Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 21.2, Problem 5E
Program Plan Intro
To show that the professor’s suspicion is well founded to describe the representation of MAKE-SET, FOUND-SET and UNION operations and these have same running time as described in the section.
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In a linked list of N nodes, how many nodes must be visited in order to locate a node?describing both the ideal and ideal search scenarios Why does a doubly-linked list have Remove but a singly-linked list has RemoveAfter? (). Can a doubly-linked list have RemoveAfter() defined for it? Describe your stance. Could the Remove() function be used on a singly-linked list? Describe your stance.
From the following sets of linked lists, which set should be chosen as the head, tominimize the time complexity, when we do union operation on them? Why?Set A: 0-3-5-6-8-10Set B: 1-2-4-9
Suppose there are two singly linked lists both of which intersect at some point and become a single linked list. The head or start pointers of both the lists are known, but the intersecting node is unknown. Also, the number of nodes in each of the list before they intersect are unknown and both the list may have it different. List1 may have n nodes before it reaches intersection point and List2 might have m nodes before it reaches intersection point where m and n may be m = n, m > n or m < n. Give an algorithm for finding the merging point.
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A brute force approach would be to compare every pointer in one list with every pointer in another list. But in this case the complexity would be O(mn)
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- Reverse a singly linked list by changing the pointers of the nodes. The datarepresented by the list should continue to remain in the same nodes of the originallist.For example, given a singly linked list START, as shown in Figure P6.9(a), the listneeds to be reversed, as shown in Figure P6.9(b), by manipulating the links alone.arrow_forwardSuppose you are given a partially-filled sorted linked list and a partially-filled unsorted linked list of the same size. Assume it is a singly linked list (no back edges).Describe the efficiency of searching for a value within each list and deleting it, including the order of such an operation.arrow_forwardIn a 2- to 3-page paper, you will build on the material given in the course to answer the following questions: What is the difference between a single and doubly linked list? When might a singly-linked list be preferable than a doubly-linked list? When might a doubly-linked list be preferable than a singly-linked list? How many nodes will be visited during a search for a node that is in a linked list with N nodes? Describe the best- and worst-case scenarios for a search. Explain why a singly-linked list has the RemoveAfter() function while a doubly-linked list has the Remove() function. Is it possible to create a RemoveAfter() method for a doubly-linked list as well? Explain why you think that is or why you don't think that is. Is it possible to create a Remove() method for a singly-linked list as well? Explain why you think that is or why you don't think that is. Format your work according to the APA standards for the course you're in.arrow_forward
- If a node is in a linked list with N nodes, how many nodes will be traversed during a search for the node? Explain the best- and worst-case search scenarios. Explain why a singly-linked list defines a RemoveAfter() function, while a doubly-linked list defines a Remove() function. Could a RemoveAfter() function also be defined for a doubly-linked list? Explain why or why not. Could a Remove() function also be defined for a singly-linked list? Explain why or why not.arrow_forwardTo add the two polynomials, we presume that the singly linked lists have theirnodes arranged in decreasing order of the exponents of the variable x.The objective is to create a new list of nodes representing the sum P1 + P2. Thisis achieved by adding the COEFF fields of the nodes of similar powers of variable xin lists P1 and P2 and adding a new node reflecting this operation in the resultant listP1 + P2. We present below the crux of the procedure.Here, P1 and P2 are the starting pointers of the singly linked lists representingpolynomials P1 and P2. Additionally, PTR1 and PTR2 are two temporary pointersinitially set to P1 and P2, respectively. Write procedure codearrow_forwardTo add the two polynomials, we presume that the singly linked lists have theirnodes arranged in decreasing order of the exponents of the variable x.The objective is to create a new list of nodes representing the sum P1 + P2. Thisis achieved by adding the COEFF fields of the nodes of similar powers of variable xin lists P1 and P2 and adding a new node reflecting this operation in the resultant listP1 + P2. We present below the crux of the procedure.Here, P1 and P2 are the starting pointers of the singly linked lists representingpolynomials P1 and P2. Additionally, PTR1 and PTR2 are two temporary pointersinitially set to P1 and P2, respectively. Write procedural codearrow_forward
- In a linked list containing N nodes, how many nodes must be traversed in order to locate a node? The best and worst case search scenariosHow do single-linked and double-linked lists vary from one another?Could a RemoveAfter() method exist for a doubly-linked list? If not, why not?Could the Remove() method be used on a single-linked list? If not, why not?arrow_forwardConsider the current elements and its indexes in the queue of size 15: {index[00]=102, index[01]=165, index[02]=115, index[03]=384, index[04]=248, index[05]=111}, draw a table (like shown below) the sequence of elements using the operations listed from number 1 to 26 using the queue approach (A) - in shifting the elements one position forward every time an element is deleted. The following are the description of other operations to be used that would result in a QUEUE that contains the elements. IsTopValue – returns the value at the TOP of the queue. IsRearValue – returns the value at the REAR of the queue. IsTopIndex – returns the index of the value at the TOP of the queue. IsRearIndex – returns the index of the value at the REAR of the queue. IsIndexOf – returns the index of the specific value. IsValueOf – returns the value of the specific index. Insert (Q, 12) Dequeue (Q) Dequeue (Q) Insert (Q, 65) Insert (Q, 100) Insert (Q, 43) Dequeue (Q) IsTopValue (Q) Insert (Q, 61) Dequeue…arrow_forwardI need a reference page for this question that was answered below. What is the difference between a singly-linked list and a doubly-linked list? In what situation would you use a singly-linked list over a doubly-linked list? In what situation would you use a doubly-linked list over a singly-linked list? If a node is in a linked list with N nodes, how many nodes will be traversed during a search for the node? Explain the best- and worst-case search scenarios. Explain why a singly-linked list defines a RemoveAfter() function, while a doubly-linked list defines a Remove() function. Could a RemoveAfter() function also be defined for a doubly-linked list? Explain why or why not. Could a Remove() function also be defined for a singly-linked list? Explain why or why not.arrow_forward
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