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

Abstract data types, Abstract Data Types :- A useful tool for specifying th...

Abstract Data Types :- A useful tool for specifying the logical properties of a data type is the abstract data type or ADT. The term "abstract data type" refers to the basic mathem

Push and pop operations, Q. Explain that how do we implement two stacks in ...

Q. Explain that how do we implement two stacks in one array A[1..n] in such a way that neither the stack overflows unless the total number of elements in both stacks together is n.

Array implementation of a queue, Since the stack is list of elements, the q...

Since the stack is list of elements, the queue is also a list of elements. The stack & the queue differ just in the position where the elements may be added or deleted. Similar to

Preliminaries, Think of a program you have used that is unacceptably slow. ...

Think of a program you have used that is unacceptably slow. Identify the specific operations that make the program slow. Identify other basic operations that the program performs q

Write an algorithm to illustrate this repeated calculation, The below formu...

The below formula is used to calculate n: n = (x * x)/ (1 - x). Value x = 0 is used to stop the algorithm. Calculation is repeated using values of x until value x = 0 is input. The

Hash function, Q. Define the graph, adjacency matrix, adjacency list, hash ...

Q. Define the graph, adjacency matrix, adjacency list, hash function, adjacency matrix, sparse matrix, reachability matrix.

Explain depth-first traversal, Depth-first traversal A depth-first t...

Depth-first traversal A depth-first traversal of a tree visit a node and then recursively visits the subtrees of that node. Likewise, depth-first traversal of a graph visits

Merge sort, #question. merging 4 sorted files containing 50,10,25,15 record...

#question. merging 4 sorted files containing 50,10,25,15 records will take time?

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