graph/2CC.h

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• Last update: 2025-11-28 15:36:49+07:00

Verified with

• tests/Biconnected_Components.test.cpp
• tests/Two_Edges_CC.test.cpp

Code

struct BCC {
  const vector<vi>& g;
  int n, ti = 0;
  vector<vi> tree, blks;
  vi tin, low, st;
  void dfs(int u, int p = -1) {
    tin[u] = low[u] = ++ti;
    st.pb(u);
    for (int v : g[u]) if (v != p) {
      if (tin[v]) low[u] = min(low[u], tin[v]);
      else {
        dfs(v, u);
        low[u] = min(low[u], low[v]);
        if (low[v] >= tin[u]) {
          blks.pb({u});
          for (int x = -1; x != v; st.pop_back()) blks.back().pb(x = st.back());
        }
      }
    }
  }
  BCC(const vector<vi>& G) : g(G), n(sz(G)), tin(n), low(n) {
    for (int i = 0; i < n; ++i) if (!tin[i]) {
      dfs(i);
      if (g[i].empty()) blks.pb({i});
    }
    tree.assign(n + sz(blks), {});
    for (int i = 0; i < sz(blks); ++i) {
      int bid = n + i;
      for (int u : blks[i]) tree[bid].pb(u), tree[u].pb(bid);
    }
  }
};

struct ECC {
  const vector<vi>& g;
  int n, ti = 0;
  vector<vi> tree, comps;
  vi tin, low, id, st;
  void dfs(int u, int p = -1) {
    tin[u] = low[u] = ++ti;
    st.pb(u);
    bool skipped = false; // Fix multiple edges
    for (int v : g[u]) {
      if (v == p && !skipped) { skipped = true; continue; }
      if (tin[v]) low[u] = min(low[u], tin[v]);
      else {
        dfs(v, u);
        low[u] = min(low[u], low[v]);
      }
    }
    if (low[u] == tin[u]) { // Component root
      comps.pb({});
      for (int x = -1; x != u; st.pop_back()) {
        id[x = st.back()] = sz(comps) - 1;
        comps.back().pb(x);
      }
    }
  }
  ECC(const vector<vi>& G) : g(G), n(sz(G)), tin(n), low(n), id(n) {
    for (int i = 0; i < n; ++i) if (!tin[i]) dfs(i);
    tree.assign(sz(comps), {});
    for (int u = 0; u < n; ++u) for (int v : g[u])
      if (id[u] != id[v]) tree[id[u]].pb(id[v]);
    for (auto& adj : tree) {
      sort(all(adj)); adj.erase(unique(all(adj)), adj.end());
    }
  }
};

#line 1 "graph/2CC.h"
struct BCC {
  const vector<vi>& g;
  int n, ti = 0;
  vector<vi> tree, blks;
  vi tin, low, st;
  void dfs(int u, int p = -1) {
    tin[u] = low[u] = ++ti;
    st.pb(u);
    for (int v : g[u]) if (v != p) {
      if (tin[v]) low[u] = min(low[u], tin[v]);
      else {
        dfs(v, u);
        low[u] = min(low[u], low[v]);
        if (low[v] >= tin[u]) {
          blks.pb({u});
          for (int x = -1; x != v; st.pop_back()) blks.back().pb(x = st.back());
        }
      }
    }
  }
  BCC(const vector<vi>& G) : g(G), n(sz(G)), tin(n), low(n) {
    for (int i = 0; i < n; ++i) if (!tin[i]) {
      dfs(i);
      if (g[i].empty()) blks.pb({i});
    }
    tree.assign(n + sz(blks), {});
    for (int i = 0; i < sz(blks); ++i) {
      int bid = n + i;
      for (int u : blks[i]) tree[bid].pb(u), tree[u].pb(bid);
    }
  }
};

struct ECC {
  const vector<vi>& g;
  int n, ti = 0;
  vector<vi> tree, comps;
  vi tin, low, id, st;
  void dfs(int u, int p = -1) {
    tin[u] = low[u] = ++ti;
    st.pb(u);
    bool skipped = false; // Fix multiple edges
    for (int v : g[u]) {
      if (v == p && !skipped) { skipped = true; continue; }
      if (tin[v]) low[u] = min(low[u], tin[v]);
      else {
        dfs(v, u);
        low[u] = min(low[u], low[v]);
      }
    }
    if (low[u] == tin[u]) { // Component root
      comps.pb({});
      for (int x = -1; x != u; st.pop_back()) {
        id[x = st.back()] = sz(comps) - 1;
        comps.back().pb(x);
      }
    }
  }
  ECC(const vector<vi>& G) : g(G), n(sz(G)), tin(n), low(n), id(n) {
    for (int i = 0; i < n; ++i) if (!tin[i]) dfs(i);
    tree.assign(sz(comps), {});
    for (int u = 0; u < n; ++u) for (int v : g[u])
      if (id[u] != id[v]) tree[id[u]].pb(id[v]);
    for (auto& adj : tree) {
      sort(all(adj)); adj.erase(unique(all(adj)), adj.end());
    }
  }
};

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