A library must build shelving to shelve 200 4-inch high books, 150 8-inch high books, 300 10-inch high books and 180 12-inch high books. Each book is 0.5 inch thick. The library has several ways to store the books. For example, an 8-inch high shelf may be built to store all books of height less than or equal to 8 inches, and a 12-inch high shelf may be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. The library believes it costs $2,300 to build a shelf and that a cost of $5 per square inch is incurred for book storage. (Assume that the area required to store a book is given by height of storage area times book’s thickness.) Formulate and solve a shortest-path problem that could be used to help the library determine how to shelve the books at minimum cost. (Hint: Have nodes 0, 4, 8, 10 and 12, with cij being the total cost of shelving all books of height >i and ≤ j on a single shelf.)

You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…

[Medium] Suppose, you have been given a non-negative integer which is the height of a ‘house of  cards’. To build such a house you at-least require 8 cards. To increase the level (or height)  of that house, you would require four sides and a base for each level. Therefore, for the top  level, you would require 8 cards and for each of the rest of the levels below you would  require 5 extra cards. If you were asked to build level one only, you would require just 8 cards. Of course, the input can be zero; in that case, you do not build a house at all.  Complete the recursive method below to calculate the number of cards required to build a  ‘house of cards’ of specific height given by the parameter. public int hocBuilder (int height){ // TO DO } OR def hocBuilder(height):