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

Depth first search and breadth first search, Q. Illustrate the result of ru...

Q. Illustrate the result of running BFS and DFS on the directed graph given below using vertex 3 as source.  Show the status of the data structure used at each and every stage.

An undirected graph g with n vertices and e edges, An undirected graph G wi...

An undirected graph G with n vertices and e edges is shown by adjacency list.  What is the time required to generate all the connected components? O (e+n)

Need help with working out. I dont really get it, Suppose there are exactly...

Suppose there are exactly five packet switches (Figure 4) between a sending host and a receiving host connected by a virtual circuit line (shown as dotted line in figure 4). The tr

ALGORITHMS, WRITE AN ALGORITHM TO READ TWO NUMBERS AND PRINT THE LOWER VALU...

WRITE AN ALGORITHM TO READ TWO NUMBERS AND PRINT THE LOWER VALUE

Methods, what is folding method?

what is folding method?

Explain the halting problem, Explain the halting problem Given a comput...

Explain the halting problem Given a computer program and an input to it, verify whether the program will halt on that input or continue working indefinitely on it.

Operations on b-trees, Operations on B-Trees Given are various operatio...

Operations on B-Trees Given are various operations which can be performed on B-Trees: Search Create Insert B-Tree does effort to minimize disk access and t

Polynomials - represented by using arrays, /* the program accepts two polyn...

/* the program accepts two polynomials as a input & prints the resultant polynomial because of the addition of input polynomials*/ #include void main() { int poly1[6][

Abstract data type-list, It is a useful tool for indicating the logical pro...

It is a useful tool for indicating the logical properties of data type. It is a collection of values & a set of operations on those values. Methodically, "a TYPE is a set, & elemen

Threaded binary tree, i need the full concept of it... please can anyone pr...

i need the full concept of it... please can anyone provide

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