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

Registers, what are registers? why we need register? Definition? Types? Wha...

what are registers? why we need register? Definition? Types? What registers can do for us?

Algorithm, implement multiple stack in one dimensional array

implement multiple stack in one dimensional array

Make adjacency matrix for un-directed graph, Q. Describe the adjacency matr...

Q. Describe the adjacency matrix and make the same for the given undirected graph.    Ans: The representation of Adjacency Matrix: This representation consists of

Explain about the string abstract data type operations, Explain about the S...

Explain about the String Abstract data type operations Symbol ADT has no concatenation operations, but presuming we have a full-featured String ADT, symbols can be concatenated

Postfix expression, : Write an algorithm to evaluate a postfix expression. ...

: Write an algorithm to evaluate a postfix expression. Execute your algorithm using the following postfix expression as your input: a b + c d +*f ­ .

Sorted list using binary search technique, Write an algorithm for searching...

Write an algorithm for searching a key from a sorted list using binary search technique 1.   if (low > high) 2.     return (-1) 3.    mid = (low +high)/2; 4    .if ( X

Doubly linked list having n nodes, The time required to delete a node x fro...

The time required to delete a node x from a doubly linked list having n nodes is O (1)

Threaded binary tree, i need the full concept of it... please can anyone pr...

i need the full concept of it... please can anyone provide

Chaining Method as Method of Collision Resolution , Q. The given values are...

Q. The given values are to be stored in a hash table 25, 42, 96, 101, 102, 162, 197 Explain how the values are hashed by using division technique of hashing with a table

Operations on sequential files, Insertion: Records has to be inserted at t...

Insertion: Records has to be inserted at the place dictated by the sequence of keys. As is obvious, direct insertions into the main data file would lead to frequent rebuilding of

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