3)ANSWER:
GIVEN THAT:
We begin by considering a 3- heap
for index k
parent(k)= (k-1)/3
child-0(k)= (3*k)+1
child-1(k)= (3*k)+2
child-2(k)= (3*k)+3
3. We begin by considering a 3-heap (a heap where each node has at most 3...
Assume that a heap is implemented using an array called items where the root of the heap is stored in items[0]. Provide the mathematical proof of the following formulas that calculate the indices of the children and parent of any node items[i]. Left child of items[i] is items [2xi + 1] - Right child of items[i] is items [2xi + 2] Parent of items[i] is items[[(i-1)/2]]
1. Which of the following is a proper array representation a binary min heap?2. A heap is implemented using an array. At what index will the right child of node at index i be found? Note, the Oth position of the array is not used.Select one:a. i/2b. 2 i+1c. i-1d. 2 i3. Consider the following array of length 6. Elements from the array are added, in the given order, to a max heap. The heap is initially empty and stored as an array.A={18,5,37,44,27,53}What...
Write a C program insertion and deletion functions for a max heap represented as a linked binary tree. Assume that each node has a parent field as well as the usual left child, right child, and key fields. -Condition : Do not use Array representation. Use the following structure. typedef struct node *treePointer; typedef struct node { int key; treePointer parent; treePointer leftChild, rightChild; }; - INPUT i k : Insert the node with the key value of k in...
Write a C program insertion and deletion functions for a max heap represented as a linked binary tree. Assume that each node has a parent field as well as the usual left child, right child, and key fields. -Condition : Do not use Array representation. Use the following structure. typedef struct node *treePointer; typedef struct node { int key; treePointer parent; treePointer leftChild, rightChild; }; - INPUT i k : Insert the node with the key value of k in...
Task: A ternary heap is like a binary heap, except instead of each node having a max of two children, each node has a max of three children. Given a ternary min heap, return true if it is a valid heap. That is, it satisfies the heap property (the parent is less than all of its children) Requirements: Implement an isValidHeap function to determine whether a particular array of integers constitutes a valid ternary min-heap. bool isValidHeap(int arr[])// example declaration...
In class, we discussed the priority queue (PQ) ADT implemented using min-heap. In a min-heap, the element of the heap with the smallest key is the root of the binary tree. On the other hand, a max-heap has as root the element with the biggest key, and the relationship between the keys of a node and its parent is reversed of that of a min-heap. We also discussed an array-based implementation of heaps. In this assignment, your task is to...
Using C++, data structures, C++ STL, inputs and expected
outputs are shown below.
Max Heap Heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either > (in a max heap) or s (in a min heap) the key of C. The node at the "top" of the heap (with no parents) is called the root node. In binary-tree based heap, it...
5. A three-heap with n elements can be stored in an array A, where A[O] contains the root of the tree. a) Draw the three-heap that results from inserting 5, 2, 8, 3, 6, 4, 9, 7, 1 in that order into an initially empty three-heap. You do not need to show the array representation of the heap. You are only required to show the final tree, although if you draw intermediate trees. b) Assuming that elements are placed in...
SECTION B (4 QUESTIONS, 90 MARKS) Question 4. [32 marks in total] For this question, assume the definition of Java class Heap given in the Appendix. The heaps referred to in this question are all maxHeaps. a. (5 marks) Insert into an empty (binary) heap the values 35, 4, 72, 36, 49, 50. Draw all intermediate steps b. (3 marks) Carry out one deletion operation on the final heap in (a.) above. c. (2 marks) Give the worst-case time complexity...
For the purposes of this assignment, the Process Control Blocks (PCB) are implementation as follows: • PCBs are implemented as an array of structures (C++ struct) of size 10. • Each process is referred to by the array index. (i.e. PCB #0 is at PCB[0], PCB #1 is at PCB[1], etc.) Initially, PCB #0 is the only process that exists. All the other processes created build off of PCB #0; meaning they will either be a child of PCB #0...