From ff4201b037c0e2a21761a87889ad96488ed14943 Mon Sep 17 00:00:00 2001
From: iagorrr04 <iagorrr04@gmail.com>
Date: Wed, 20 Dec 2023 21:16:19 -0300
Subject: [PATCH] :white_check_mark: graphs, bridges

---
 submissions/CSES/Necessary Roads.cpp | 108 +++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)
 create mode 100644 submissions/CSES/Necessary Roads.cpp

diff --git a/submissions/CSES/Necessary Roads.cpp b/submissions/CSES/Necessary Roads.cpp
new file mode 100644
index 00000000..9883a8d5
--- /dev/null
+++ b/submissions/CSES/Necessary Roads.cpp	
@@ -0,0 +1,108 @@
+#include <bits/stdc++.h>
+using namespace std;
+#ifdef LOCAL
+#include "debug.cpp"
+#else
+#define dbg(...) 42
+#endif
+#define endl '\n'
+#define fastio                      \
+  ios_base::sync_with_stdio(false); \
+  cin.tie(0);                       \
+  cout.tie(0);
+#define len(__x) (int)__x.size()
+using ll = long long;
+using ull = unsigned long long;
+using ld = long double;
+using vll = vector<ll>;
+using pll = pair<ll, ll>;
+using vll2d = vector<vll>;
+using vi = vector<int>;
+using vi2d = vector<vi>;
+using pii = pair<int, int>;
+using vii = vector<pii>;
+using vc = vector<char>;
+#define all(a) a.begin(), a.end()
+#define pb(___x) push_back(___x)
+#define mp(___a, ___b) make_pair(___a, ___b)
+#define eb(___x) emplace_back(___x)
+int lg2(ll x) {
+  return __builtin_clzll(1) - __builtin_clzll(x);
+}
+
+// vector<string> dir({"LU", "U", "RU", "R", "RD", "D",
+// "LD", "L"}); int dx[] = {-1, -1, -1, 0, 1, 1, 1, 0}; int
+// dy[] = {-1, 0, 1, 1, 1, 0, -1, -1};
+vector<string> dir({"U", "R", "D", "L"});
+int dx[] = {-1, 0, 1, 0};
+int dy[] = {0, 1, 0, -1};
+
+const ll oo = 1e18;
+int T(1);
+const int MAXN(1'000'000);
+
+int tin[MAXN], low[MAXN], timer, N;
+char vis[MAXN];
+vi2d G(MAXN);
+vector<pii> bridges;
+
+void dfs(int u, int p = -1) {
+  vis[u] = true;
+  tin[u] = low[u] = timer++;
+
+  for (auto v : G[u]) {
+    if (v == p) continue;
+    if (vis[v]) {
+      low[u] = min(low[u], tin[v]);
+    } else {
+      dfs(v, u);
+      low[u] = min(low[u], low[v]);
+      if (low[v] > tin[u]) {
+        bridges.emplace_back(u, v);
+      }
+    }
+  }
+}
+void findBridges() {
+  timer = 0;
+
+  memset(vis, 0, sizeof(vis));
+  memset(tin, -1, sizeof(tin));
+  memset(low, -1, sizeof(low));
+  bridges.clear();
+
+  for (int i = 0; i < N; i++) {
+    if (not vis[i]) dfs(i);
+  }
+}
+
+int M;
+
+auto solve() {
+  cin >> N >> M;
+  while (M--) {
+    int u, v;
+    cin >> u >> v;
+    u--, v--;
+    G[u].emplace_back(v);
+    G[v].emplace_back(u);
+  }
+
+  findBridges();
+  cout << len(bridges) << endl;
+  for (auto &[a, b] : bridges) {
+    cout << a + 1 << ' ' << b + 1 << endl;
+  }
+}
+
+int32_t main(void) {
+#ifndef LOCAL
+  fastio;
+#endif
+
+  // cin >> T;
+
+  for (int i = 1; i <= T; i++) {
+    solve();
+  }
+}