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 6.3, Problem 1E
Program Plan Intro
To illustrate the operation of BUILD-MAX-HEAP on the array
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// Suppose we have the following min-heap:// 2, 3, 4, 16, 7, 11, 9, 31, 18, 21, 12// After calling delFront(), the min-heap now looks as follows:// 3, 7, 4, 16, 12, 11, 9, 31, 18, 21
In java language
in a min heap create a method that deletes the min element
all details under method with examples
please and thank you
essentially just a method that deletes the min number and resorts the heap
This question is about heap.a. Suppose array S = [10, 12, 1, 14, 6, 5, 8, 15, 3, 9, 7, 4, 11, 13, 2]. Show the result of a min-heap after heaplifying the array S.b. Suppose 0 is inserted to the result of (a). Show the result of the min-heap after insertion.c. Suppose the root of the min-heap in (b) is removed twice. Show the result after each deletion.
Show a merge of the following skew heaps.
(Show each step).
h1
h2
19
11
54
39
12
30
61 65 68
30
14 50
59
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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- multiple choice: consider an array based implementation of a stack and its push operation. Beginning with an array of length 1 = (2^0), consider where the array’s length will be doubled whenever an insertion(via the push operation) is attempted when the array is full. What is the amortized complexity of performing a sequence of n push operations. a) Θ(log n) b) Θ(n) c) Θ(n^2) d) Θ(1)arrow_forwardPlease assume that you have been given an implementation of a stack that supports both push and pop in O(1) time. With this information, you would like to implement a queue with these stacks. (a) In what way can you efficiently implement a queue using two of these stacks? “Efficiently” in this case means in a way which will allow you to do part B. (b) Please prove that the amortized cost of each dequeue and enqueue operation is O(1) for your stack-based queue by using the aggregate amortized analysis technique.arrow_forwardConsider the following max-heap: [1, 2, 3, 4, 5, 6, 7, 8] Use Floyd’s “heapifying” algorithm to convert the heap into a min-heap. Show the resulting array and all steps.arrow_forward
- Use the procedure MAX-HEAPIFY in a bottom-up manner to convert the array A = <1, 4, 3, 5, 8, 9, 0, 7, 2, 6> to build a max heaparrow_forwardb) Given the following arrays, which ones could represent a max-heap? Choose all that apply. Assume the indices start from 1. {23, 17, 14, 6, 13, 10, 1, 12, 7, 5} {23, 17, 14, 6, 13, 10, 1, 5, 7, 12} . {23, 17, 14, 7, 13, 10, 1, 5, 6, 12} {23, 17, 14, 7, 13, 10, 1, 12, 5, 7}arrow_forwardCreate a Max-Heap from the following data 3, 8, 10, 7, 20 Show (in detail) for each steparrow_forward
- A 4-ary max heap is like a binary max heap, but instead of 2 children, nodes have 4 children. A 4-ary heap can be represented by an array as shown in Figure (up to level 2). Write down MAX_HEAPIFY(A,i) function for a 4-ary max-heap that restores the heap property for ith node.arrow_forwardConsider the following infix expression.( 5 + 8 ) * 9 – 7 * 10 + 9.Apply infix-to-postfix conversion algorithm to generate the correspondingpostfix expression from the given infix expression. You have to show thecontent of stack at each stage of conversion.arrow_forward2) Using Fig. 6.4 as a model, illustrate theoperation of HeapSort on the array ? = {3, 4, 2, 3, 1, 6, 5, 7, 5}.arrow_forward
- Given the array: 63 53 86 35 99 34 75 Heapify into a max-heap. Ex: 86, 75, 30arrow_forwardAlgorithm 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. Example 4.14 Demonstrate, step by step, how to construct a max-heap for the list of integers A[1..8] = (10, 8, 14, 15, 12,5, 6, 1). Assume the heap is empty initially. 10 10 8 8 14 8 10 8 10 15 10 14 10 (a) (b) (c)i (c)i 15 (d)i 8 (d)i (dji 15 15 15 15 10 8 12 8 12 5 8 12 5 6 12 5 6 (e) (1) (g) 1 (h)arrow_forwardConsider a fixed-size circular array-based implementation of the LRU quasi-stack. Explain step-by-step the algorithm to keep the last referenced page at the top of the stack. Note that the page being referenced may, but does not need to, be already in the stack. Your algorithm must handle both cases. What is the complexity of updating the stack on each new page reference? That is, how many operations are required to add a new page number at the top, or to move an already existing page number from some location in the stack to the top?arrow_forward
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