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

Explain principle of optimality, Explain principle of Optimality It ind...

Explain principle of Optimality It indicates that an optimal solution to any instance of an optimization problem is composed of  optimal solutions to its subinstances.

How do you find the complexity of an algorithm, How do you find the complex...

How do you find the complexity of an algorithm?  Complexity of an algorithm is the measure of analysis of algorithm. Analyzing an algorithm means predicting the resources that

Number of operations possible on ordered lists and arrays, Q. Enumerate num...

Q. Enumerate number of operations possible on ordered lists and arrays.  Write procedures to insert and delete an element in to array.

Calculus, basic calculation for algorith.

basic calculation for algorith.

Queues, Queue is a linear data structure utilized in several applications o...

Queue is a linear data structure utilized in several applications of computer science. Such as people stand in a queue to get a specific service, several processes will wait in a q

Sequential files, In this section, we will discuss about Sequential file or...

In this section, we will discuss about Sequential file organization. Sequential files have data records stored in a particular sequence. A sequentially organized file might be stor

Tree traversals, There are three kinds of tree traversals, namely, Postorde...

There are three kinds of tree traversals, namely, Postorder , Preorder and Inorder. Preorder traversal: Each of nodes is visited before its children are visited; first the roo

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

Program for all pairs shortest paths algorithm, Program segment for All pai...

Program segment for All pairs shortest paths algorithm AllPairsShortestPaths(int N, Matrix C, Matrix P, Matrix D) { int i, j, k if i = j then C[i][j] = 0  for ( i =

What do you mean by hash clash, What do you mean by hash clash? Hashing...

What do you mean by hash clash? Hashing is not perfect. Occasionally, a collision occurs when two different keys hash into the same hash value and are assigned to the same arra

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