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

Four applications or implementation of the stack, Q. Write down any four ap...

Q. Write down any four applications or implementation of the stack.                                     Ans. (i)       The Conversion of infix to postfix form (ii)

Abstract data type-tree, Definition: A set of data values & related operati...

Definition: A set of data values & related operations that are accurately specified independent of any particular implementation. As the data values and operations are described

Multiqueue, data structure for multiqueue

data structure for multiqueue

Sorting, Sort the following array of elements using quick sort: 3, 1, 4, 1,...

Sort the following array of elements using quick sort: 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8.

State in brief about assertion, State  in brief about assertion Asser...

State  in brief about assertion Assertion: A statement which should be true at a designated point in a program.

Deletion algorithm for dequeue, Deletion Algorithm for dequeue Step 1:...

Deletion Algorithm for dequeue Step 1: [check for underflow]   If front = 0 and rear = 0   Output "underflow" and return Step 2: [delete element at front end]   If front

Representation of a sparse matrix, Let us assume a sparse matrix from stora...

Let us assume a sparse matrix from storage view point. Assume that the entire sparse matrix is stored. Then, a significant amount of memory that stores the matrix consists of zeroe

Name the five popular hashing functions, Five popular hashing functions are...

Five popular hashing functions are as follows: 1) Division Method 2) Midsquare Method 3) Folding Method 4) Multiplicative method 5) Digit Analysis

BST has two children, If a node in a BST has two children, then its inorder...

If a node in a BST has two children, then its inorder predecessor has No right child

Collision resolution techniques, complete information about collision resol...

complete information about collision resolution techniques

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