Question 4 13 pts Design a backtracking algorithm to solve the k-coloring problem (defined below). You have to use the general framework discussed in class. All other attempts will not be graded (10 pts) Write the pseudo-code 3 pts) Analyze its worst-case running time. k-Coloring Problem: Given k colors c1, C2,..,Ck, and an undirected graph G(V,E) we seek to assign a color to each vertex such that for any edge (u, u) E E. u and v are assigned different colors. Is the graph G k- colorable? If yes, then return the color of each vertex. If not, then return a message "The graph cannot be k-colored" Upload Choose a File Question 4 13 pts Design a backtracking algorithm to solve the k-coloring problem (defined below). You have to use the general framework discussed in class. All other attempts will not be graded (10 pts) Write the pseudo-code 3 pts) Analyze its worst-case running time. k-Coloring Problem: Given k colors c1, C2,..,Ck, and an undirected graph G(V,E) we seek to assign a color to each vertex such that for any edge (u, u) E E. u and v are assigned different colors. Is the graph G k- colorable? If yes, then return the color of each vertex. If not, then return a message "The graph cannot be k-colored" Upload Choose a File