Solution: Implement Depth-First Search

The depth-first search (DFS) algorithm for traversing a directed graph involves starting from a specified source vertex and exploring as deeply as possible along each branch before backtracking. To implement this, an empty list is initialized to store the traversal order, and a boolean array tracks visited vertices to prevent cycles. The algorithm uses a stack to manage the vertices, pushing the source vertex onto it and marking it as visited. The process continues until all vertices are explored, resulting in a list that reflects the order of traversal. The time complexity is O(V + E), and the space complexity is O(V).