From d7f3dafa12613fddcddbc5e9beb4188e8a6f7993 Mon Sep 17 00:00:00 2001
From: subcrip <contact@subc.rip>
Date: Wed, 20 Nov 2024 14:47:57 +0000
Subject: [PATCH] Add graph/ebcc.cc

Signed-off-by: subcrip <contact@subc.rip>
---
 graph/ebcc.cc | 98 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 98 insertions(+)
 create mode 100644 graph/ebcc.cc

diff --git a/graph/ebcc.cc b/graph/ebcc.cc
new file mode 100644
index 0000000..0cc6480
--- /dev/null
+++ b/graph/ebcc.cc
@@ -0,0 +1,98 @@
+// WARN: Input should be a simple graph
+//
+// Returns: (BCC count, indices of BCC of each vertex)
+//
+// BCC index starts from 1
+pair<int, vector<int>> ebcc(const vector<vector<int>>& ch) {
+    int n = ch.size() - 1;
+    vector<int> c(n + 1);
+
+    vector<int> low(n + 1), dfn(n + 1);
+    vector<bool> vis(n + 1);
+    vector<int> stack;
+
+    int time = 0;
+    int cnt = 0;
+
+    auto dfs = [&] (auto dfs, int v, int pa) -> void {
+        low[v] = dfn[v] = ++time;
+        stack.emplace_back(v);
+        vis[v] = 1;
+        for (auto&& u : ch[v]) {
+            if (u == pa) continue;
+            if (not dfn[u]) {
+                dfs(dfs, u, v);
+                chmin(low[v], low[u]);
+            } else if (vis[u]) {
+                chmin(low[v], dfn[u]);
+            }
+        }
+        if (dfn[v] == low[v]) {
+            cnt += 1;
+            c[v] = cnt;
+            while (stack.back() != v) {
+                c[stack.back()] = cnt;
+                vis[stack.back()] = 0;
+                stack.pop_back();
+            }
+            stack.pop_back();
+        }
+    };
+
+    for (int i = 1; i <= n; ++i) {
+        if (not dfn[i]) {
+            dfs(dfs, i, 0);
+        }
+    }
+    return { cnt, c };
+}
+
+
+// INFO: This function treats vertex pairs that have multiple edges as eBCCs.
+//
+// Returns: (BCC count, indices of BCC of each vertex)
+//
+// BCC index starts from 1
+pair<int, vector<int>> ebcc_with_mult(const vector<vector<pii>>& ch) {
+    int n = ch.size() - 1;
+    vector<int> c(n + 1);
+
+    vector<int> low(n + 1), dfn(n + 1);
+    vector<bool> vis(n + 1);
+    vector<int> stack;
+
+    int time = 0;
+    int cnt = 0;
+
+    auto dfs = [&] (auto dfs, int v, int prev_idx) -> void {
+        low[v] = dfn[v] = ++time;
+        stack.emplace_back(v);
+        vis[v] = 1;
+        for (auto&& [u, i] : ch[v]) {
+            if (i == prev_idx) continue;
+            if (not dfn[u]) {
+                dfs(dfs, u, i);
+                chmin(low[v], low[u]);
+            } else if (vis[u]) {
+                chmin(low[v], dfn[u]);
+            }
+        }
+        if (dfn[v] == low[v]) {
+            cnt += 1;
+            c[v] = cnt;
+            while (stack.back() != v) {
+                c[stack.back()] = cnt;
+                vis[stack.back()] = 0;
+                stack.pop_back();
+            }
+            stack.pop_back();
+        }
+    };
+
+    for (int i = 1; i <= n; ++i) {
+        if (not dfn[i]) {
+            dfs(dfs, i, -1);
+        }
+    }
+    return { cnt, c };
+}