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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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.
Both array lists and linked lists are examples of how a list may be implemented. Discuss a scenario when a linked list might be preferable than a list stored in an array. Explain your reasoning in each situation.
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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- Problem 1. Suppose you are doing sequential search of the list [15, 18, 2, 19, 18, 0, 8, 14, 19, 14]. Utilizing both a linked list and an array approach to the list, use sequential search and identify how many comparisons would be necessary to find the key '18'?arrow_forwardYou are implementing two queues for the same data set, one by using array and one by using linked list. Compare the operations of insertion and deletion of the elements for time and space complexity separately.arrow_forwardConsider a Single Linked List (SLL) of nodes, where ‘node’ is a type with two fields: integer data and the node type reference ‘next’ that refers to the next node in the list. For each part given below consider the SLL and the code given in the second column. Following the execution of the code, show the resulting list (in the answer box, for each part, use the arrow key to draw the list as: head-----> ? -------> ? --------> ?). List and Java Code a head ⟶ 1⟶ 2⟶ 3⟶ 4⟶ null node ptr=head; node newnode = new node(0); // data=0 head = newnode; newnode.next=ptr; b head ⟶ 1⟶ 2⟶ 3⟶ 4⟶ null node ptr=head; node newnode = new node(6); // data=6 while(ptr.next!=null) { ptr=ptr.next; } ptr.next=newode; c head ⟶ 1⟶ 2⟶ 3⟶ 4⟶ null node ptr=head; ptr=ptr.next; head=ptr;arrow_forward
- Consider a Single Linked List (SLL) of nodes, where 'node' is a type with two fields: integer data and the node type reference 'next' that refers to the next node in the list. For each part given below consider the SLL and the code given in the second column. Following the execution of the code, show the resulting list (in the answer box, for each part, use the arrow key to draw the list as: head-----> ? -------> ? -------> ?). List and Java Code | head →1-2-3→4→ null node ptr=head; node newnode = new node(0); // data=0 head = newnode; newnode.next=ptr; b head 1→2→3→4→ null node ptr=head; node newnode = new node(6); // data=6 while(ptr.next!=null) { ptr=ptr.next; } ptr.next=newode; head -1-2- 3→ 4→ mull node ptr=head; ptr=ptr.next; head=ptr;arrow_forwardReverse 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_forwardNote: Use less than 500 characters to describe the solution! The functions of a linked list can be performed with an array or vector (insert, delete, search, etc). Discuss or explain why would we go through the complexity of building a linked list.arrow_forward
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- Perform the previous project, but use a doubly linked list. Moreover, your implementation of remove(i) should make the fewest number of pointer hops to get to the game entry at index i. You need to implement the doubly linked list yourself. Problem 3!!arrow_forwardIn this question, you are to implement two functions for reversing linked lists. One function, reverse_iter(..), must use an iterative approach (i.e., loops), whereas the other function, reverse_rec(..), must use recursion instead. We have already implemented the linked list as well as all its helper-functions in the Ilist-module.arrow_forwardConsider a software that creates and manipulates a linked list: What are the two particular nodes that the software would usually keep track of? Explain two popular applications for the null reference in the linked list node.arrow_forward
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