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

Several operations on a aa-tree, The following are several operations on a ...

The following are several operations on a AA-tree: 1. Searching: Searching is done using an algorithm which is similar to the search algorithm of a binary search tree. 2. Ins

Problem logicall, Given a list containing Province, CustomerName and SalesV...

Given a list containing Province, CustomerName and SalesValue (sorted by Province and CustomerName), describe an algorithm you could use that would output each CustomerName and Sal

Give the example of bubble sort algorithm, Give the example of bubble sort ...

Give the example of bubble sort algorithm For example List: - 7 4 5 3 1. 7 and 4 are compared 2. Since 4 3. The content of 7 is now stored in the variable which was h

Representation of sets?, A set s is conveniently shown in a computer store ...

A set s is conveniently shown in a computer store by its characteristic function C(s). This is an array of logical numbers whose ith element has the meaning "i is present in s". As

Dqueue, how can i delete from deque while deletion is restricted from one e...

how can i delete from deque while deletion is restricted from one end

Explain graph traversal, Graph Traversal In many problems we wish to in...

Graph Traversal In many problems we wish to investigate all the vertices in a graph in some systematic order. In graph we often do not have any single vertex singled out as spe

Graph, explain the prims''s algorithm with suitable example?

explain the prims''s algorithm with suitable example?

C++ function, Write c++ function to traverse the threaded binary tree in in...

Write c++ function to traverse the threaded binary tree in inorder traversal

Tree traversals, There are three kinds of tree traversals, namely, Postorde...

There are three kinds of tree traversals, namely, Postorder , Preorder and Inorder. Preorder traversal: Each of nodes is visited before its children are visited; first the roo

Estimate cost of an optimal diapath, Normally a potential y satisfies y r ...

Normally a potential y satisfies y r = 0 and 0 ³ y w - c vw -y v . Given an integer K³0, define a K-potential to be an array y that satisfies yr = 0 and K ³ y w - c vw -y v

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