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

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

Types of tree ?, Binary: Each node has one, zero, or two children. This ...

Binary: Each node has one, zero, or two children. This assertion creates many tree operations efficient and simple. Binary Search : A binary tree where each and every left

Determine the warnock algorithm, Warnock's Algorithm A divide and conqu...

Warnock's Algorithm A divide and conquer algorithm Warnock (PolyList PL, ViewPort VP) If (PL simple in VP) then Draw PL in VP, else Split VP vertically and horiz

Graphs with negative edge costs, We have discussed that the above Dijkstra'...

We have discussed that the above Dijkstra's single source shortest-path algorithm works for graphs along with non-negative edges (like road networks). Given two scenarios can emerg

Java code and algorythem, Suppose that you want to develop a program that a...

Suppose that you want to develop a program that accepts a postfix expression and asks values for variables in the expression. Then you need to calculate the answer for the expressi

Explain backtracking, Explain Backtracking The  principal idea is to co...

Explain Backtracking The  principal idea is to construct solutions single component  at a time  and evaluate such  partially constructed candidates as follows. If a partiall

Find strongly connected components - dfs, A striking application of DFS is ...

A striking application of DFS is determine a strongly connected component of a graph. Definition: For graph G = (V, E) , where V refer to the set of vertices and E refer to the

Deletion from a red-black tree, Deletion in a RBT uses two main processes, ...

Deletion in a RBT uses two main processes, namely, Procedure 1: This is utilized to delete an element in a given Red-Black Tree. It involves the method of deletion utilized in

Elaborate the symbols of abstract data type, Elaborate the symbols of abstr...

Elaborate the symbols of abstract data type length(a)-returns the number of characters in symbol a. capitalize(a)-returns the symbol generated from a by making its first cha

Explain circular queues, Circular Queues:- A more efficient queue repre...

Circular Queues:- A more efficient queue representation is get by regarding the array Q(1:n) as circular. It becomes more convenient to declare the array as Q(O: n-1), when  re

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