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

Explain all-pair shortest-paths problem, Explain All-pair shortest-paths pr...

Explain All-pair shortest-paths problem Given a weighted linked graph (undirected or directed), the all pairs shortest paths problem asks to find the distances (the lengths of

Implement a min-heap, Description A heap is an efficient tree-based data...

Description A heap is an efficient tree-based data structure that can be used as a priority queue. Recall that the abstract data type of a priority queue has the following opera

Representation of records, Records are mapped onto a computer store by simp...

Records are mapped onto a computer store by simply juxtaposing their elements. The address of a component (field) r relative to the origin address of the record r is named the fiel

Compute the shortest paths to all network nodes, (i)  Consider a system usi...

(i)  Consider a system using flooding with hop counter. Suppose that the hop counter is originally set to the "diameter" (number of hops in the longest path without traversing any

Graph connectivity, A connected graph is a graph wherein path exists among ...

A connected graph is a graph wherein path exists among every pair of vertices. A strongly connected graph is a directed graph wherein every pair of distinct vertices is connecte

Design a time algorithm, Q. An, array, A comprises of n unique integers fro...

Q. An, array, A comprises of n unique integers from the range x to y(x and y inclusive where n=y-x). Which means, there is only one member that is not in A. Design an O(n) time alg

Explain the concept of colouring, Colouring The use of colours in CAD/C...

Colouring The use of colours in CAD/CAM has two main objectives : facilitate creating geometry and display images. Colours can be used in geometric construction. In this case,

Multiple queue, What is multiple queue and explain them

What is multiple queue and explain them

Pseudo code, I need help writing a pseudocode for my assignment can anyone ...

I need help writing a pseudocode for my assignment can anyone help?

Creation of a linked list, Program: Creation of a linked list In the ne...

Program: Creation of a linked list In the next example, wewill look to the process of addition of new nodes to the list with the function create_list(). #include #includ

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