Write a program that implements the following weighted directed graph and then does a DFS and a BFS search from node E printing out the paths and the cost of each traversal $($assume there is no cost to "backing up$".$ Then write a function that takes two nodes $($source and destination$)$ and determines if there is a path from the source to the destination and if there is one outputs the path and the length of the path or if there is not one it should output an appropriate message.

Write it in c$++$