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
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
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)
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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- 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.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_forwardCreate a Max-Heap from the following data 3, 8, 10, 7, 20 Show (in detail) for each steparrow_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_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_forwardpython This question is on heapsort. (a) We aim to construct a max heap based on an array A. When we call heapify(A,i) for i > size(A)/2, what will happen? (b) Assuming the elements in the array A are in a decreasing order, what is the running time of heapsort on A (using a max heap when constructing the heap)?arrow_forward
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