From ed319a8f85e721f8cbc5c037bde8c30361377308 Mon Sep 17 00:00:00 2001
From: eemoreira <112673452+eemoreira@users.noreply.github.com>
Date: Thu, 29 Aug 2024 16:47:29 -0300
Subject: [PATCH] codigo da block cut tree (#166)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* codigo da block cut tree

* tinha esquecido do clang format

* Update Codigos/Grafos/Block-Cut-Tree/README.md

Co-authored-by: João Oliveira <70975757+joaomarcosth9@users.noreply.github.com>

---------

Co-authored-by: João Oliveira <70975757+joaomarcosth9@users.noreply.github.com>
---
 Codigos/Grafos/Block-Cut-Tree/README.md       |  8 +++
 .../Grafos/Block-Cut-Tree/block_cut_tree.cpp  | 65 +++++++++++++++++++
 2 files changed, 73 insertions(+)
 create mode 100644 Codigos/Grafos/Block-Cut-Tree/README.md
 create mode 100644 Codigos/Grafos/Block-Cut-Tree/block_cut_tree.cpp

diff --git a/Codigos/Grafos/Block-Cut-Tree/README.md b/Codigos/Grafos/Block-Cut-Tree/README.md
new file mode 100644
index 00000000..6c40a631
--- /dev/null
+++ b/Codigos/Grafos/Block-Cut-Tree/README.md
@@ -0,0 +1,8 @@
+# [Block Cut Tree](block_cut_tree.cpp)
+
+Algoritmo que separa o grafo em componentes biconexas em $\mathcal{O}(V + E)$.
+
+- `id[u]` é o index do nodo `u` na Block Cut Tree.
+- `is_articulation_point(u)` diz se o nodo `u` é ou não é um ponto de articulação.
+- `number_of_splits(u)` diz a quantidade de componentes conexas que o grafo
+    terá se o nodo `u` for removido.
diff --git a/Codigos/Grafos/Block-Cut-Tree/block_cut_tree.cpp b/Codigos/Grafos/Block-Cut-Tree/block_cut_tree.cpp
new file mode 100644
index 00000000..9a1d403a
--- /dev/null
+++ b/Codigos/Grafos/Block-Cut-Tree/block_cut_tree.cpp
@@ -0,0 +1,65 @@
+struct Bct {
+    int T;
+    vector<int> tin, low, stk, art, id, splits;
+    vector<vector<int>> adj, g, comp, up;
+    int n, sz, m;
+    void build(int _n, int _m) {
+        n = _n, m = _m;
+        adj.resize(n);
+    }
+    void add_edge(int u, int v) {
+        adj[u].emplace_back(v);
+        adj[v].emplace_back(u);
+    }
+    void dfs(int u, int p) {
+        low[u] = tin[u] = ++T;
+        stk.emplace_back(u);
+        for (auto v : adj[u]) {
+            if (tin[v] == -1) {
+                dfs(v, u);
+                low[u] = min(low[u], low[v]);
+                if (low[v] >= tin[u]) {
+                    int x;
+                    sz++;
+                    do {
+                        assert(stk.size());
+                        x = stk.back();
+                        stk.pop_back();
+                        comp[x].emplace_back(sz);
+                    } while (x != v);
+                    comp[u].emplace_back(sz);
+                }
+            } else if (v != p) {
+                low[u] = min(low[u], tin[v]);
+            }
+        }
+    }
+    inline bool is_articulation_point(int u) { return art[id[u]]; }
+    inline int number_of_splits(int u) { return splits[id[u]]; }
+    void work() {
+        T = sz = 0;
+        stk.clear();
+        tin.resize(n, -1);
+        comp.resize(n);
+        low.resize(n);
+        for (int i = 0; i < n; i++)
+            if (tin[i] == -1) dfs(i, 0);
+        art.resize(sz + n + 1);
+        splits.resize(n + sz + 1, 1);
+        id.resize(n);
+        g.resize(sz + n + 1);
+        for (int i = 0; i < n; i++) {
+            if ((int)comp[i].size() > 1) {
+                id[i] = ++sz;
+                art[id[i]] = 1;
+                splits[id[i]] = (int)comp[i].size();
+                for (auto u : comp[i]) {
+                    g[id[i]].emplace_back(u);
+                    g[u].emplace_back(id[i]);
+                }
+            } else if (comp[i].size()) {
+                id[i] = comp[i][0];
+            }
+        }
+    }
+};