Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 6.4, Problem 2E
Program Plan Intro
To describe the correctness of the loop variant for the heap sort.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
3. Sort the array A= [10, 15, 11, 12, 6, 28, 19] by using the operation (insertion and
deletion) of Heapsort.
Assume we have k heaps, each with a maximum of n items. These are to be combined into a single heap. Each of the following sub-parts provides a different method for merging the heaps, and you are required to calculate the large O running time for each method.
We build a new linked list, L, that is empty. We continually remove the highest priority element from each of the k piles hi and insert it at the beginning of L, until hi is empty. The items of L are then transferred to an array and the array is heapified. What is the worst-case running time for a huge O?
ASAP!!
Consider the following series of random numbers:80 35 50 18 36 29 25 17 67 23 12 19 5 3 2a. Create a Priority Queue using an array data structure, draw and explainarray at each stepb. Draw a d-heap, where ? = 4c. Explain steps of removing min i.e. deleteMin(), identify hole location(s), slide-down, bubble-up and last elementd. Explain steps of inserting 1
Chapter 6 Solutions
Introduction to Algorithms
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3E
Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3P
Knowledge Booster
Similar questions
- 30. In the implementation for a breadth-first search we studied, a queue was used. The code below replaces the queue with a stack. List the pre-order enumeration that the vertices in the graph below are visited using this modified method, starting from vertex 0. } 3 /** stack-based search */ static void modSearch (Graph G, int start) { Stack S new AStack (G.n()); S.push(start); } 6 G.setMark (start, VISITED); while (S.length) > 0) { } modSearch: intv S.pop(); PreVisit (G, v); for (int w = G.first (v); w < G.n(); w = G.next(v, w)) if (G.getMark (w) == UNVISITED) { G.setMark (w, VISITED); S.push(w);arrow_forwardWrite pseudo code for Min_Heap_Delete(A,i) which deletes the item at position i in Min_Heap A. Assume that A is a one-dimensional array. Hint:Think about “bubbling up” and “bubbling down” and the operations that do these, then give the best upper bound you can on the worst case running time of your method, in ordered notations.arrow_forwardCreate a min-heap from a binary search tree. Show the technique in action using the following binary search tree.arrow_forward
- Outline an algorithm in pseudo code for checking whether an array H[1..n] is a heap and determine its time efficiency.arrow_forwardDo B,C,D ASAP!! PLEASE Time is short Consider the following series of random numbers:80 35 50 18 36 29 25 17 67 23 12 19 5 3 2a. Create a Priority Queue using an array data structure, draw and explainarray at each stepb. Draw a d-heap, where ? = 4c. Explain steps of removing min i.e. deleteMin(), identify hole location(s),slide-down, bubble-up and last elementd. Explain steps of inserting 1arrow_forwardHeapsort We will call heapsort on the array of size 11 with values 0, 2, 7, 6, 8, 3, 1, 4, 7, 10, 9 a) In Phase 1: Draw the INITIAL TREE and redraw the tree AFTER EACH CALL TO FIXHEAP. That means you will draw a total of six trees. b) In Phase 2: Draw the tree after the first swap, the first call to fixeheap, the second swap and the second call to fixheap. The means you'll draw a total of four trees. After the first swap omit the last array value from the tree. After the second swap, omit both the second to last and last array values from the tree. For the purposes of grading please draw neat, easy-to-read diagrams.arrow_forward
- Develop a topological sort implementation thatmaintains a vertex-indexed array that keeps track of the indegree of each vertex. Initialize the array and a queue of sources in a single pass through all the edges. Then, perform the following operations until the source queue is empty:■ Remove a source from the queue and label it.■ Decrement the entries in the indegree array corresponding to the destination vertex of each of the removed vertex’s edges If decrementing any entry causes it to become 0, insert the corresponding vertex onto the source queue.arrow_forwardConsider the array with elements: 18, 10, 20, 5, 8, 9, 3. Applying the heapify() to convert the list to a minimum heap rearranges the elements to: 18 10 3 58 9 20 3 10 9 5 8 18 20 359 10 8 18 20 3 10 18 5 8 9 20 Consider DFS in the graph below starting form node E. The next node visited in the partial traversal E H GCFwill be node A. True False Consider the following maximum heap: 20 10 18 5 8 9 4. After inserting node 15, the heap elements will rearrange to 15 20 18 10 8945 15 18 20 4 9 8 10 5 20 15 18 10 894 5 20 10 18 158945arrow_forward: A binary search tree was created by traversing through an array from left to rightand inserting each element. Given a binary search tree with distinct elements, print all possiblearrays that could have led to this tree.EXAMPLEInput: 1<-2->3Output: {2, 1, 3}, {2, 3, 1}arrow_forward
- Create a min-heap from a binary search tree. Use the following binary search tree to demonstrate the method.arrow_forwardcreate the remove method for a threaded binary search tree. here is a description for a binary search tree: Since a binary search tree with N nodes has N + 1 NULL pointers, half the space allocated in a binary search tree for pointer information is wasted. Suppose that if a node has a NULL left child, we make its left child pointer link to its inorder predecessor, and if a node has a NULL right child, we make its right child pointer link to its inorder successor. This is known as a threaded tree and the extra links are called threads. here is my .h file: #ifndef THREADEDBST_H #define THREADEDBST_H #include "Node.cpp" class ThreadedBST { private: Node* root; public: /** * Constructs an empty ThreadedBST object. * Pre-condition: None. * Post-condition: An empty ThreadedBST object is created with a null root. */ ThreadedBST(); /** * Destroys the ThreadedBST object and frees the associated memory. * Pre-condition: None. * Post-condition: The ThreadedBST object is destroyed, and all the…arrow_forwardIn Heapsort, we assume that arrays are indexed from 1 to n. For example, if A = [16,4,10,14,7,9,3,2,8,1], then A[2] = 4 (highlighted in red). %3D %3D The MAX-HEAPIFY(A, i) procedure inputs an array A and an index i. It assumes that the binary trees rooted at LEFT(i) and RIGHT(1) are max heaps, and ensures that A[i] "floats down" so that the output is an array that obeys the max-heap property. An example is provided on pg. 155 of the textbook. In this example, A = [16,4,10,14,7,9,3,2,8,1]. Then MAX-HEAPIFY(A, 2) corrects the 2nd element of A, which is 4, moving this number to the correct position. The output is [16,14,10,8,7,9,3,2,4,1]. Let A = [2,11,10,9,6,7,8,3,5,4,1]. Determine MAX-HEAPIFY(A,1).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education