Another scc golf (#123)

* golf

* [auto-verifier] verify commit 596f983

* golf

---------

Co-authored-by: GitHub <noreply@github.com>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -49,19 +49,18 @@
 "tests/library_checker_aizu_tests/flow/dinic_lib_checker.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/hungarian.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/min_cost_max_flow.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/graphs/biconnected_components.test.cpp": "2024-12-14 19:50:29 -0600",
+"tests/library_checker_aizu_tests/graphs/biconnected_components.test.cpp": "2024-12-15 08:00:27 -0600",
 "tests/library_checker_aizu_tests/graphs/connected_components_of_complement_graph.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/dijkstra_aizu.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/dijkstra_lib_checker.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/graphs/directed_cycle.test.cpp": "2024-12-15 06:41:10 -0600",
 "tests/library_checker_aizu_tests/graphs/enumerate_triangles.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_aizu.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/hopcroft_karp_lib_checker.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/mst.test.cpp": "2024-11-17 14:04:03 -0600",
-"tests/library_checker_aizu_tests/graphs/offline_incremental_scc.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/graphs/strongly_connected_components_aizu.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/graphs/strongly_connected_components_lib_checker.test.cpp": "2024-12-14 19:50:29 -0600",
-"tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp": "2024-12-14 19:50:29 -0600",
+"tests/library_checker_aizu_tests/graphs/offline_incremental_scc.test.cpp": "2024-12-15 08:00:27 -0600",
+"tests/library_checker_aizu_tests/graphs/strongly_connected_components_aizu.test.cpp": "2024-12-15 08:00:27 -0600",
+"tests/library_checker_aizu_tests/graphs/strongly_connected_components_lib_checker.test.cpp": "2024-12-15 08:00:27 -0600",
+"tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp": "2024-12-15 08:00:27 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/count_paths_forest.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/dsu_size.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/handmade_tests/dynamic_bitset.test.cpp": "2024-11-22 10:47:44 -0600",

library/graphs/bridges_cuts/bridges.hpp

@@ -20,18 +20,17 @@
 //! @time O(n + m)
 //! @space O(n + m)
 auto bridges(const auto& adj, int m) {
-  int n = sz(adj), num_ccs = 0, timer = 0;
-  vi br_id(n, -1), is_br(m), tin(n), st;
-  auto dfs = [&](auto&& self, int v, int p_id) -> int {
-    int low = tin[v] = ++timer, siz = sz(st);
-    st.push_back(v);
-    for (auto [u, e_id] : adj[v])
-      if (e_id != p_id && br_id[u] < 0)
-        low = min(low, tin[u] ?: self(self, u, e_id));
+  int n = sz(adj), num_ccs = 0, q = 0, s = 0;
+  vi br_id(n, -1), is_br(m), tin(n), st(n);
+  auto dfs = [&](auto&& self, int v, int p) -> int {
+    int low = tin[v] = ++q;
+    st[s++] = v;
+    for (auto [u, e] : adj[v])
+      if (e != p && br_id[u] < 0)
+        low = min(low, tin[u] ?: self(self, u, e));
     if (tin[v] == low) {
-      if (p_id != -1) is_br[p_id] = 1;
-      rep(i, siz, sz(st)) br_id[st[i]] = num_ccs;
-      st.resize(siz);
+      if (p != -1) is_br[p] = 1;
+      while (br_id[v] < 0) br_id[st[--s]] = num_ccs;
       num_ccs++;
     }
     return low;

library/graphs/bridges_cuts/cuts.hpp

@@ -21,31 +21,22 @@
 //! @time O(n + m)
 //! @space O(n + m)
 auto cuts(const auto& adj, int m) {
-  int n = sz(adj), num_bccs = 0, timer = 0;
-  vi bcc_id(m, -1), is_cut(n), tin(n), st;
-  auto dfs = [&](auto&& self, int v, int p_id) -> int {
-    int low = tin[v] = ++timer, deg = 0;
-    for (auto [u, e_id] : adj[v]) {
+  int n = sz(adj), num_bccs = 0, q = 0, s = 0;
+  vi bcc_id(m, -1), is_cut(n), tin(n), st(m);
+  auto dfs = [&](auto&& self, int v, int p) -> int {
+    int low = tin[v] = ++q;
+    for (auto [u, e] : adj[v]) {
       assert(v != u);
-      if (e_id == p_id) continue;
-      if (!tin[u]) {
-        int siz = sz(st);
-        st.push_back(e_id);
-        int low_ch = self(self, u, e_id);
-        if (low_ch >= tin[v]) {
-          is_cut[v] = 1;
-          rep(i, siz, sz(st)) bcc_id[st[i]] = num_bccs;
-          st.resize(siz);
-          num_bccs++;
-        }
-        low = min(low, low_ch);
-        deg++;
-      } else if (tin[u] < tin[v]) {
-        st.push_back(e_id);
-        low = min(low, tin[u]);
+      if (e == p) continue;
+      if (tin[u] < tin[v]) st[s++] = e;
+      int lu = -1;
+      low = min(low, tin[u] ?: (lu = self(self, u, e)));
+      if (lu >= tin[v]) {
+        is_cut[v] = p >= 0 || tin[v] + 1 < tin[u];
+        while (bcc_id[e] < 0) bcc_id[st[--s]] = num_bccs;
+        num_bccs++;
       }
     }
-    if (p_id == -1) is_cut[v] = (deg > 1);
     return low;
   };
   rep(i, 0, n) if (!tin[i]) dfs(dfs, i, -1);

library/graphs/strongly_connected_components/scc.hpp

@@ -13,17 +13,16 @@
 //! @time O(n + m)
 //! @space O(n)
 auto sccs(const auto& adj) {
-  int n = sz(adj), num_sccs = 0, timer = 0;
-  vi scc_id(n, -1), tin(n), st;
+  int n = sz(adj), num_sccs = 0, q = 0, s = 0;
+  vi scc_id(n, -1), tin(n), st(n);
   auto dfs = [&](auto&& self, int v) -> int {
-    int low = tin[v] = ++timer, siz = sz(st);
-    st.push_back(v);
+    int low = tin[v] = ++q;
+    st[s++] = v;
     for (int u : adj[v])
       if (scc_id[u] < 0)
         low = min(low, tin[u] ?: self(self, u));
     if (tin[v] == low) {
-      rep(i, siz, sz(st)) scc_id[st[i]] = num_sccs;
-      st.resize(siz);
+      while (scc_id[v] < 0) scc_id[st[--s]] = num_sccs;
       num_sccs++;
     }
     return low;