Draw G7,2, and insert your drawing into your solutions. For this drawing, you do not need vertex…

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A. Draw G7,2, and insert your drawing into your solutions. For this drawing,
you do not need vertex weights. List three maximal free sets for G7,2.
B. The Free Set problem takes as an instance a braid Gn,k and a weight
function w on Gn,k and returns as a solution a free set U such that w(U) is
maximum among all free sets in Gn,k. State the Free Set problem in the
formal instance/solution format that we use in class.
C. Figure 1 contains pseudocode for a greedy algorithm Greedy-Free-Set
that attempts to solve the Free Set problem. Draw an instance Gn,k, w of
Free Set for which Greedy-Free-Set does not return a correct solution.
(Here, you need to assign weights to vertices in your drawing.) Explain
your result, and include your drawing in your solution PDF.
D. Use the dynamic programming paradigm from class to develop a dynamic
programming algorithm to solve the Free Set problem for the special case
where k = 1. Give CLRS pseudocode for your algorithm. You may skip
the backtrace step. Give the T asymptotic worst-case time complexity for
your algorithm.
E. Use the dynamic programming paradigm from class to develop a dynamic
programming algorithm to solve the Free Set problem for the special case
where k = 2. Give CLRS pseudocode for your algorithm. You may skip
the backtrace step. Give the T asymptotic worst-case time complexity for
your algorithm.