Consider a fixed-size circular array-based implementation of the LRU quasi-stack. Explain step-by-step the algorithm to keep the last referenced page at the top of the stack. Note that the page being referenced may, but does not need to, be already in the stack. Your algorithm must handle both cases. What is the complexity of updating the stack on each new page reference? That is, how many operations are required to add a new page number at the top, or to move an already existing page number from some location in the stack to the top?

You are going to be asked to make a singly-linked list of singly-linked lists. How are you designing your data structure to best facilitate this design? Be sure to explain how the data is internally stored within your linked list of linked lists. (PI 1.1/ABET[1], PI 6.1/ABET[6])   #Python

Implement MSD string sorting using queues, as follows: Keep onequeue for each bin. On a first pass through the items to be sorted, insert each item intothe appropriate queue, according to its leading character value. Then, sort the sublistsand stitch together all the queues to make a sorted whole. Note that this method doesnot involve keeping the count[] arrays within the recursive method.

A singly linked list contains n - 1 strings that are binary representations of numbers from the set {0, 1,.…, n – 1} where n is an exact power of 2. However, the string corresponding to one of the numbers is missing. For example, if n = 4, the list will contain any three strings from 00, 01,10 and 11. Note that the strings in the list may not appear in any specific order. Also note that the length of each string is lgn, hence the time to compare two strings in O(lgn). Write an algorithm that generates the missing string in O(n).

The circular array queue implementation increased the dequeue operation's performance from O(n) to O(1) by doing away with the requirement to move array items. Adding or removing members from a list can occur anywhere along its length, not simply at the front or back, thus this is not true.

In a programming language (Pascal), the declaration of a node in a singly linked list is shown in Figure P6.7(a). The list referred to for the problem is shown in Figure P6.7(b). Given P to be a pointer to a node, the instructions DATA(P) and LINK(P) referring to the DATA and LINK fields, respectively, of node P are equivalently represented by P↑. DATA and P↑. LINK in the programming language. What do the following commands do to the logical representation of the list T? i) ii) TYPE POINTER=NODE; NODE RECORD DATA: integer; LINK: POINTER END; VAR P, Q R: T POINTER (a) Declaration of a node in a singly linked list T 31 TE 57 12 (b) A singly linked list T iii) R₁.LINK: = Q iv) R₁.DATA: = P₁.DATA: Q₁.DATA + R₁.DATA Q: = P |R Figure P6.7. (a and b) Declaration of a node in a programming language and the logical representation of a singly linked list T Q.LINK.DATA + 10 91 Linked Lists 189

This program will use an array implementation of a linked list to keep an ascending sorted list of numbers. The input data consists of two fields: a single character and an integer value. The single character gets interpreted as one of the following: A - represents a value that is to be added to the linked listD - represents a value to be deleted from the linked listP - indicates that all values are to be printed in ascending order The character is only used to determine which process is to be executed; it should not be printed, entered into the linked list, or processed in any way. The main program should be mainly function calls. Process input data until end of file. All output should be sent to an output file and be appropriately formatted and labeled. Keep a running log of everything that is going on in the processing. Input file: A 54A -17A 32 A 81 A -30 A 18 P A 41 A 93 A 65 A 80 A 104 A -20 D 81 D 54 D -30 A 79 A 63 A 77 A –33 D 104 D -20 D 80 D 32 P