7. The following backtracking algorithm is used to 3-color the graph shown below. Recall that in a proper k-coloring of a graph, nodes are each assigned one of k colors, such that no adjacent nodes have the same color. o Start from source node S . Color priority is Lavender (L), Orange(O), Teal (T). That is, we will always first try to use L, then O, then T for any given node. Strategy A: To break ties, always try to assign a color to the lexicographically smallest uncolored node. Strategy B: To break ties, always try to assign a color to the lexicographically largest uncolored node. For each Strategy, report the following details a. The valid coloring found by the Strategy, for nodes S, A, B, C, D, E in that order. E.g., "T, O, L, T, O, L" assigns color T to nodes S and C; color O to nodes A and D; and color L to nodes B and E. b. The total number of nodes (partial solution vectors) in the tree explored by the backtracking algo- rithm, i.e., the number of times a color is tried out on a vertex during the backtracking