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 first - fit method, First - Fit Method: -    The free list is trave...

First - Fit Method: -    The free list is traversed sequentially to search the 1st free block whose size is larger than or equal to the amount requested. Once the block is found it

Algorithm, Define what an algorithm is and outline the characteristics of a...

Define what an algorithm is and outline the characteristics of a good algorithm.

Explain decision tree, Decision Tree A decision tree is a diagram that ...

Decision Tree A decision tree is a diagram that shows conditions and actions sequentially and therefore shows which condition is to be considered first, second and so on. It is

Generate a single sorted list of all n elements, Q. Assume that we have sep...

Q. Assume that we have separated n elements in to m sorted lists. Explain how to generate a single sorted list of all n elements in time O (n log m )?

Data searching, In file access: what is the difference between serial, seq...

In file access: what is the difference between serial, sequential and indexed sequential searching

Pseudocodes, how to draw a 5 inch square on the screen using * symbol

how to draw a 5 inch square on the screen using * symbol

Storing street addresses with doubly linked lists, Write a C++ program with...

Write a C++ program with header and source les to store street addresses using the Doubly Linked List ADT. Modify the Node class from Lab Assignment 3 so that it becomes a node in

Graph traversal schemes, Q. Explain various graph traversal schemes and wri...

Q. Explain various graph traversal schemes and write their advantages and disadvantages. A n s . Graph Traversal Scheme is explained below In many troubles we wish

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