please write the pseudocode clearly.

and answer all questions

2) (30 pts) Consider the Minimum Cost Vertex Coloring Problem in which we assign different colors to the adjacent vertices on a given graph G = (VE). The objective is to color the vertices of the graph with minimum total coloring cost. Let V = n be the number of vertices in the graph G. Input: A graph G = (V, E), where V is the set of vertices and is the set of edges of the graph G. Colors (1,0,..., Cn) with prices P = (P1, P2, ...,P.). Output: Color assignments of the vertices having minimum total coloring cost. Ex: For the graph G in figure, the set of vertices is V = {01, 22, ..., 010} and the set of edges is E= {(1,02), (,05), (01, U6), (012, 03), (12,04), ---, (017, 010)}. We are given n = 10 different colors, namely 1, 2,..., C10. Let the price of using these colors be P=(3, 2, 1, 2, 4, 3, 2, 3, 4, 2). For instance, the price of using color for one time is P2 = 2 and for two times is 2 x P2 = 4. As an example in the figure, we use color ca for 4 times (price = 4xP2 = 8), color y for 3 times (price = 3 x P = 3), and color for 3 times (price = 3 x 4 6). Hence, we color the graph G using three different colors with total cost 8 +3+ 6 = 17. a. (15 pts) Design a greedy algorithm that solves the Minimum Cost Ver- ter Coloring Problem using a greedy color selection rule. Give the pseudocode of your algorithm. h 15 pts) What is the time complexity of your algorithm? Is it efficient? Can your algorithm find the optimum solution? c. (10 pts) Step-by-step implement your algorithm on the instance given in the example