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 12.1, Problem 2E
Program Plan Intro
To describe the difference of binary search tree property and the min-heap property and also discuss whether it is possible to print out the keys of an n -node tree in
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What is the difference between the binary-tree search property versus the min heap property? Can a binary tree print out a sorted list of its keys in O(n) time? Can a heap print out a sorted list of its keys in O(n) time?
Analyze the similarities and differences between AVL Trees and Binary Search Trees. Is it feasible to include discussions about efficient operations into what you have to say?
Describe the differences and similarities between Binary Search Trees and AVL Trees. Can efficiency operations be included in your discussion?
Chapter 12 Solutions
Introduction to Algorithms
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5E
Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4P
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- Say you set the key for each position p of a binary tree T equal to its pre-order rank. Under what circumstances is T a heap? In other words, what property should T have to be a heap? Discuss about such a property. If we are to insert "43," "18," and "2," on the binary tree shown below (it's also a heap!), what is the end result? Remember we need three steps to complete inserting in a heap: a) Place the new element in the next available position in the array. b) Compare the new element with its parent. If the new element is smaller, than swap it with its parent. c) Continue this process until either the new element’s parent is smaller than the new element or it reaches the root. HERE IS THE IMAGE Consider a red-black tree (RBT) T storing 1,024 elements. What is the worst-case height of T? As you recall, the height is the black height. You do not have to be correct in terms of the answer, but try to show the reason why it should be that number. You can…arrow_forwardExamine the variations between AVL Trees and Binary Search Trees. Do you think you'll be able to include efficiency operations into your discussion?arrow_forwardConsider Figure 2 and answer the following. Give reason of your answer. a)Is this a complete binary tree? b) Is this a binary search tree? c) Is this a max heap? d) Is this a graph? e) Write the post-order traversal of the tree presented in Figure 2.arrow_forward
- Discuss the difference between a Binary Search Tree and an AVL Tree. Include in your discussion the efficiency operations.arrow_forwardExplain in essay form: What is a degenerate tree? What is the cause of having a degenerate binary search tree? Why is it important for a binary tree to be balanced (or close to balanced)?arrow_forwardAnalyze the similarities and differences between a Heap and a Binary Tree. Would you be interested in a conversation about how efficient our operations are?arrow_forward
- A tree with n (n≥1) distinct elements is both a max-heap and a binary search tree. What are possible values of n? Justify your answer.arrow_forwardWhat impact will keeping linked list pointers in an AVL tree have on insertions, deletions, and hash table searches? Your answer must explain the running time in terms of the size of the hash table. Does Big-Ohnotation need to exist?arrow_forwardDraw a Balanced search tree where keys are 210435. How many comparison operation you performed to insert all keys in your tree. Discuss what are advantages of Balanced Search Trees? When they can be considered in-efficient?arrow_forward
- Is there any work that a red-black tree could execute with a time complexity of O(log n)? Pick one: To find a predecessor or a successor; to insert and delete; or to do all three togetherarrow_forwardShow the result of inserting 30, 10, 40, 60, 90, 20, 50, 70 into an initially empty binary search tree. b) Is the above tree a full binary tree? Why? Why not? c)Draw the subtree with the root node as 60.arrow_forwardWhat is the difference between a min heap search and a binary tree search? Is it feasible to generate a sorted list of the keys of a binary tree in the amount of time specified by O(n)? How much time does it take to compile a list of the keys in a heap that has been sorted?arrow_forward
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