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

Graph with n vertices will absolutely have a parallel edge, A graph with n ...

A graph with n vertices will absolutely have a parallel edge or self loop if the total number of edges is greater than n-1

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

Write procedure to the insert a node into the linked list, Q. Write a proce...

Q. Write a procedure to the insert a node into the linked list at a particular position and draw the same by taking an example?

Tower of hanoi, how do we use 4-discs stack to solve tower of hanoi problem...

how do we use 4-discs stack to solve tower of hanoi problem and write an algorithm to solve it?

Flow chart, that will determine the volume of the sphere or the volume of c...

that will determine the volume of the sphere or the volume of cone or volume of pyramid depending on the choice of the user

Stack, Explain the array and linked list implementation of stack

Explain the array and linked list implementation of stack

The searching technique that takes o (1) time to find a data, The searching...

The searching technique that takes O (1) time to find a data is    Hashing is used to find a data

Determine the complexity, 1)    The set of the algorithms whose order is O ...

1)    The set of the algorithms whose order is O (1) would run in the identical time.  True/False 2)    Determine the complexity of the following program into big O notation:

Define midsquare method, Midsquare Method :- this operates in 2 steps. In t...

Midsquare Method :- this operates in 2 steps. In the first step the square of the key value K is taken. In the 2nd step, the hash value is obtained by deleting digits from ends of

Hotel reservation system, pls i want a psuedo code for hotel reservation sy...

pls i want a psuedo code for hotel reservation system.

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