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

Dijkstra's algorithm, Q. Explain Dijkstra's algorithm for finding the short...

Q. Explain Dijkstra's algorithm for finding the shortest path in the graph given to us.  Ans: The Dijkstra's algorithm: This is a problem which is concerned with finding

Relationship between shortest path distances of modified, a) Given a digrap...

a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by usin

Rl rotation - avl tree, Example: (Double left rotation while a new node is ...

Example: (Double left rotation while a new node is added into the AVL tree (RL rotation)) Figure: Double left rotation when a new node is inserted into the AVL tree A

Sorting algorithms, Sorting is significant application activity. Several so...

Sorting is significant application activity. Several sorting algorithms are obtainable. But, each is efficient for a specific situation or a specific kind of data. The choice of a

Explain multiplication method, Multiplication Method: The multiplication m...

Multiplication Method: The multiplication method operates in 2 steps. In the 1ststep the key value K is multiplied by a constant A in the range O

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

Estimate best first search nodes , Given the following search tree, state t...

Given the following search tree, state the order in which the nodes will be searched for breadth first, depth first, hill climbing and best first search, until a solution is reache

Registers, what are registers? why we need register? Definition? Types? Wha...

what are registers? why we need register? Definition? Types? What registers can do for us?

Depth first traversal, A depth-first traversal of a tree visits a nodefirst...

A depth-first traversal of a tree visits a nodefirst and then recursively visits the subtrees of that node. Similarly, depth-first traversal of a graph visits a vertex and then rec

General Tree, How to create an General Tree and how to search general tree?...

How to create an General Tree and how to search general tree?

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