Data Structures and Algorithm Analysis - Computer Science at ...

140 Chap. 4 Lists, Stacks, and Queues(a) Modify the code of Figure 4.8 to implement circular singly linked lists.(b) Modify the code of Figure 4.15 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. Statewhen the linked list needs less space than the array.(a) The data field is eight bytes, a pointer is four bytes, and the array holdstwenty elements.(b) The data field is two bytes, a pointer is four bytes, and the array holdsthirty elements.(c) The data field is one byte, a pointer is four bytes, and the array holdsthirty elements.(d) The data field is 32 bytes, a pointer is four bytes, and the array holdsforty elements.4.12 Determine the size of an int variable, a double variable, and a pointer onyour computer.(a) Calculate the break-even point, as a function of n, beyond which thearray-based list is more space efficient than the linked list for listswhose elements are of type int.(b) Calculate the break-even point, as a function of n, beyond which thearray-based list is more space efficient than the linked list for listswhose elements are of type double.4.13 Modify the code of Figure 4.19 to implement two stacks sharing the samearray, as shown in Figure 4.21.4.14 Modify the array-based queue definition of Figure 4.27 to use a separateBoolean member to keep track of whether the queue is empty, rather thanrequire that one array position remain empty.4.15 A palindrome is a string that reads the same forwards as backwards. Usingonly a fixed number of stacks and queues, the stack and queue ADT functions,and a fixed number of int and char variables, write an algorithm todetermine if a string is a palindrome. Assume that the string is read fromstandard input one character at a time. The algorithm should output true orfalse as appropriate.