feat: Implement StrongConnectedComponents class and add test case

Author: weilycoder

test/strongly_connected_components.test.cpp

@@ -0,0 +1,31 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/scc"
+
+#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;
+
+  StrongConnectedComponents 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.sccs.size() << '\n';
+  for (const auto &ecc : graph.sccs) {
+    cout << ecc.size();
+    for (size_t u : ecc)
+      cout << ' ' << u;
+    cout << '\n';
+  }
+  return 0;
+}

weilycoder/graph/tarjan.hpp

@@ -1,6 +1,7 @@
 #ifndef WEILYCODER_TARJAN_HPP
 #define WEILYCODER_TARJAN_HPP
 
+#include <algorithm>
 #include <cstddef>
 #include <stack>
 #include <utility>
@@ -56,6 +57,51 @@ template <typename ptr_t = size_t> struct TwoEdgeConnectedComponents {
         tarjan(i, 0);
   }
 };
+
+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;
+
+  StrongConnectedComponents(ptr_t n)
+      : in_stack(n, false), dfn(n, 0), low(n, 0), graph(n) {}
+
+  void add_edge(ptr_t u, ptr_t v) { graph[u].push_back(v); }
+
+  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();
+    }
+  }
+
+  void solve() {
+    for (size_t i = 0; i < graph.size(); ++i)
+      if (!dfn[i])
+        tarjan(i);
+    std::reverse(sccs.begin(), sccs.end());
+  }
+};
 } // namespace weilycoder
 
 #endif