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

Cohen sutherland algorithm, Using the cohen sutherland. Algorithm. Find the...

Using the cohen sutherland. Algorithm. Find the visible portion of the line P(40,80) Q(120,30) inside the window is defined as ABCD A(20,20),B(60,20),C(60,40)and D(20,40)

Representation of linked list in memory, Representation of Linked list in M...

Representation of Linked list in Memory:- Each node has an info part and a pointer to the next node also known as link. The number of pointers is two in case of doubly linked

Merging 4 sorted files containing 50, Merging 4 sorted files having 50, 10,...

Merging 4 sorted files having 50, 10, 25 and 15 records will take time  O (100)

Design and implement a software system, In this assignment, you are invited...

In this assignment, you are invited to design and implement a software system for catalogue sale. A catalogue is organised in a tree structure. Each node of the catalogue tree repr

Graph, adjacency multilist

adjacency multilist

Write an algorithm to find outputs number of cars, A company is carrying ou...

A company is carrying out a survey by observing traffic at a road junction. Every time a car, bus or lorry passed by road junction it was noted down. 10 000 vehicles were counted d

Explain how two dimensional arrays are represented in memory, Explain how t...

Explain how two dimensional arrays are represented in memory. Representation of two-dimensional arrays in memory:- Let grades be a 2-D array as grades [3][4]. The array will

Draw a flowchart that takes temperatures input, Write an algorithm in form ...

Write an algorithm in form of a flowchart that takes temperatures input over a 100 day period (once per day) and outputs the number of days when temperature was below 20C and numbe

Sparse matrix, memory address of any element of lower left triangular spars...

memory address of any element of lower left triangular sparse matrix

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