Consider the following algorithm for generating a tree on N vertices: Number the vertices 1 to N. Processing the vertices in order, draw an edge between vertex i and one of the previous vertices {1, 2, 3, ..., i-1}, selected uniformly at random. Part A: Write a program to generate trees in this way. Draw an example tree this produces on 20 vertices. Do you think this program can generate every possible tree of a given size? Why or why

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