graphs

Author: whoparthgarg

17. Graphs/01 Graphs Introduction.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	/*
+
+	V : vertices, E : edges
+
+	1.Directed Graph :
+
+		sum of indegrees = E
+		sum of outdegrees = E
+		maximum number of edges = V * ( V - 1 )
+
+	2.Undirected Graph :
+
+		sum of degrees = 2*E
+		maximum number of edges = ( V * ( V - 1 ) ) / 2
+
+	3.Some common graph terms :
+
+		a. walk : A walk is a sequence of vertices and edges of a graph i.e.
+		if we traverse a graph then we get a walk.
+		Vertex can be repeated
+		Edges can’t be repeated
+
+		b. path : A special walk in which Vertex and Edges can't be repeated.
+
+		c. cyclic : A special walk which begins and ends at same vertex.
+
+		d. acyclic : A graph which doesn't contain a cycle.
+
+	*/
+}

17. Graphs/01_Adjacency_List_Representaion.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	/*
+
+	Adjacency Matrix :
+
+		A    B    C
+	-----------------
+	A   0    1     1
+
+	B   1    0     1
+
+	C   1    1     0
+
+	1. size of matrix : (V * V)
+
+	2. for undirected graph : matrix is symmetric
+
+	3. 1 represents there is edge
+	   0 represents there is no edge
+
+	4. handle arbitrary vertices names with hash table eg: m["ABC"] = 2
+
+	5. Properties :
+
+		a. space required O(V*V)
+
+		b. check u and v adjacent O(V)
+
+		c. find all vertices adjacent to u O(V)
+
+		d. find degree of u O(V)
+
+		e. add/remove edge O(1)
+
+		f. add/remove vertex O(V*V)
+
+	*/
+
+	return 0;
+}

17. Graphs/02a Graphs Representation.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	/*
+
+	Adjacency List :
+
+
+	0 - 1-->2
+	1 - 0-->2
+	2 - 0-->1-->3
+	3 -	2
+
+	Properties :
+
+		a. space required O(V+E)
+
+			1. undirected O(V + 2 * E)
+			2. directed O(V + E)
+
+		b. check u and v adjacent O(V)
+
+		c. find all vertices adjacent to u O(degree(u))
+
+		d. find degree of u O(1)
+
+		e. add edge O(1)
+
+		f. remove edge O(V)
+
+	*/
+
+	return 0;
+}

17. Graphs/02b Graphs Representation.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+//Adjacenecy Matrix
+class Graph
+{
+	bool **adj;
+	int v;
+
+public:
+
+	//constructor
+	Graph(int vertices)
+	{
+		v = vertices;
+		adj = new bool *[v];
+
+		//intialise matrix
+		for (int i = 0; i < v; i++)
+		{
+			adj[i] = new bool[v];
+			for (int j = 0; j < v; j++)
+			{
+				adj[i][j] = false;
+			}
+		}
+	}
+
+	//add edge
+	void addEdge(int i, int j)
+	{
+		adj[i][j] = true;
+		adj[j][i] = true;
+	}
+
+	//remove edge
+	void removeEdge(int i, int j)
+	{
+		adj[i][j] = false;
+		adj[j][i] = false;
+	}
+
+	//print matrix
+	void print()
+	{
+		for (int i = 0; i < v; i++)
+		{
+			cout << i << " : ";
+			for (int j = 0; j < v; j++)
+			{
+				cout << adj[i][j] << " ";
+			}
+			cout << endl;
+		}
+	}
+};
+
+int main()
+{
+	Graph g(4);
+
+	g.addEdge(0, 1);
+	g.addEdge(0, 2);
+	g.addEdge(1, 2);
+	g.addEdge(2, 0);
+	g.addEdge(2, 3);
+
+	g.print();
+	return 0;
+}

17. Graphs/03a DFS.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+
+//Adjacency List
+void addEdge(vector<int> adj[], int u, int v)
+{
+	adj[u].push_back(v);
+	adj[v].push_back(u);
+}
+
+void print(vector<int> adj[], int v)
+{
+	for (int i = 0; i < v; i++)
+	{
+		cout << i << " : ";
+		for (auto x : adj[i])
+		{
+			cout << x << " ";
+		}
+		cout << endl;
+	}
+}
+
+int main()
+{
+	int v = 4;
+	vector<int> adj[v];
+
+	addEdge(adj, 0, 1);
+	addEdge(adj, 0, 2);
+	addEdge(adj, 1, 2);
+	addEdge(adj, 1, 3);
+
+	print(adj, v);
+	return 0;
+}