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

Array and two-dimensional array, Q. Describe the term array.  How do we rep...

Q. Describe the term array.  How do we represent two-dimensional arrays in memory?  Explain how we calculate the address of an element in a two dimensional array.

Explain the stack, QUESTION Explain the following data structures: ...

QUESTION Explain the following data structures: (a) List (b) Stack (c) Queues Note : your explanation should consist of the definition, operations and examples.

What is binary space partition, Binary Space Partition A binary space-p...

Binary Space Partition A binary space-partitioning (BSP) tree is an efficient method for determining object visibility by painting surfaces onto the screen from back to front,

Depth First Search Through Un-weighted Connected Graph , Q. Write down the ...

Q. Write down the algorithm which does depth first search through an un-weighted connected graph. In an un-weighted graph, would breadth first search or depth first search or neith

Multiple stack, implement multiple stack in single dimensionl array.write a...

implement multiple stack in single dimensionl array.write algorithms for various stack operation for them

Memory mapping, lower triangular matrix and upper triangular matrix

lower triangular matrix and upper triangular matrix

Spanning trees, Spanning Trees: A spanning tree of a graph, G, refer to a ...

Spanning Trees: A spanning tree of a graph, G, refer to a set of |V|-1 edges which connect all vertices of the graph. There are different representations of a graph. They are f

Define the internal path length, Define the Internal Path Length The In...

Define the Internal Path Length The Internal Path Length I of an extended binary tree is explained as the sum of the lengths of the paths taken over all internal nodes- from th

Compound interest, Write the algorithm for compound interest

Write the algorithm for compound interest

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