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 insertion sort, Q. Explain the insertion sort with a proper algorit...

Q. Explain the insertion sort with a proper algorithm. What is the complication of insertion sort in the worst case?

The complexity of multiplying two matrices, The complexity of multiplying t...

The complexity of multiplying two matrices of order m*n and n*p is    mnp

Complexity of quick sort, Q. What do you mean by the best case complexity o...

Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?

Explain insertion procedure into a b-tree, Ans: I nsertion into the B...

Ans: I nsertion into the B-tree: 1.  First search is made for the place where the new record must be positioned. As soon as the keys are inserted, they are sorted into th

Insertion of a node into a binary search tree, A binary search tree is cons...

A binary search tree is constructed through the repeated insertion of new nodes in a binary tree structure. Insertion has to maintain the order of the tree. The value to the lef

Enumerate about the data structure, Enumerate about the Data structure ...

Enumerate about the Data structure An arrangement of data in memory locations to signify values of the carrier set of an abstract data type. Realizing computational mechanis

Explain b tree (binary tree), B Tree Unlike a binary-tree, every node o...

B Tree Unlike a binary-tree, every node of a B-tree may have a variable number of keys and children. The keys are stored in non-decreasing order. Every key has an associated ch

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

Comparisons between linear and binary search, Comparative Study of Linear a...

Comparative Study of Linear and Binary Search Binary search is lots quicker than linear search. Some comparisons are following: NUMBER OF ARRAY ELEMENTS EXAMINED array

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