Binary trees, Data Structure & Algorithms

Assignment Help:

A binary tree is a special tree where each non-leaf node can have atmost two child nodes. Most important types of trees which are used to model yes/no, on/off, higher/lower, i.e., binary decisions are binary trees.

Recursive Definition: A binary tree is either empty or a node that has left and right sub-trees that are binary trees. Empty trees are represented as boxes (but we will almost always omit the boxes).

In a formal way, we can described binary tree as a finite set of nodes which is either empty or partitioned in to sets of T0, Tl, Tr , where T0 is the root and Tl and Tr are left and right binary trees, respectively.

Properties of a binary tree are following

  • If a binary tree contains n nodes, then it have exactly n - 1 edges;
  • A Binary tree of height h contains 2h - 1nodes or less.
  • If we have a binary tree having n nodes, then the height of the tree is at most n and at least ceiling log2(n + 1).
  • If a binary tree contain n nodes at a level l then, it has at most 2n nodes at a level l+1
  • The total number of nodes in binary tree with depth d (root has depth zero) is

                       N = 20 + 21 + 22 + .......+ 2d = 2d+1 - 1


Related Discussions:- Binary trees

Objectives of lists, After going through this unit, you will be able to: ...

After going through this unit, you will be able to: • define and declare Lists; • understand the terminology of Singly linked lists; • understand the terminology of Doubly

Financial index data analysis, need c++ algorithmic software program to der...

need c++ algorithmic software program to derive one numerical outcome from 10 levels of variables with 135 combinations cross computed

Determine about the logic gates, Determine about the logic gates Many e...

Determine about the logic gates Many electronic circuits operate using binary logic gates. Logic gates essentially process signals that represent true or false or equivalent i.

Illustrate an example of algorithm, Illustrate an example of algorithm ...

Illustrate an example of algorithm Consider that an algorithm is a sequence of steps, not a program. You might use the same algorithm in different programs, or express same alg

Explain cam software, Explain CAM software CAD/CAM software has been re...

Explain CAM software CAD/CAM software has been recognized as an essential tool in the designing and manufacturing of a product due to its ability to depict the designs and tool

State the painter algorithm, Painter's Algorithm As the name suggests, ...

Painter's Algorithm As the name suggests, the algorithm follows the standard practice of a painter, who  would paint the background (such as a backdrop) first, then the major d

Sorted list followed by a few "random" elements, You have to sort a list L ...

You have to sort a list L having of a sorted list followed by a few "random" elements. Which sorting methods would be especially suitable for this type of task?   Insertion sort

Deletion of an element from the linked list, A LGORITHM (Deletion of an ele...

A LGORITHM (Deletion of an element from the linked list) Step 1  Begin Step 2  if the list is empty, then element cannot be deleted Step 3  else, if the element to be del

Determine about the unreachable code assertion, Determine about the unreach...

Determine about the unreachable code assertion An unreachable code assertion is an assertion that is placed at a point in a program that shouldn't be executed under any circum

Queues, what is the difference between data type and abstract data type

what is the difference between data type and abstract data type

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