n }\n\n graph.solve();\n\
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\n cout << graph.dccs.size() << '\\n';\n for (const auto &dcc : graph.dccs)\
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\ {\n cout << dcc.size();\n for (size_t u : dcc)\n cout << ' ' << u;\n\
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\ cout << '\\n';\n }\n return 0;\n}\n"
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code: "#define PROBLEM \"https://judge.yosupo.jp/problem/biconnected_components\"\
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\n\n#include \"../weilycoder/graph/tarjan.hpp\"\n#include <iostream>\nusing namespace\
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\ std;\nusing namespace weilycoder;\n\nint main() {\n cin.tie(nullptr)->sync_with_stdio(false);\n\
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isVerificationFile: true
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path: test/biconnected_components.test.cpp
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requiredBy: []
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timestamp: '2025-10-29 23:28:06+08:00'
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timestamp: '2025-10-30 21:08:13+08:00'
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verificationStatus: TEST_ACCEPTED
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verifiedWith: []
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documentation_of: test/biconnected_components.test.cpp

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