Merge pull request kothariji#597 from aakankshaa23/patch-1

Create Possible path between 2 vertices.cpp

Author: kothariji

Graph/Possible path between 2 vertices.cpp

@@ -0,0 +1,91 @@
+/*
+* C++ program to count all paths from a source to a
+* destination
+*/
+#include <vector>
+#include <cassert>
+#include <list>
+#include<iostream>
+using namespace std;
+
+/*
+* A directed graph using adjacency list representation;
+* every vertex holds a list of all neighbouring vertices
+* that can be reached from it.
+*/
+class Graph {
+public:
+	// Construct the graph given the number of vertices...
+	Graph(int vertices);
+	// Specify an edge between two vertices
+	void add_edge(int src, int dst);
+	// Call the recursive helper function to count all the
+	// paths
+	int count_paths(int src, int dst, int vertices);
+
+private:
+	int m_vertices;
+	list<int>* m_neighbours;
+	void path_counter(int src, int dst, int& path_count, vector<bool>visited);
+};
+
+Graph::Graph(int vertices)
+{
+	m_vertices = vertices; // unused!!
+	/* An array of linked lists - each element corresponds
+	to a vertex and will hold a list of neighbours...*/
+	m_neighbours = new list<int>[vertices];
+}
+
+void Graph::add_edge(int src, int dst)
+{
+	m_neighbours[src].push_back(dst);
+}
+
+int Graph::count_paths(int src, int dst, int vertices)
+{
+	int path_count = 0;
+	vector<bool>visited(vertices,false);
+	path_counter(src, dst, path_count, visited);
+	return path_count;
+}
+
+/*
+* A recursive function that counts all paths from src to
+* dst. Keep track of the count in the parameter.
+*/
+void Graph::path_counter(int src, int dst, int& path_count, vector<bool> visited)
+{
+	// If we've reached the destination, then increment
+	// count...
+	visited[src]=true;
+if (src == dst) {
+		path_count++;
+	}
+	// ...otherwise recurse into all neighbours...
+	else {
+		for (auto neighbour : m_neighbours[src]) {
+		if(!visited[neighbour])
+			path_counter(neighbour, dst, path_count, visited);
+		}
+	}
+}
+
+// Tests...
+int main()
+{
+	// Create a graph given in the above diagram - see link
+	Graph g(5);
+	g.add_edge(0, 1);
+	g.add_edge(0, 2);
+	g.add_edge(0, 4);
+	g.add_edge(1, 3);
+	g.add_edge(1, 4);
+	g.add_edge(2, 3);
+	g.add_edge(2, 1);
+	g.add_edge(3, 2);
+	// Validate it...
+	cout<<g.count_paths(0, 4,5);
+
+	return 0;
+}