add cuts with callback

Author: lrvideckis

library/graphs/bridges_cuts/cuts_callback.hpp

@@ -0,0 +1,61 @@
+#pragma once
+//! https://cp-algorithms.com/graph/cutpoints.html
+//! @code
+//!   {
+//!     vector<vector<pii>> adj(n);
+//!     auto [num_bccs, bcc_id, is_cut] = cuts(adj, m);
+//!   }
+//!   vector<basic_string<array<int, 2>>> adj(n);
+//!   rep (i, 0, m) {
+//!     int u, v;
+//!     cin >> u >> v;
+//!     u--, v--;
+//!     //self edges not allowed
+//!     adj[u] += {v, i};
+//!     adj[v] += {u, i};
+//!   }
+//!   auto [num_bccs, bcc_id, is_cut] = cuts(adj, m);
+//! @endcode
+//! @time O(n + m)
+//! @space O(n + m)
+/*
+auto cuts(const auto& adj, int m) {
+  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 == 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++;
+      }
+    }
+    return low;
+  };
+  rep(i, 0, n) if (!tin[i]) dfs(dfs, i, -1);
+  return tuple{num_bccs, bcc_id, is_cut};
+}
+*/
+void cuts_callback(const auto& adj, auto f) {
+  int n = ssize(adj), q = 0, s = 0;
+  vector<int> tin(n), st(n);
+  auto dfs = [&](auto&& self, int v, int p) -> int {
+    int low = tin[v] = ++q;
+    for (int u : adj[v]) if (u != p) {
+      int siz = s, lu = 0;
+      low = min(low, tin[u] ?: (lu = self(self, st[s++] = u, v)));
+      if (lu >= tin[v]) {
+        f(v, vector<int>(begin(st) + siz, begin(st) + s));
+        s = siz;
+      }
+    }
+    return low;
+  };
+  for (int i = 0; i <n; i++) if (!tin[i]) dfs(dfs, i, i);
+}

tests/library_checker_aizu_tests/graphs/cuts_callback.test.cpp

@@ -0,0 +1,43 @@
+#define PROBLEM \
+  "https://judge.yosupo.jp/problem/biconnected_components"
+#include "../template.hpp"
+#include "../../../library/graphs/bridges_cuts/cuts_callback.hpp"
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  int n,m;
+  cin>>n>>m;
+  vector<basic_string<int>> adj(n);
+  for (int i = 0; i <n; i++) {
+    adj[i] += i;
+  }
+  for (int i = 0; i <m; i++) {
+    int u,v;
+    cin>>u>>v;
+    adj[u] += v;
+    adj[v] += u;
+  }
+  vector<bool> vis(n, 0);
+  vector<vector<int>> all_bccs;
+  cuts_callback(adj, [&](int v, const vi& nodes_bcc) {
+    vis[v] = 1;
+    for(int u : nodes_bcc){
+      vis[u] = 1;
+    }
+    all_bccs.push_back(nodes_bcc);
+    all_bccs.back().push_back(v);
+  });
+  for (int i = 0; i <n; i++) {
+    if(!vis[i]) {
+      all_bccs.push_back({i});
+    }
+  }
+  cout << ssize(all_bccs) << '\n';
+  for(const vector<int>& other_nodes : all_bccs) {
+    cout<<ssize(other_nodes)<<' ';
+    for(int v : other_nodes){
+      cout<<v<<' ';
+    }
+    cout<<'\n';
+  }
+  return 0;
+}