Added articulation bridges

Articulation_Bridges.cpp

@@ -0,0 +1,61 @@
+#include<bits/stdc++.h>
+#define turbo() ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
+#define ll long long
+#define mod (1000000007)
+#define inf ((ll)1e18)
+#define eps (1e-9)
+#define ff first
+#define ss second
+#define pb push_back
+#define endl "\n"
+using namespace std;
+
+vector<vector<int>> adj;
+vector<int> dfs_low , dfs_num , dfs_parent; 
+vector<pair<int , int> > res;
+int dfscnt = 1;
+void dfs(int u)
+{
+	dfs_low[u] = dfs_num[u] = dfscnt++;
+	for(int x : adj[u])
+	{
+		if(dfs_num[x] == 0)
+		{
+			dfs_parent[x] = u;
+			dfs(x);
+			if(dfs_low[x] > dfs_num[u])
+				res.push_back({u , x});
+			dfs_low[u] = min(dfs_low[u] , dfs_low[x]);
+		}
+		else if(x != dfs_parent[u])
+			dfs_low[u] = min(dfs_low[u] , dfs_num[x]);
+
+	}
+}
+
+int main()
+{
+	int n = 10 ; // number of vertices;
+	// cin>>n;
+	int m = 15 ; // number of edges;
+	// cin>>m;
+	adj.resize(n + 1);
+	dfs_low.resize(n + 1);
+	dfs_num.resize(n + 1);
+	dfs_parent.resize(n + 1);
+	// store the adj list int adj;
+	for(int i = 0 ; i < m ; i++ )
+	{
+		int x , y;
+		cin>>x>>y;
+		adj[x].pb(y);
+		adj[y].pb(x);
+	}
+	dfs(1);
+	cout<<"Bridges:\n";
+	for(auto x : res)
+	{
+		cout<<x.ff<<" "<<x.ss<<endl;
+	}
+	return 0;
+}

Gaussian Elimination.cpp

@@ -1,77 +1,77 @@
-struct Gauss 
-{
-	int bits = 60;
-	vector<int> table;
-	
-	Gauss()
-	{
-		table = vector<int> (bits, 0);
-	}
-
-	Gauss(int _bits) 
-	{
-		bits = _bits;
-		table = vector<int> (bits, 0);
-	}
- 
-	int size() 
-	{
-		int ans = 0;
-		for(int i = 0; i < bits; i++) 
-		{
-			if(table[i]) 
-				ans++;
-		}
-		return ans;
-	}
- 
-	bool can(int x) 
-	{
-		for(int i = bits - 1; i >= 0; i--) 
-			x = min(x, x ^ table[i]);
-		return x == 0;
-	}
- 
-	void add(int x) 
-	{
-		for(int i = bits - 1; i >= 0 && x; i--) 
-		{
-			if(table[i] == 0) 
-			{
-				table[i] = x;
-				x = 0;
-			} 
-			else 
-				x = min(x, x ^ table[i]);
-		}
-	}
- 
-	int getBest() 
-	{
-		int x = 0;
-		for(int i = bits - 1; i >= 0; i--) 
-			x = max(x, x ^ table[i]);
-		return x;
-	}
- 
-	void merge(Gauss &other)
-	{
-		for(int i = bits - 1; i >= 0; i--)
-			add(other.table[i]);
-	}
-};
-
-//Logic: https://math.stackexchange.com/questions/48682/maximization-with-xor-operator
-//Source: https://codeforces.com/profile/tfg
-
-//Problem 1: http://codeforces.com/contest/959/problem/F
-//Solution 1: https://codeforces.com/contest/959/submission/50314871
-
-//Problem 2: https://codeforces.com/contest/1101/problem/G
-//Solution 2: https://codeforces.com/contest/1101/submission/50315103
-
-//Problem 3: https://atcoder.jp/contests/abc141/tasks/abc141_f
-//Solution 3: https://atcoder.jp/contests/abc141/submissions/15096631
-
-//Problem 4: https://codeforces.com/contest/1336/problem/E1 (MITM)
-//Solution 4: https://codeforces.com/contest/1336/submission/76891926
+struct Gauss 
+{
+	int bits = 60;
+	vector<int> table;
+
+	Gauss()
+	{
+		table = vector<int> (bits, 0);
+	}
+
+	Gauss(int _bits) 
+	{
+		bits = _bits;
+		table = vector<int> (bits, 0);
+	}
+
+	int size() 
+	{
+		int ans = 0;
+		for(int i = 0; i < bits; i++) 
+		{
+			if(table[i]) 
+				ans++;
+		}
+		return ans;
+	}
+
+	bool can(int x) 
+	{
+		for(int i = bits - 1; i >= 0; i--) 
+			x = min(x, x ^ table[i]);
+		return x == 0;
+	}
+
+	void add(int x) 
+	{
+		for(int i = bits - 1; i >= 0 && x; i--) 
+		{
+			if(table[i] == 0) 
+			{
+				table[i] = x;
+				x = 0;
+			} 
+			else 
+				x = min(x, x ^ table[i]);
+		}
+	}
+
+	int getBest() 
+	{
+		int x = 0;
+		for(int i = bits - 1; i >= 0; i--) 
+			x = max(x, x ^ table[i]);
+		return x;
+	}
+
+	void merge(Gauss &other)
+	{
+		for(int i = bits - 1; i >= 0; i--)
+			add(other.table[i]);
+	}
+};
+
+//Logic: https://math.stackexchange.com/questions/48682/maximization-with-xor-operator
+//Source: https://codeforces.com/profile/tfg
+
+//Problem 1: http://codeforces.com/contest/959/problem/F
+//Solution 1: https://codeforces.com/contest/959/submission/50314871
+
+//Problem 2: https://codeforces.com/contest/1101/problem/G
+//Solution 2: https://codeforces.com/contest/1101/submission/50315103
+
+//Problem 3: https://atcoder.jp/contests/abc141/tasks/abc141_f
+//Solution 3: https://atcoder.jp/contests/abc141/submissions/15096631
+
+//Problem 4: https://codeforces.com/contest/1336/problem/E1 (MITM)
+//Solution 4: https://codeforces.com/contest/1336/submission/76891926