From 575e29874c84de1104663d03bcd888fbbf72c172 Mon Sep 17 00:00:00 2001
From: baluteshih <brian369999@gmail.com>
Date: Sat, 6 Apr 2024 21:26:50 +0800
Subject: [PATCH] Split SCC out from 2SAT

---
 codebook/2_Graph/2SAT.cpp | 46 ++++++++-------------------------------
 codebook/2_Graph/SCC.cpp  | 27 +++++++++++++++++++++++
 codebook/content.tex      |  4 +++-
 3 files changed, 39 insertions(+), 38 deletions(-)
 create mode 100644 codebook/2_Graph/SCC.cpp

diff --git a/codebook/2_Graph/2SAT.cpp b/codebook/2_Graph/2SAT.cpp
index c7a71c23..78a1e0fb 100644
--- a/codebook/2_Graph/2SAT.cpp
+++ b/codebook/2_Graph/2SAT.cpp
@@ -1,47 +1,19 @@
 struct SAT { // 0-base
-  int low[N], dfn[N], bln[N], n, Time, nScc;
-  bool instack[N], istrue[N];
-  stack<int> st;
-  vector<int> G[N], SCC[N];
-  void init(int _n) {
-    n = _n; // assert(n * 2 <= N);
-    for (int i = 0; i < n + n; ++i) G[i].clear();
-  }
-  void add_edge(int a, int b) { G[a].pb(b); }
+  int n;
+  vector<bool> istrue;
+  SCC scc;
+  SAT(int _n): n(_n), istrue(n + n), scc(n + n) {}
   int rv(int a) {
-    if (a >= n) return a - n;
-    return a + n;
+    return a >= n ? a - n : a + n;
   }
   void add_clause(int a, int b) {
-    add_edge(rv(a), b), add_edge(rv(b), a);
-  }
-  void dfs(int u) {
-    dfn[u] = low[u] = ++Time;
-    instack[u] = 1, st.push(u);
-    for (int i : G[u])
-      if (!dfn[i])
-        dfs(i), low[u] = min(low[i], low[u]);
-      else if (instack[i] && dfn[i] < dfn[u])
-        low[u] = min(low[u], dfn[i]);
-    if (low[u] == dfn[u]) {
-      int tmp;
-      do {
-        tmp = st.top(), st.pop();
-        instack[tmp] = 0, bln[tmp] = nScc;
-      } while (tmp != u);
-      ++nScc;
-    }
+    scc.add_edge(rv(a), b), scc.add_edge(rv(b), a);
   }
   bool solve() {
-    Time = nScc = 0;
-    for (int i = 0; i < n + n; ++i)
-      SCC[i].clear(), low[i] = dfn[i] = bln[i] = 0;
-    for (int i = 0; i < n + n; ++i)
-      if (!dfn[i]) dfs(i);
-    for (int i = 0; i < n + n; ++i) SCC[bln[i]].pb(i);
+    scc.solve();
     for (int i = 0; i < n; ++i) {
-      if (bln[i] == bln[i + n]) return false;
-      istrue[i] = bln[i] < bln[i + n];
+      if (scc.bln[i] == scc.bln[i + n]) return false;
+      istrue[i] = scc.bln[i] < scc.bln[i + n];
       istrue[i + n] = !istrue[i];
     }
     return true;
diff --git a/codebook/2_Graph/SCC.cpp b/codebook/2_Graph/SCC.cpp
new file mode 100644
index 00000000..ce472f08
--- /dev/null
+++ b/codebook/2_Graph/SCC.cpp
@@ -0,0 +1,27 @@
+struct SCC { // 0-base
+  int n, dft, nscc;
+  vector<int> low, dfn, bln, instack, stk;
+  vector<vector<int>> G;
+  void dfs(int u) {
+    low[u] = dfn[u] = ++dft;
+    instack[u] = 1, stk.pb(u);
+    for (int v : G[u])
+      if (!dfn[v])
+        dfs(v), low[u] = min(low[u], low[v]);
+      else if (instack[v] && dfn[v] < dfn[u])
+        low[u] = min(low[u], dfn[v]);
+    if (low[u] == dfn[u]) {
+      for (; stk.back() != u; stk.pop_back())
+        bln[stk.back()] = nscc, instack[stk.back()] = 0;
+      instack[u] = 0, bln[u] = nscc++, stk.pop_back();
+    }
+  }
+  SCC(int _n): n(_n), dft(), nscc(), low(n), dfn(n), bln(n), instack(n), G(n) {}
+  void add_edge(int u, int v) {
+    G[u].pb(v);
+  }
+  void solve() {
+    for (int i = 0; i < n; ++i)
+      if (!dfn[i]) dfs(i);
+  }
+}; // scc_id(i): bln[i]
diff --git a/codebook/content.tex b/codebook/content.tex
index c13f19f9..707f42a6 100644
--- a/codebook/content.tex
+++ b/codebook/content.tex
@@ -18,7 +18,9 @@ \subsection{BCC Vertex*} % test by Library Checker Biconnected Components, block
 \lstinputlisting{2_Graph/BCC_Vertex.cpp}
 \subsection{Bridge*} % test by Library Checker Two-Edge-Connected Components
 \lstinputlisting{2_Graph/Bridge.cpp}
-\subsection{2SAT (SCC)*} % SCC test by TIOJ 2143, 2SAT test by ARC069 F
+\subsection{SCC*} % SCC test by Library Checker Strongly Connected Components
+\lstinputlisting{2_Graph/SCC.cpp}
+\subsection{2SAT*} % test by ARC069 F
 \lstinputlisting{2_Graph/2SAT.cpp}
 \subsection{MinimumMeanCycle*} % test by TIOJ 1934
 \lstinputlisting{2_Graph/MinimumMeanCycle.cpp}