Answer the following questions about the MysteryPath algorithm below, which takes in a graph and returns a path.

1. What is returned by MysteryPath for the graph below?

2. What is the worst-case time complexity of MysteryPath when using an adjacency list to represent the graph and a direct map to represent count? Justify your answer. You may assume that the algorithm will never visit the same vertex twice and that it takes (1) time to return the degree of a vertex.

Input: E): graph with n vertices and m edges Input: m, n: size and order of G, respectively 1 Algorithm Mystery Path 2 count Map(V Z) 3 for each v E V do 4 count v deg(v); 5 end 6 path f); V[1] 8 while countlvl 0 do 9 Add v to path 10 count v-oo; 11 foreach u E N(v) do 12 if countlul oo then. 13 I count count aj 1 end 14 15 end 16 Let v be the neighbor of u with the smallest value of count 17 end 18 Add v to path; 19 return path