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

Need it urgently, Write an assembly program to separate the number of posit...

Write an assembly program to separate the number of positive numbers and negative numbers from a given series of signed numbers.

Exact analysis of insertion sort, Exact analysis of insertion sort: Let...

Exact analysis of insertion sort: Let us assume the following pseudocode to analyse the exact runtime complexity of insertion sort. T j   is the time taken to execute the s

A binary tree in which levels except possibly the last, A binary tree in wh...

A binary tree in which if all its levels except possibly the last, have the maximum number of nodes and all the nodes at the last level appear as far left as possible, is called as

#titlestrings, given the string "Data Structures & , Algorithms", write a p...

given the string "Data Structures & , Algorithms", write a program that uses sequential search to return index of ''&''

How do collisions happen during hashing, How do collisions happen during ha...

How do collisions happen during hashing? Usually the key space is much larger than the address space, thus, many keys are mapped to the same address. Assume that two keys K1 an

Use of asymptotic notation in the study of algorithm, Q. What is the need o...

Q. What is the need of using asymptotic notation in the study of algorithm? Describe the commonly used asymptotic notations and also give their significance.

Undirected graph and adjacency matrix, Q. Consider the specification writte...

Q. Consider the specification written below of a graph G V(G ) = {1,2,3,4} E(G ) = {(1,2), (1,3), (3,3), (3,4), (4,1)} (i)        Draw the undirected graph. (

Kruskals algorithm, Krushkal's algorithm uses the concept of forest of tree...

Krushkal's algorithm uses the concept of forest of trees. At first the forest contains n single node trees (and no edges). At each of the step, we add on one (the cheapest one) edg

Binary search trees, A Binary Search Tree is binary tree which is either em...

A Binary Search Tree is binary tree which is either empty or a node having a key value, left child & right child. By analyzing the above definition, we notice that BST comes int

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

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