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

Push and pop operations, Q. Explain that how do we implement two stacks in ...

Q. Explain that how do we implement two stacks in one array A[1..n] in such a way that neither the stack overflows unless the total number of elements in both stacks together is n.

Array, how to define the size of array

how to define the size of array

Linked list, Write a program for reversing the Linked list

Write a program for reversing the Linked list

Multilist file organisation, what is multilist length file organisation? ex...

what is multilist length file organisation? explain with an example

Determine the space complexity of euclid algorithm, 1)      Why space compl...

1)      Why space complexity is comparatively more critical than time complexity? 2)      Determine the space complexity of Euclid Algorithm?

Give the example of bubble sort algorithm, Give the example of bubble sort ...

Give the example of bubble sort algorithm For example List: - 7 4 5 3 1. 7 and 4 are compared 2. Since 4 3. The content of 7 is now stored in the variable which was h

Type of qualitative method, Type of Qualitative Method: Different  qua...

Type of Qualitative Method: Different  qualitative methods are suitable for different  types of study. Quite often we can  combine  qualitative and quantitative  methods. Many

Structures for complete undirected graphs, Q. Draw  the structures of compl...

Q. Draw  the structures of complete  undirected  graphs  on  one,  two,  three,  four  and  five vertices also prove that the number of edges in an n vertex complete graph is n(n-1

A bst is traversed in which order recursively, A  BST is traversed in the ...

A  BST is traversed in the following order recursively: Right, root, left e output sequence will be in In Descending order

Algorithms, write short note on algorithms

write short note on algorithms

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