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

Pseudocodes, how to draw a 5 inch square on the screen using * symbol

how to draw a 5 inch square on the screen using * symbol

Advanced trees, Linked list representations contain great advantages of fle...

Linked list representations contain great advantages of flexibility on the contiguous representation of data structures. However, they contain few disadvantages also. Data structur

In order post order, illlustraate the construction of tree of a binary tree...

illlustraate the construction of tree of a binary tree given its in order and post order transversal

Complexity of quick sort, Q. What do you mean by the best case complexity o...

Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?

Enumerate about the carrier set members, Enumerate about the carrier set me...

Enumerate about the carrier set members Ruby is written in C, so carrier set members (which is, individual symbols) are implemented as fixed-size arrays of characters (which is

Indexed sequential files, Indexed Sequential Files An index is inserted...

Indexed Sequential Files An index is inserted to the sequential file to provide random access. An overflow area required to be maintained to permit insertion in sequence. I

Rules for abstract data type-tree, null(nil) = true                     // ...

null(nil) = true                     // nil refer for empty tree null(fork(e, T, T'))= false   //  e : element , T and T are two sub tree leaf(fork(e, nil, nil)) = true leaf(

Algorithm for sorting a deck of cards, What is wrong with the following alg...

What is wrong with the following algorithm for sorting a deck of cards (considering the basic properties of algorithms)? I. Put the cards together into a pile II. For each ca

Acyclic graph, Tree is a widely used data structure employed for representi...

Tree is a widely used data structure employed for representing several problems. We studied tree like a special case of acyclic graph. Though, rooted trees are most prominent of al

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