A Practical Introduction to Data Structures and Algorithm Analysis

148 Chap. 4 Lists, Stacks, and Queues4.5 In the linked list implementation presented in Section 4.1.2, the current positionis implemented using a pointer to the element ahead of the logicalcurrent node. The more “natural” approach might seem to be to have currpoint directly to the node containing the current element. However, if thiswas done, then the pointer of the node preceding the current one cannot beupdated properly because there is no access to this node from curr. Analternative is to add a new node after the current element, copy the value ofthe current element to this new node, and then insert the new value into theold current node.(a) What happens if curr is at the end of the list already? Is there still away to make this work? Is the resulting code simpler or more complexthan the implementation of Section 4.1.2?(b) Will deletion always work in constant time if curr points directly tothe current node?4.6 Add to the LList class implementation a member function to reverse theorder of the elements on the list. Your algorithm should run in Θ(n) time fora list of n elements.4.7 Write a function to merge two linked lists. The input lists have their elementsin sorted order, from smallest to highest. The output list should also be sortedfrom highest to lowest. Your algorithm should run in linear time on the lengthof the output list.4.8 A circular linked list is one in which the next field for the last link nodeof the list points to the first link node of the list. This can be useful whenyou wish to have a relative positioning for elements, but no concept of anabsolute first or last position.(a) Modify the code of Figure 4.8 to implement circular singly linked lists.(b) Modify the code of Figure 4.14 to implement circular doubly linkedlists.4.9 Section 4.1.3 states “the space required by the array-based list implementationis Ω(n), but can be greater.” Explain why this is so.4.10 Section 4.1.3 presents an equation for determining the break-even point forthe space requirements of two implementations of lists. The variables are D,E, P , and n. What are the dimensional units for each variable? Show thatboth sides of the equation balance in terms of their dimensional units.4.11 Use the space equation of Section 4.1.3 to determine the break-even point foran array-based list and linked list implementation for lists when the sizes forthe data field, a pointer, and the array-based list’s array are as specified.