Array-based representation of a binary tree, Data Structure & Algorithms

Assignment Help:

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

1724_Array-based representation of a Binary Tree.png

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

1

B

3

4

2

C

-1

-1

3

D

5

6

4

E

7

8

5

G

-1

-1

6

H

-1

-1

7

I

-1

-1

8

J

-1

-1

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.)


Related Discussions:- Array-based representation of a binary tree

Discuss the properties of adt, Question 1 Write a program in 'C' to rea...

Question 1 Write a program in 'C' to read N numbers and print them in descending order Question 2 Discuss the properties of ADT Question 3 Write a note on

Tradeoff between space and time complexity, We might sometimes seek a trade...

We might sometimes seek a tradeoff among space & time complexity. For instance, we may have to select a data structure which requires a lot of storage to reduce the computation tim

Pre-order and post order traversal of a binary tree, The pre-order and post...

The pre-order and post order traversal of a Binary Tree generates the same output. The tree can have maximum One node

Multiple stacks in a single array, implement multiple stacks in an array an...

implement multiple stacks in an array and write different algorithms to perform operations on it

Breadth first search, While BFS is applied, the vertices of the graph are d...

While BFS is applied, the vertices of the graph are divided into two categories. The vertices, that are visited as part of the search & those vertices that are not visited as part

The best average behaviour, The best average behaviour is shown by  Qui...

The best average behaviour is shown by  Quick Sort

Question, A binary search tree is used to locate the number 43. Which of th...

A binary search tree is used to locate the number 43. Which of the following probe sequences are possible and which are not? Explain. (a) 61 52 14 17 40 43 (b) 2 3 50 40 60 43 (c)

Rooted tree, It does not have any cycles (circuits, or closed paths), which...

It does not have any cycles (circuits, or closed paths), which would imply the existence of more than one path among two nodes. It is the most general kind of tree, and might be co

Explain about the string abstract data type operations, Explain about the S...

Explain about the String Abstract data type operations Symbol ADT has no concatenation operations, but presuming we have a full-featured String ADT, symbols can be concatenated

Average case anaysis, what is the impoartance of average case analysis of ...

what is the impoartance of average case analysis of algorithm

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd