a) Construct an initial min-heap from the given initial sequence above, based on the Heap Initialization with Sink technique learnt in our course. Draw this initial min-heap. NO steps of construction required. b) With heap sorting, a second min-heap can be reconstructed after removing the root of the initial min-heap above. A third min-heap can then be reconstructed after removing the root of the second min-heap. Represent these second and third min-heaps with array (list) representation in the table form below. NO steps of construction required

a) Construct an initial min-heap from the given initial sequence above, based on the Heap Initialization with Sink technique learnt in our course. Draw this initial min-heap. NO steps of construction required. b) With heap sorting, a second min-heap can be reconstructed after removing the root of the initial min-heap above. A third min-heap can then be reconstructed after removing the root of the second min-heap. Represent these second and third min-heaps with array (list) representation in the table form below. NO steps of construction required

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Problem 2: Binary search tree and min heap.(i) Write down an algorithm, which in time O(n), transforms a binary search tree Twith n elements into a heap which contains the same elements as T.(ii) Does there exist an algorithm, which in time O(n), transforms a heap K with nelements into a binary search tree which contains the same elements as K? Elaborate
Suppose we have p max heaps, with q elements in each. We wish to combine these into a single heap. Each of the following sub-parts describes one approach merging the heaps, and you are asked to derive the big O running time. MUST show derivation We create a new, empty heap H. From each of the input heaps, P, until P is empty we repeatedly remove the highest priority element using the heap delete method, and insert it into H using the heap insert method. What is the worst-case big O running time? Show derivation. We create a new, empty linked list L. For each of the input heaps, P, we iterate over its internal array and insert each element at the front of L. We then transfer the elements of L into an array, and heapify the array using repeated sift downs. What is the worst-case running time? Show derivation. We divide the p input heaps into p/2 pairs, and apply the algorithm from part (b) on each pair, resulting in p/2 heaps. We then repeat this process until we are left with a…
3. Неаps In PS1, we worked with an Extract-Insert-Stable (EIS) min heap which was defined as a min heap with no duplicate elements where the result of calling ExtractMin and immediately re-inserting the same element was the original heap. In this question we want to consider a related concept Insert-Extract-Stability IES. The pair (H, x) is the combination of min heap H with no duplicate elements and an element x. The pair is together considered IES if the result of inserting x into H and immediately calling ExtractMin results in the original heap H. (a) Formally describe the relationship between the elements of H and also the new element x so that (H, x) is IES. (b) Prove that your description holds by showing that it applies to all IES (H,x) pairs and does not hold for any (H, x) which is not IES.
9. Aa operater delete for a binary heap data structure is to be designed to delete the item in the i-h node. Assume that dhe heap is implemented in an armay and i refers to the a inder of the amay. If the heap tree bas depth d (number of adges on the path from the root to the farthest leaf), thea what is the time complexity to re-fx the heap efficiently ater the removal of the clement?
1. Insert the following elements in the given order to an empty binary (d = 2) max-heap. Draw out the tree representation of the heap after all elements are inserted. Then, store the array representation of the heap in variable output located within the method insertion Result. Elements to insert: [45, 22, 36, 50, 87, 25, 79, 51, 95, 90, 104, 5]
Give only new solution.
Please show steps clearly
explain
Suppose we are given access to a min-heap, but not the code that supports it. What changes to the comparable data might we make to force themin-heap to work like a max-heap?
Fig 1.a : Insert 6 and redraw AVL tree in figure 1 Fig 1.b : After that, insert 9 and redraw also new AVL Tree---Fig 2.a Insert 1 and redraw Heap in fig 2.Fig 2.b : After that, remove a value from heap and redraw it.
Algorithm Demonstrate, step by step, how to construct a max-heap for the list of integers A[1..8] = (12, 8, 15, 5, 6, 14, 1, 10) (in the given order), following Example 4.14.
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