please solve all.

2) (30 pts) Consider the Minimum Cost Vertes 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 IV = 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 (C., ..., C) with prices P = (P1, P2, ...,Pa). 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, 02, ..., 010} and the set of edges is E = {(1, 2), (01, 05), (01, 46), (02, 03), (12,27), ---, (17, 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 for 4 times (price = 4xP2 = 8), color cy for 3 times (price = 3 x P = 3), and color for 3 times (price = 3 X P4 = 6). Hence, we color the graph G using three different colors with total cost 8+3+ 6 = 17. " (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. b. (5 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