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Assume a complete binary tree T with n nodes where each node has an item (value). Label the nodes of the complete binary tree T from top to bottom & from left to right 0, 1, ..., n-1. Relate with T the array A where the ith entry of A is the item in the node labeled i of T, i = 0, 1, ..., n-1. Table illustrates the array representation of a Binary tree of Figure
Given the index i of a node, we can efficiently & easily compute the index of its parent and left & right children:
Index of Parent: (i - 1)/2, Index of Left Child: 2i + 1, Index of Right Child: 2i + 2.
Node #
Item
Left child
Right child
0
A
1
2
B
3
4
C
-1
D
5
6
E
7
8
G
H
I
J
9
?
Table: Array Representation of a Binary Tree
First column illustrates index of node, second column contain the item stored into the node & third & fourth columns mention the positions of left & right children
(-1 shows that there is no child to that specific node.)
Assertions and Abstract Data Types Even though we have defined assertions in terms of programs, notion can be extended to abstract data types (which are mathematical entities).
Let us assume a file of 5 records that means n = 5 And k is a sorted array of keys of those 5 records. Let key = 55, low = 0, high = 4 Iteration 1: mid = (0+4)/2 = 2
Explain principle of Optimality It indicates that an optimal solution to any instance of an optimization problem is composed of optimal solutions to its subinstances.
State in detail about the Integer Carrier set of the Integer ADT is the set {..., -2, -1, 0, 1, 2, ...}, and operations on these values are addition, multiplication, subtrac
Q. Reverse the order of the elements on a stack S (i) by using two additional stacks (ii) by using one additional queue. Ans : L e t S be the stac
In this project you will write a program to produce a discrete time simulation of a queue as shown in Fig. 1. Time is slotted on the input and the output. Each input packet follows
This unit discussed about data structure called Arrays. The easiest form of array is a one-dimensional array which may be described as a finite ordered set of homogeneous elements
Write a C++ program with header and source les to store street addresses using the Doubly Linked List ADT. Modify the Node class from Lab Assignment 3 so that it becomes a node in
Q. Construct a binary tree whose nodes in inorder and preorder are written as follows: Inorder : 10, 15, 17, 18, 20, 25, 30, 35, 38, 40, 50 Preorder: 20, 15, 10
Example of pre order traversal: Reading of a book, since we do not read next chapter unless we complete all sections of previous chapter & all its sections. Figure : Rea
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