A binary heap is called a max heap if it has the property that for every node i other than the root, the value of the node is at most the value of its parent. Let P be a permutation of the first 7 positive integers. Sometimes this permutation is a max heap; examples include [7,6,5,4,3,2,1], [7,6,4,2,5,1,3], [7,5,6,2,4,3,1], and [7,3,6,2,1,4,5]. If P is a randomly-chosen permutation of [1,2,3,4,5,6,7], determine the probability that it is a max heap. Clearly and carefully justify your answer.

Q: Assume you are given n different values to store in a complete heap—a heap kept in a full binary…

A: A binary tree is defined as a rooted tree which is also an ordered tree in which every node has at…

Q: In a stack, (size of 1 to n) the comm access ith element from the top of the stack S will be known…

A: The Answer is in Below Steps

Q: Let H1 and H2 be two (binary) max-heaps with n1 and n2 elements respectively. If every element in H1…

A: Answer: To merge two binary max-heaps H1 and H2 with n1 and n2 elements respectively, such that…

Q: Suppose that binary heaps are represented using explicit links. Give a simple algorithm to find the…

A: Below is the method:- node * find( node *root, index i) { 1. B = binary(i); //B will be array of 0…

Q: Suppose we use a 0-based array h[] to implement a heap of 200 elements. If an element of the heap is…

A: Heap Tree - It is a non linear data structure or tree based data structure which stores the elements…

Q: Given a heap that contains 128 nodes, the height of the heap rooted at level 4 is TEULVIO a. 3 b.…

A: height of the heap:-   Height of a node in a heap to the number of edges and the longest simple…

Q: a. Suppose array S = [10, 12, 1, 14, 6, 5, 8, 15, 3, 9, 7, 4, 11, 13, 2]. Show the result of a…

A: Min-Heap: A Min-Heap is a complete binary tree in which the value in each internal node is smaller…

Q: You are expected to create a maximum heap data structure by inserting the 32, 15, 20, 30, 12, 25, 16…

A: The answer is given below.

Q: eap, represented by the 0, 15, 16, 17, 8, 4. 3 4 5 6 7 8 2010 15 16 17 8

A:

Q: Demonstrate, step by step, how to sort a list of integers (2, 4, 1, 5, 6, 7) using a max-heap,…

A: Every thing is explained in the images follow the images   For reference: After building the heap…

Q: gorithm emonstrate, step by step, how to construct a max-heap for the list of integers 1..8] = (12,…

A: Solution:

Q: Mapping the elements of a heap into an array is straightforward: assuming that the root node is…

A: The java code for mapping the elements of a heap into an array is straightforward: assuming that the…

Q: Consider an unsorted array of n elements. Recall that the Heapsort Algorithm consists of two parts:…

A:

Q: except that nodes can have up to d children. Suppose d= 3, insert the following items into a max…

A: As d is 3 so maximum possible children are 3. Now let us understand what is a max heap. In max heap,…

Q: Suppose you have started with a list of numbers and have built the following max-heap: 75 3 4 2 1.…

A: To Do: To find the first and second swaps.

Q: Sketch your algorithm. (List all the steps)

A: Solution a) Let's build a Max-Heapify. A Max-heapify is a process of arranging the nodes in the…

Q: A heap is represented using an array. Is the array [1, 2, 4, 5, 9, 3] a heap? True False

A: To state True or false. Is the array [1,2,4,5,9,3] a heap.

Q: 4. You've probably seen in previous courses how to build a min-heap on n elements in O(n) time and…

A: Note - As per the guidelines we are only allowed to answer 1 question at a time. Build_Heap takes…

Q: Show the result of inserting 10, 12, 1, 14,6, 5,8, 15,3,9,7, 4, 11, 13, and 2, one at a time, into…

A:

Q: Consider the binary heap that uses the following array a[ ]=[ 9, 7, 4, 2, 6, 1, 3] to store its…

A: binary heap

Q: Consider an unsorted array of n elements. Recall that the Heapsort Algorithm consists of two parts:…

A:

Q: Illustrate the execution of the heap-sort algorithm on the following sequence:…

A: The answer for the given question is as follows.

Q: Given the following array of numbers, draw max the heap which is constructed after adding all the…

A: Here is the max heap for the array above:

Q: Suppose we have to do m inserts and n deletions, starting from an empty heap. When would it be more…

A: 1) A binary heap is a binary tree that satisfies the heap property, which means that the value of…

Q: Starting with an empty priority queue, represented as heap, draw the heap that results from: enqueue…

A:

Q: operations.

A: Actually, the code has given below:

Q: Given the following binary heap, represented with the array (1, 3, 5, 7, 9), indicate which would be…

A: A binary heap can be either a maximum or minimum heap. The root key of a min binary heap must be the…

Q: Suppose that we have some binary heaps that are represented using linked binary tree structures.…

A:

Q: 3-heap

A: Step 1:-  In the Step 1st we need to write all the element in the array representation.  Step 2:-…

Q: Consider an unsorted array of n elements. Recall that the Heapsort Algorithm consists of two parts:…

A:

Q: A d-heap is similar to a binary heap, except that nodes can have up to d children. Suppose d= 3,…

A: Given that, d-heap is similar to binary heap except that nodes can have up to d children. The value…

Q: please illustrate the process of HEAPSORT with A = [50, 30, 37, 22, 7, 9, 5]. Here, BUILD-MAX-HEAP…

A: Max Heap : A complete binary tree called a max heap has nodes whose values are greater than or equal…

Q: Show how you can implement insert in O(log n) time in a binary heap.

A: Here is the Answer and Explanation

Q: The Heap [2, 13, 10, 9, 1, 5, 6, 7] violates the "Max Heap" property. What will the heap become…

A: Max_heapify is a process of arranging the nodes in correct order so that they follow max_heap…

Q: 10. Instead of a binary heap, we could implement a d-ary heap, which uses d-ary tree. In such a…

A: The answer to the question is given below:

Q: s Inserting into a heap-based priority queue is O(n) because you have to traverse to find the right…

A: Given a question of heap and queues. This falls under Data Structures and Algorithms A heap is a…

Q: A max-heap is a heap where the value of each parent is greater than or equal to the value of its…

A: In a Max-Heap the key present at the root node must be greater than or equal among the keys present…

Q: 5. Demonstrate, step by step, how to construct a max-heap for the list of integers A[1..8] = (12, 8,…

A: 5.) We will insert node and swap with parent node only if parent node is smaller than child node.

Q: Given the following incorrect heap:

A: Consider the given data :

Heap Sort

A Heap is a type of data structure that is built on trees. It's a binary tree that's virtually complete. Except for the very bottom level, all levels of the tree must be filled in a heap. The last (bottom) level should be filled from left to right. The heap data structure is used for the efficient implementation of priority queues.Heap can be of two types: