add: 桥

Author: nephrenn233

README.md

@@ -48,8 +48,9 @@
 + 树上差分 (Difference On Tree.cpp)
 + 连通性相关
     + 割点 (Tarjan1.cpp)
-    + 点双连通分量 (Tarjan2.cpp)
-    + 边双连通分量 (Tarjan3.cpp)
+    + 割边 (Tarjan2.cpp)
+    + 点双连通分量 (Tarjan3.cpp)
+    + 边双连通分量 (Tarjan4.cpp)
 
 ## 杂项 various
 

graph theory/Tarjan2.cpp

@@ -1,55 +1,14 @@
-int dfn[MAXN], low[MAXN], idx = 0;
-stack<int> st;
-vector<vector<int>> ans;
-
-void tarjan(int u, bool is_root) {
-    dfn[u] = low[u] = ++idx;
-    st.push(u);
-    if(is_root && g[u].size() == 0) {
-        vector<int> res;
-        res.push_back(u);
-        ans.push_back(res);
-        return;
-    }
-    for(auto v : g[u]) {
-        if(!dfn[v]) {
-            tarjan(v, 0);
-            low[u] = min(low[u], low[v]);
-            if(low[v] >= dfn[u]) {
-                vector<int> res;
-                int w;
-                do {
-                    w = st.top();
-                    st.pop();
-                    res.push_back(w);
-                }while(w != v);
-                res.push_back(u);
-                ans.push_back(res);
-            }
-        } else {
-            low[u] = min(low[u], dfn[v]);
-        }
-    }
-}
-
-void solve () {
-    cin >> n >> m;
-    for(int i = 1; i <= m; ++i) {
-        int u, v;
-        cin >> u >> v;
-        if(u == v) continue;
-        g[u].push_back(v);
-        g[v].push_back(u);
-    }
-
-    for(int i = 1; i <= n; ++i) {
-        if(!dfn[i]) tarjan(i, 1);
-    }
-
-    cout << ans.size() << "\n";
-    for(auto i : ans) {
-        cout << i.size() << " ";
-        for(auto j : i) cout << j << " ";
-        cout << "\n";
-    }
+void tarjan(int x, int in_edge) {
+	dfn[x] = low[x] = ++num;
+	for (int i = head[x]; i; i = Next[i]) {
+		int y = ver[i];
+		if (!dfn[y]) {
+			tarjan(y, i);
+			low[x] = min(low[x], low[y]);
+			if (low[y] > dfn[x])
+				bridge[i] = bridge[i ^ 1] = true;
+		}
+		else if (i != (in_edge ^ 1))
+			low[x] = min(low[x], dfn[y]);
+	}
 }

graph theory/Tarjan3.cpp

@@ -1,32 +1,35 @@
-int dfn[MAXN], low[MAXN], tt = 0;
+int dfn[MAXN], low[MAXN], idx = 0;
 stack<int> st;
-map<PII, bool> vis;
-
 vector<vector<int>> ans;
 
-void tarjan(int u, int f) {
-    dfn[u] = low[u] = ++tt;
+void tarjan(int u, bool is_root) {
+    dfn[u] = low[u] = ++idx;
     st.push(u);
-    for(auto [v, id] : g1[u]) {
-        if(id == (f ^ 1)) continue;
+    if(is_root && g[u].size() == 0) {
+        vector<int> res;
+        res.push_back(u);
+        ans.push_back(res);
+        return;
+    }
+    for(auto v : g[u]) {
         if(!dfn[v]) {
-            tarjan(v, id);
+            tarjan(v, 0);
             low[u] = min(low[u], low[v]);
+            if(low[v] >= dfn[u]) {
+                vector<int> res;
+                int w;
+                do {
+                    w = st.top();
+                    st.pop();
+                    res.push_back(w);
+                }while(w != v);
+                res.push_back(u);
+                ans.push_back(res);
+            }
         } else {
             low[u] = min(low[u], dfn[v]);
         }
     }
-
-    if(dfn[u] == low[u]) {
-        vector<int> res;
-        res.push_back(u);
-        while(st.size() && st.top() != u) {
-            res.push_back(st.top());
-            st.pop();
-        }
-        st.pop();
-        ans.push_back(res);
-    }
 }
 
 void solve () {
@@ -35,12 +38,12 @@ void solve () {
         int u, v;
         cin >> u >> v;
         if(u == v) continue;
-        g1[u].push_back({v, i << 1});
-        g1[v].push_back({u, i << 1 | 1});
+        g[u].push_back(v);
+        g[v].push_back(u);
     }
 
     for(int i = 1; i <= n; ++i) {
-        if(!dfn[i]) tarjan(i, 0);
+        if(!dfn[i]) tarjan(i, 1);
     }
 
     cout << ans.size() << "\n";

graph theory/Tarjan4.cpp

@@ -0,0 +1,52 @@
+int dfn[MAXN], low[MAXN], tt = 0;
+stack<int> st;
+map<PII, bool> vis;
+
+vector<vector<int>> ans;
+
+void tarjan(int u, int f) {
+    dfn[u] = low[u] = ++tt;
+    st.push(u);
+    for(auto [v, id] : g1[u]) {
+        if(id == (f ^ 1)) continue;
+        if(!dfn[v]) {
+            tarjan(v, id);
+            low[u] = min(low[u], low[v]);
+        } else {
+            low[u] = min(low[u], dfn[v]);
+        }
+    }
+
+    if(dfn[u] == low[u]) {
+        vector<int> res;
+        res.push_back(u);
+        while(st.size() && st.top() != u) {
+            res.push_back(st.top());
+            st.pop();
+        }
+        st.pop();
+        ans.push_back(res);
+    }
+}
+
+void solve () {
+    cin >> n >> m;
+    for(int i = 1; i <= m; ++i) {
+        int u, v;
+        cin >> u >> v;
+        if(u == v) continue;
+        g1[u].push_back({v, i << 1});
+        g1[v].push_back({u, i << 1 | 1});
+    }
+
+    for(int i = 1; i <= n; ++i) {
+        if(!dfn[i]) tarjan(i, 0);
+    }
+
+    cout << ans.size() << "\n";
+    for(auto i : ans) {
+        cout << i.size() << " ";
+        for(auto j : i) cout << j << " ";
+        cout << "\n";
+    }
+}