update bridges

Author: lrvideckis

library/graphs/bridges_cuts/bridge_tree.hpp

@@ -11,11 +11,11 @@
 //! @time O(n + m)
 //! @space O(n)
 template<class G>
-vector<vi> bridge_tree(const G& adj,
-  const bridges<G>& br) {
-  vector<vi> tree(br.num_ccs);
+vector<vi> bridge_tree(const G& adj, int num_ccs,
+  const vi& br_id, const vi& is_br) {
+  vector<vi> tree(num_ccs);
   rep(i, 0, sz(adj)) for (auto [u, e_id] : adj[i]) if (
-    br.is_bridge[e_id]) tree[br.br_id[i]]
-    .push_back(br.br_id[u]);
+    is_br[e_id]) tree[br_id[i]]
+    .push_back(br_id[u]);
   return tree;
 }

library/graphs/bridges_cuts/bridges.hpp

@@ -9,39 +9,36 @@
 //!     adj[u].emplace_back(v, i);
 //!     adj[v].emplace_back(u, i);
 //!   }
-//!   auto [num_ccs, is_bridge, br_id] = bridges(adj, m);
+//!   auto [num_ccs, is_br, br_id] = bridges(adj, m);
 //!   vector<basic_string<array<int,2>>> adj1(n);
 //!   auto [num_ccs1, is_bridge1, br_id1] = bridges(adj1,
 //!   m);
 //! @endcode
-//! is_bridge[edge id] = 1 iff bridge edge
+//! is_br[edge id] = 1 iff bridge edge
 //! br_id[v] = id, 0<=id<num_ccs
 //! @time O(n + m)
 //! @space O(n + m)
-template<class G> struct bridges {
-  int num_ccs = 0;
-  vector<bool> is_bridge;
-  vi br_id;
-  bridges(const G& adj, int m):
-    is_bridge(m), br_id(sz(adj), -1) {
-    int n = sz(adj), timer = 1;
-    vi 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) continue;
+template<class G>
+tuple<int, vi, vi> bridges(const G& 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) {
+        // TODO golf this
         if (!tin[u]) low = min(low, self(self, u, e_id));
         low = min(low, tin[u]);
       }
-      if (tin[v] == low) {
-        if (p_id != -1) is_bridge[p_id] = 1;
-        rep(i, siz, sz(st)) br_id[st[i]] = num_ccs;
-        st.resize(siz);
-        num_ccs++;
-      }
-      return low;
-    };
-    rep(i, 0, n) if (!tin[i]) dfs(dfs, i, -1);
-  }
-};
+    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);
+      num_ccs++;
+    }
+    return low;
+  };
+  rep(i, 0, n) if (!tin[i]) dfs(dfs, i, -1);
+  return {num_ccs, br_id, is_br};
+}

tests/library_checker_aizu_tests/graphs/two_edge_components.test.cpp

@@ -16,54 +16,52 @@ int main() {
     adj[v].emplace_back(u, i);
     edges[i] = {u, v};
   }
-  bridges br(adj, m);
-  vector<vector<int>> bt = bridge_tree(adj, br);
-  assert(find(begin(br.br_id), end(br.br_id), -1) ==
-    end(br.br_id));
+  auto [num_ccs, br_id, is_br] = bridges(adj, m);
+  vector<vector<int>> bt =
+    bridge_tree(adj, num_ccs, br_id, is_br);
+  assert(find(begin(br_id), end(br_id), -1) == end(br_id));
   // check correctness of bridge tree
   {
-    assert(sz(bt) == br.num_ccs);
-    for (int v = 0; v < br.num_ccs; v++)
+    assert(sz(bt) == num_ccs);
+    for (int v = 0; v < num_ccs; v++)
       for (auto to : bt[v])
         assert(to != v); // didn't add any non-bridge
     int sum_deg = accumulate(begin(bt), end(bt), 0,
       [](int sum, const auto& neighbors) -> int {
         return sum + sz(neighbors);
       });
-    int cnt_bridges = accumulate(begin(br.is_bridge),
-      end(br.is_bridge), 0);
+    int cnt_bridges =
+      accumulate(begin(is_br), end(is_br), 0);
     assert(sum_deg % 2 == 0 && sum_deg / 2 == cnt_bridges);
   }
   dsu_restorable dsu(n);
   int num_sets_dsu = n;
   for (int i = 0; i < m; i++) {
-    if (!br.is_bridge[i]) {
+    if (!is_br[i]) {
       auto [u, v] = edges[i];
       num_sets_dsu -= dsu.join(u, v);
     }
   }
   assert(num_sets_dsu == sz(bt));
   for (int i = 0; i < m; i++) {
-    if (br.is_bridge[i]) {
+    if (is_br[i]) {
       auto [u, v] = edges[i];
       bool same_set = dsu.same_set(u, v);
       assert(!same_set);
     }
   }
   for (int i = 0; i < n; i++) {
     int par_of_cc = dsu.find(i);
-    assert(br.br_id[i] == br.br_id[par_of_cc]);
+    assert(br_id[i] == br_id[par_of_cc]);
   }
   for (int i = 0; i < m; i++) {
     auto [u, v] = edges[i];
     // bridge if nodes are from different 2-edge CCs
-    assert(
-      br.is_bridge[i] == (br.br_id[u] != br.br_id[v]));
+    assert(is_br[i] == (br_id[u] != br_id[v]));
   }
-  vector<vector<int>> ccs(br.num_ccs);
-  for (int i = 0; i < n; i++)
-    ccs[br.br_id[i]].push_back(i);
-  cout << br.num_ccs << '\n';
+  vector<vector<int>> ccs(num_ccs);
+  for (int i = 0; i < n; i++) ccs[br_id[i]].push_back(i);
+  cout << num_ccs << '\n';
   for (const auto& curr_cc : ccs) {
     cout << sz(curr_cc) << " ";
     for (auto node : curr_cc) cout << node << " ";