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

Time complexity of merge sort and heap sort algorithms, What is the time co...

What is the time complexity of Merge sort and Heap sort algorithms? Time complexity of merge sort is O(N log2 N) Time complexity of heap sort is   O(nlog2n)

Demonstration of polynomial using linked list, Demonstration of Polynomial ...

Demonstration of Polynomial using Linked List # include # include Struct link { Char sign; intcoef; int expo; struct link *next; }; Typedefstruct link

Which data structure is used for implementing recursion, Which data structu...

Which data structure is used for implementing recursion Stack.

Preorder traversal of a binary tree, Preorder traversal of a binary tree ...

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

Depth-first search (dfs) , In this respect depth-first search (DFS) is the...

In this respect depth-first search (DFS) is the exact reverse process: whenever it sends a new node, it immediately continues to extend from it. It sends back to previously explore

Recursion, difference between recursion and iteration

difference between recursion and iteration

Reverse order of elements on a slack, Q. Describe the representations of gr...

Q. Describe the representations of graph. Represent the graph which is given to us using any two methods Ans: The different ways by which we can represent graphs are:

Randomized algorithm, need an expert to help me with the assignment

need an expert to help me with the assignment

Execute algorithm to convert infix into post fix expression, Q. Execute you...

Q. Execute your algorithm to convert the infix expression to the post fix expression with the given infix expression as input Q = [(A + B)/(C + D) ↑ (E / F)]+ (G + H)/ I

Splaying algorithm, Insertion & deletion of target key requires splaying of...

Insertion & deletion of target key requires splaying of the tree. In case of insertion, the tree is splayed to find the target. If, target key is found out, then we have a duplicat

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