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 search using iterative deepening, Prove that uniform cost search and ...

Prove that uniform cost search and breadth- first search with constant steps are optimal when used with the Graph-Search algorithm (see Figure). Show a state space with varying ste

File organisation, File organisation might be described as a method of stor...

File organisation might be described as a method of storing records in file. Also, the subsequent implications approaching these records can be accessed. Given are the factors invo

Define different types of sparse matrix, Q1. Define a sparse matrix. Explai...

Q1. Define a sparse matrix. Explain different types of sparse matrices? Evaluate the method to calculate address of any element a jk of a matrix stored in memory. Q2. A linear

Avl tree, Example: (Single rotation into AVL tree, while a new node is inse...

Example: (Single rotation into AVL tree, while a new node is inserted into the AVL tree (LL Rotation)) Figure: LL Rotation The rectangles marked A, B & C are trees

What is bubble sort, What is bubble sort? Bubble Sort: The basic ide...

What is bubble sort? Bubble Sort: The basic idea in bubble sort is to scan the array to be sorted sequentially various times. Every pass puts the largest element in its corr

Elaborate the symbols of abstract data type, Elaborate the symbols of abstr...

Elaborate the symbols of abstract data type length(a)-returns the number of characters in symbol a. capitalize(a)-returns the symbol generated from a by making its first cha

How to write binary search algorithm?, Q. Write down the binary search algo...

Q. Write down the binary search algorithm and trace to search element 91 in following given list: 13          30          62           73         81         88             91

State hsv colour model, HSV Colour Model Instead of a set of colour pri...

HSV Colour Model Instead of a set of colour primaries, the HSV model uses colour descriptions that have a more intuitive appeal to a user. To give a colour specification, a use

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