if anyone could solve this as soon as possible

stanbul Bilgi University Industrial Engineering Department IE 211 - Introduction to Algorithms Fall 2022 - Assignment \# 3 Instructor: Banu Kabakulak, PhD Due Date: January 16th, 2023 until 23:59 Question 1: (50 pts) Consuler the Fructional Knopsark Problesp. 1. (25 pts) Desiga a grecdy algorithun for Fractional Knaprack Problem that finds aas optimam solution in O(n log n). Report the priradocode of your algorithm. 2. (25 pts) laplenent your algorithm in Python. Randotnly graverate the inguts and report the console outpuats. Report your Python code scripts. Question 2: (50 pts) Cotsider the Vicrtex Coloring Problem in which we assiga differen: colors to the adjacent vertices on a given graph G=(V,E). The objective is to colot the vertices of the graph using minimum namber of colors. Input: A graph G=(V,E), where V is the set of vertion and E is the set of edges of the graph G. Output: Color assignments of the vertices using minimum number of colors. Ex: For the graph G in Figure 1, a vertex is a node in the graph and the set of vertices is V={e1,v2,,v10}. An ellge is the line between two vestions and the set of edgos is E={(v1,v2),(v1,v5),(v1,v6),(v2,v3),(v2,v2),,(v7,v10)}. The vertioes v1 and v2 are adjacent since there is aa colge (v1,v2) betwern them. On the otber hand, v1 and v7 are bot adjaceat since there is no edge(v1,v7) in the graph. Notice that the adjacent vertices v1 and 22 have differeat colors (red and geean, respectively). whereas noth-adjacent vertices kI and r7can hase the sause color (red). We olnerve that we can color the vertices of the graph G in Figure 1 with 3 afifferent colors, i.e., red, green, bloc. Figure 1: Vertex color assignment on a graph G 1. (5 pts) Discuss the problem couplexity of the Verter Coloring Problem. Is it in P or NP? Is it an easy or a hard problenn? 2. (20 pts) Design a greedy algorithm that solves the Vertex Coloring Problem using a greedy color selection rake. Report the jxeudocode of your algorithan. 3. (5 pts) What is the time complexity of your algorithm? Is it efficient? Can youz algorithm find the optimsum solution? 4. (20 pts) Implement your algorithan in Python. Wse the input given in the example and report the console outputs, Repart your Python code scripts