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

Define tree ?, A tree is a non-empty set one component of which is designat...

A tree is a non-empty set one component of which is designated the root of the tree while the remaining components are partitioned into non-empty groups each of which is a subtree

How does an array differ from an ordinary variable, Normal 0 fa...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Lists, In the earlier unit, we have discussed about the arrays. Arrays are ...

In the earlier unit, we have discussed about the arrays. Arrays are data structures of fixed size. Insertion & deletion involves reshuffling of array elements. Thus, arraymanipulat

Define a procedure called make-avl-tree, This question deals with AVL trees...

This question deals with AVL trees. You must use mutable pairs/lists to implement this data structure: (a) Define a procedure called make-avl-tree which makes an AVL tree with o

Algorithm, give me algorithm of simple interest

give me algorithm of simple interest

Implementing abstract data types, Implementing abstract data types A co...

Implementing abstract data types A course in data structures and algorithms is hence a course in implementing abstract data types. It may seem that we are paying a lot of atten

Adjacency matrix representation of a graph, An adjacency matrix representat...

An adjacency matrix representation of a graph cannot having information of : Parallel edges

Stack, implement multiple stacks ina single dimensional array. write algori...

implement multiple stacks ina single dimensional array. write algorithams for various stack operation for them.

Complexity of an algorithm, compare two functions n and 2n for various valu...

compare two functions n and 2n for various values of n. determine when second becomes larger than first

Flowcharts, draw a flowchart which prints all the even numbers between 1-50...

draw a flowchart which prints all the even numbers between 1-50

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