Number of paths with k edges using Dynamic programming and Divide and Conquer

Given a directed graph, we need to find the number of paths with exactly k edges from source u to the destination v. We use adjacency matrix of the given graph in which value of adj[i][j] represents if there is an edge from vertex i to vertex j in the graph. If the value is 1 then there is an edge from vertex i to vertex j else, if value is 0 then there is no edges from vertex i to vertex j in the graph. To understand the problem let's take an example of a graph with 6 vertices {0, 1, 2, 3, 4, 5} and edges. Now let's find number of paths from vertex 0 to vertex 2 with 2 edges. Below a diagram of the graph is given:


This is a companion discussion topic for the original entry at http://iq.opengenus.org/number-of-paths-with-k-edges/