Find a Mother Vertex in a Graph

C++/find_mother_vertex_in_graph.cpp

@@ -0,0 +1,89 @@
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class Graph {
+	int V; // No. of vertices
+	list<int>* adj; // adjacency lists
+
+	// A recursive function to print DFS starting from v
+	void DFSUtil(int v, vector<bool>& visited);
+
+public:
+	Graph(int V);
+	void addEdge(int v, int w);
+	int findMother();
+};
+
+Graph::Graph(int V)
+{
+	this->V = V;
+	adj = new list<int>[V];
+}
+
+
+void Graph::DFSUtil(int v, vector<bool>& visited)
+{
+	// Mark the current node as visited and print it
+	visited[v] = true;
+
+	// Recur for all the vertices adjacent to this vertex
+	list<int>::iterator i;
+	for (i = adj[v].begin(); i != adj[v].end(); ++i)
+		if (!visited[*i])
+			DFSUtil(*i, visited);
+}
+
+void Graph::addEdge(int v, int w)
+{
+	adj[v].push_back(w); // Add w to v’s list.
+}
+
+// Returns a mother vertex if exists. Otherwise returns -1
+int Graph::findMother()
+{
+	// visited[] is used for DFS. Initially all are initialized as not visited
+	vector<bool> visited(V, false);
+
+	// To store last finished vertex (or mother vertex)
+	int v = 0;
+
+	// Do a DFS traversal and find the last finished  vertex
+	for (int i = 0; i < V; i++) {
+		if (visited[i] == false) {
+			DFSUtil(i, visited);
+			v = i;
+		}
+	}
+
+
+	// Now check if v is actually a mother vertex (or graph has a mother vertex). We basically check if every vertex is reachable from v or not.
+
+	// Reset all values in visited[] as false and do
+	// DFS beginning from v to check if all vertices are reachable from it or not.
+	fill(visited.begin(), visited.end(), false);
+	DFSUtil(v, visited);
+	for (int i = 0; i < V; i++)
+		if (visited[i] == false)
+			return -1;
+
+	return v;
+}
+
+// Driver code
+int main()
+{
+
+	Graph g(7);
+	g.addEdge(0, 1);
+	g.addEdge(0, 2);
+	g.addEdge(1, 3);
+	g.addEdge(4, 1);
+	g.addEdge(6, 4);
+	g.addEdge(5, 6);
+	g.addEdge(5, 2);
+	g.addEdge(6, 0);
+	cout << "A mother vertex is " << g.findMother();
+
+	return 0;
+}

find_mother_vertex_in_graph.cpp

@@ -0,0 +1,89 @@
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class Graph {
+	int V; // No. of vertices
+	list<int>* adj; // adjacency lists
+
+	// A recursive function to print DFS starting from v
+	void DFSUtil(int v, vector<bool>& visited);
+
+public:
+	Graph(int V);
+	void addEdge(int v, int w);
+	int findMother();
+};
+
+Graph::Graph(int V)
+{
+	this->V = V;
+	adj = new list<int>[V];
+}
+
+
+void Graph::DFSUtil(int v, vector<bool>& visited)
+{
+	// Mark the current node as visited and print it
+	visited[v] = true;
+
+	// Recur for all the vertices adjacent to this vertex
+	list<int>::iterator i;
+	for (i = adj[v].begin(); i != adj[v].end(); ++i)
+		if (!visited[*i])
+			DFSUtil(*i, visited);
+}
+
+void Graph::addEdge(int v, int w)
+{
+	adj[v].push_back(w); // Add w to v’s list.
+}
+
+// Returns a mother vertex if exists. Otherwise returns -1
+int Graph::findMother()
+{
+	// visited[] is used for DFS. Initially all are initialized as not visited
+	vector<bool> visited(V, false);
+
+	// To store last finished vertex (or mother vertex)
+	int v = 0;
+
+	// Do a DFS traversal and find the last finished  vertex
+	for (int i = 0; i < V; i++) {
+		if (visited[i] == false) {
+			DFSUtil(i, visited);
+			v = i;
+		}
+	}
+
+
+	// Now check if v is actually a mother vertex (or graph has a mother vertex). We basically check if every vertex is reachable from v or not.
+
+	// Reset all values in visited[] as false and do
+	// DFS beginning from v to check if all vertices are reachable from it or not.
+	fill(visited.begin(), visited.end(), false);
+	DFSUtil(v, visited);
+	for (int i = 0; i < V; i++)
+		if (visited[i] == false)
+			return -1;
+
+	return v;
+}
+
+// Driver code
+int main()
+{
+
+	Graph g(7);
+	g.addEdge(0, 1);
+	g.addEdge(0, 2);
+	g.addEdge(1, 3);
+	g.addEdge(4, 1);
+	g.addEdge(6, 4);
+	g.addEdge(5, 6);
+	g.addEdge(5, 2);
+	g.addEdge(6, 0);
+	cout << "A mother vertex is " << g.findMother();
+
+	return 0;
+}