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

Algorithm, Example of worse case of time

Example of worse case of time

Graph & optimal scheduling, You are given an undirected graph G = (V, E) in...

You are given an undirected graph G = (V, E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1,2,...,W}, where W

Explain the method of overlapping and intersecting, Overlapping or Interse...

Overlapping or Intersecting A polygon overlaps or intersects the current background if any of its sides cuts the edges of the viewport as depicted at the top right corner of th

Merging 4 sorted files containing 50, Merging 4 sorted files having 50, 10,...

Merging 4 sorted files having 50, 10, 25 and 15 records will take time  O (100)

Queues, Queue is a linear data structure utilized in several applications o...

Queue is a linear data structure utilized in several applications of computer science. Such as people stand in a queue to get a specific service, several processes will wait in a q

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

Design the system for seller, Your program should include three components ...

Your program should include three components selling, buying and managing for the use of sellers, buyers and the Manager, respectively. Provide a menu for a user to enter each comp

find shortest path from a to z using dijkstra''s algorithm., Q.  In the gi...

Q.  In the given figure find the shortest path from A to Z using Dijkstra's Algorithm.    Ans: 1.  P=φ;  T={A,B,C,D,E,F,G,H,I,J,K,L,M,Z} Let L(A)

Programme in c to create a single linked list, Q. Write  down a   p...

Q. Write  down a   programme  in  C  to  create  a  single  linked  list also  write the functions to do the following operations (i)  To insert a new node at the end (ii

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