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

Define ordinary variable, Ordinary variable An ordinary variable of a e...

Ordinary variable An ordinary variable of a easy data type can store a one element only

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

Algorithm to add element in the end of circular linked list, Q. Write down ...

Q. Write down an algorithm to add an element in the end of the circular linked list.        A n s . Algo rithm to Add the Element at the End of Circular Linked Lists

Flow chart, that will determine the volume of the sphere or the volume of c...

that will determine the volume of the sphere or the volume of cone or volume of pyramid depending on the choice of the user

The various ways in which lc code can be accessed, Problem Your LC code...

Problem Your LC code is stored in a memory location as shown and the variable name is LC                  LC Memory address       Content(LC code)

Complexity of quick sort, Q. What do you mean by the best case complexity o...

Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?

Tic Tac Toe game , Book to refer: Introduction to Algorithms, 3rd Ed, by Cl...

Book to refer: Introduction to Algorithms, 3rd Ed, by Clifford Stein, Thomas H. Cormen, Ronald Rivest, Charles E. Leiserson Question: Tic Tac Toe game -Design a GUI and implement

Algorithmic implementation of multiple stacks, So far, we now have been con...

So far, we now have been concerned only with the representation of single stack. What happens while a data representation is required for several stacks? Let us consider an array X

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