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 6.4, Problem 5E
Program Plan Intro
To show that the best case running time of heap sort is
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What is the worst case time complexity of inserting a node in a doubly linked list?
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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
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- Show that the problem of finding the kth smallest element in a heap takes at least Ω(k) time in the worst case.arrow_forwardNote: Your solution should have O(n) time complexity, where n is the number of elements in l, and O(1) additional space complexity, since this is what you would be asked to accomplish in an interview. Given a linked list l, reverse its nodes k at a time and return the modified list. k is a positive integer that is less than or equal to the length of l. If the number of nodes in the linked list is not a multiple of k, then the nodes that are left out at the end should remain as-is. You may not alter the values in the nodes - only the nodes themselves can be changed.arrow_forwardIn an array-based list implementation, the addition of new elements requires linear time complexity in the worst case. True or False?arrow_forward
- Python - Implement the heap-sort algorithm. Experimentally compare its running time with that of insertion sort and the built-in Python sorted function. You could use dummy functions with O(n^2) and O(nlogn) and use them as benchmarks in your graph. Results: Print a graph showing the curves for heap-sort, insertion sort, and built-in the sorted function. Show the code that generates the data used in the graph.arrow_forwardWhat is the worst case complexity for accessing an element in a LinkedList? O(n) O 0 (1) O n log n O O (2)arrow_forwardIt is required to implement the TDA graph (variant 1, Shiflet) using adjacency represented by simply chained unordered lists. The following will be implemented operators: InitGraf, GrafVid, InserNod, InserArc, DeleteNode, DeleteArc. the performance of the operators implemented in terms of the O function.arrow_forward
- Multiple Choice: Select one only: Suppose we cannot use a priority queue (either due to unavailability of libraries, or constraints on operations). If we still want to implement Dijkstra’s algorithm, we must look for the “next closest vertex” by iterating across all vertices and storing distance data on an array, instead of letting the priority queue find this efficiently for us. What would then be the time complexity of this version of Dijkstra’s algorithm without priority queues? a. O(V^2) b. O(V+E) c. O(VE) d. O(VElogV)arrow_forwardQuestion 8 In the worst case, what is the time complexity to implement a get() method in a singly linked list of length n : log 2 n log 2 n – 1 n/2arrow_forwardDevelop 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 destinationvertex of each of the removed vertex’s edges.arrow_forward
- This question concerns complexity, recurrence, sorting, and hashing. (a) Show that nlog(n) + n² = O(n²).arrow_forwardan array A[1... 8] = (2, 6, 5, 4, 1, 2, 4, 3). Run Max-heapify on You're given the root. What is A[1... 8]?arrow_forwardDevelop 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_forward
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