Prove that if there exists some h ∈Hnk that has zero error over S(G) then G is k-colorable. 

1. Prove that if there exists some Hnk that has zero error over S(G) then is k-colorable. Hint: Let = !k

j=1 h j be an ERM classifier in Hnk over S. Define a coloring of by setting (vi ) to be the minimal such that hj (e) = −1. Use the fact that halfspaces are convex sets to show that it cannot be true that two vertices that are connected by an edge have the same color.

2. Prove that if is k-colorable then there exists some ∈ Hn k that has zero error over S(G). Hint: Given a coloring of the vertices of G, we should come up with hyperplanes, h. . .hk whose intersection is a perfect classifier for S(G). Let = 0.6 for all of these hyperplanes and, for ≤ let the ’th weight of the t’th hyperplane, wt,i, be −1 if (vi ) = and 0 otherwise.

find the cost of your paper

Suggest a modification of the binary search algorithm that emulates this strategy for a list of names.

1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

Explain why insertion sort works well on partially sorted lists.

1. Which configuration of data in a list causes the smallest number of exchanges in a selection sort? Which configuration of data causes the largest number of exchanges? 2. Explain….

Draw a class diagram that shows the relationships among the classes in this new version of the system

Jack decides to rework the banking system, which already includes the classes BankView, Bank, SavingsAccount, and RestrictedSavingsAccount. He wants to add another class for checking accounts. He sees that savings….