Update Data Structures Class Template.cpp

Data Structures Class Template.cpp

@@ -270,22 +270,33 @@ struct update {
 //Segment Tree end
 
 //DSU start
-struct node2
-{
-	int p; ll sum;
-};
-
 struct DSU
 {
 	int S;
-	vector<node2> dsu;
+
+	struct node
+	{
+		int p; ll sum;
+	};
+	vector<node> dsu;
 
 	DSU(int n)
 	{
 		S = n;
 		for(int i = 0; i < n; i++)
 		{
-			node2 tmp;
+			node tmp;
+			tmp.p = i; tmp.sum = 0;
+			dsu.pb(tmp);
+		}
+	}
+
+	void reset(int n)
+	{
+		S = n;
+		for(int i = 0; i < n; i++)
+		{
+			node tmp;
 			tmp.p = i; tmp.sum = 0;
 			dsu.pb(tmp);
 		}
@@ -623,6 +634,19 @@ template<int N> struct Matrix
 		return R;
 	}
 
+	Matrix operator + (const Matrix &A) const
+	{
+		Matrix R = Matrix();
+		for (int i = 0; i < N; i++)
+		{
+			for (int j = 0; j < N; j++)
+			{
+				R.a[i][j] = a[i][j] + A.a[i][j];
+			}
+		}
+		return R;
+	}
+
 	Matrix binpow(Matrix A, ll p)
 	{
 		if(p == 0) return Matrix();
@@ -1034,6 +1058,203 @@ struct ConvexHull
 };
 //End Convex Hull Trick
 
+//Graph (Basic Algos)
+struct Graph
+{
+	struct edge
+	{
+		int v; ll weight;
+	};
+	vector<vector<edge> > adj;
+	int n;
+
+	Graph(int _n)
+	{
+		adj.resize(_n);
+		n = _n;
+	}
+
+	void addedge(int u, int v, ll c)
+	{
+		edge tmp;
+		tmp.v = v; tmp.weight = c;
+		adj[u].pb(tmp);
+		tmp.v = u;
+		adj[v].pb(tmp);
+	}
+
+	vi dist;
+	vi par;
+
+	void bfs(int s)
+	{
+		ll INFI = ll(1e18);
+		dist.assign(n, INFI);
+		par.assign(n, -1);
+		dist[s] = 0; par[s] = -1;
+		queue<int> q; q.push(s);
+		while(!q.empty())
+		{
+			int u = q.front(); q.pop();
+			for(int i = 0; i < adj[u].size(); i++)
+			{
+				int v = adj[u][i].v;
+				if(dist[v] >= INFI)
+				{
+					dist[v] = dist[u] + 1;
+					par[v] = u;
+					q.push(v);
+				}
+			}
+		}
+	}
+
+	void bfs01(int s)
+	{
+		ll INFI = ll(1e18);
+		dist.assign(n, INFI);
+		par.assign(n, -1);
+		dist[s] = 0; par[s] = -1;
+		deque<int> q; q.pb(s);
+		while(!q.empty())
+		{
+			int u = q.front(); q.pop_front();
+			for(int i = 0; i < adj[u].size(); i++)
+			{
+				int v = adj[u][i].v; ll w = adj[u][i].weight;
+				if(dist[v] >= INFI)
+				{
+					if(w == 1)
+					{
+						dist[v] = dist[u] + 1;
+						par[v] = u;
+						q.push_back(v);
+					}
+					else
+					{
+						dist[v] = dist[u];
+						par[v] = u;
+						q.push_front(v);
+					}
+				}
+			}
+		}
+	}
+
+	void dijkstra(int s)
+	{
+		ll INFI = ll(1e18);
+		dist.assign(n, INFI);
+		par.assign(n, -1);
+		dist[s] = 0; par[s] = -1;
+		priority_queue<ii, vector<ii>, greater<ii> > pq;
+		pq.push(ii(0, s));
+		while(!pq.empty())
+		{
+			int u = pq.top().se; ll d = pq.top().fi; pq.pop();
+			for(int i = 0; i < adj[u].size(); i++)
+			{
+				int v = adj[u][i].v; ll w = adj[u][i].weight;
+				if(d + w < dist[v])
+				{
+					dist[v] = d + w;
+					par[v] = u;
+					pq.push(ii(dist[v], v));
+				}
+			}
+		}
+	}
+
+	vector<vector<ll> > d;
+
+	void Floyd()
+	{
+		ll INFIN = ll(1e18);
+		d.resize(n);
+		for(int i = 0; i < n; i++)
+		{
+			d[i].assign(n, INFIN);
+		}
+		for(int i = 0; i < n; i++)
+		{
+			for(int j = 0; j < adj[i].size(); j++)
+			{
+				d[i][adj[i][j].v] = adj[i][j].weight;
+			}
+			d[i][i] = 0;
+		}
+		for(int k = 0; k < n; k++)
+		{
+			for(int i = 0; i < n; i++)
+			{
+				for(int j = 0; j < n; j++)
+				{
+					d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
+				}
+			}
+		}
+	}
+
+	bool BellmanFord(int s) //returns true if negative weight cycle exists
+	{
+		ll INFI = ll(1e18);
+		dist.assign(n, INFI);
+		par.assign(n, -1);
+		dist[s] = 0;
+		for(int step = 1; step <= n; step++)
+		{
+			for(int i = 0; i < n; i++)
+			{
+				for(int j = 0; j < adj[i].size(); j++)
+				{
+					int u = i; int v = adj[i][j].v; ll w = adj[i][j].weight;
+					if(dist[v] > dist[u] + w)
+					{
+						if(step == n)
+						{
+							return true;
+						}
+						dist[v] = dist[u] + w;
+					}
+				}
+			}
+		}
+		return false;
+	}
+
+	ll shortest(int s, int e) //returns the distance by Dijkstra
+	{
+		return dist[e];
+	}
+
+	vector<pair<ll, ii> > edges;
+
+	ll Kruskal()
+	{
+		DSU dsu(n);
+		for(int i = 0; i < n; i++)
+		{
+			for(int j = 0; j < adj[i].size(); j++)
+			{
+				int u = i; int v = adj[i][j].v; ll w = adj[i][j].weight;
+				edges.pb(mp(w, mp(u, v)));
+			}
+		}
+		sort(edges.begin(), edges.end());
+		ll ans = 0; int cnt = 0;
+		for(int i = 0; i < edges.size(); i++)
+		{
+			int u = edges[i].se.fi; int v = edges[i].se.se;
+			if(dsu.sameset(u, v)) continue;
+			dsu.merge(u, v);
+			cnt++; ans += edges[i].fi;
+			if(cnt >= n - 1) break;
+		}
+		return ans;
+	}
+};
+//End Graph
+
 //Tree
 
 //End Tree
@@ -1049,6 +1270,7 @@ struct ConvexHull
 17. KMP
 18. Trie
 19. Suffix Tree (?)
+20. Treap
 */
 int main() //Testing Zone
 {