Develop a linear-time (i.e., O(m)-time) algorithm that solves the Single-Source Shortest Path problem for graphs whose edge weights are positive integers bounded by 10. (Hint. You can either modify Dijstras algorithm or consider using Breath-First-Search.) Consider an extended version of the Shortest-Path problem above. Suppose that you want to traverse from city s to city t. In addition, for some reason, you also need to pass through cities x, y, and z (in any order) during your trip. Your objective is to minimize the cost of the trip. The problem can be formulated as a graph problem as follows: Given a positively weighted directed graph G and ve vertices s, t, x, y, z, nd a path from s to t that contains the vertices x, y, z such that the path is the shortest over all paths from s to t that contain x, y, z, assuming that these paths are allowed to contain repeated vertices and edges. Develop an O(mlogn)-time algorithm for this problem.