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

Explain the different types of traversal on binary tree, Question 1 What i...

Question 1 What is a data structure? Discuss briefly on types of data structures Question 2 Explain the insertion and deletion operation of linked list in detail Qu

Data structure queue, In this unit, we described about the data structure Q...

In this unit, we described about the data structure Queue. It had two ends. One is front from where the elements can be removed and the other is rear where the elements can be inse

What is binary search, What is binary search?   Binary search is most ...

What is binary search?   Binary search is most useful when list is sorted. In binary search, element present in middle of the list is determined. If key (the number to search)

Explain the stack, QUESTION Explain the following data structures: ...

QUESTION Explain the following data structures: (a) List (b) Stack (c) Queues Note : your explanation should consist of the definition, operations and examples.

Multiple stacks, how multiple stacks can be implemented using one dimension...

how multiple stacks can be implemented using one dimensional array

Standard ways of traversing a graph, Q. Which are the two standard ways of ...

Q. Which are the two standard ways of traversing a graph?  Explain them with an example of each.  Ans:   T he two ways of traversing a graph are written below

Decision tree - id3 algorithm, Decision Tree - ID3 algorithm: Imagine ...

Decision Tree - ID3 algorithm: Imagine you only ever do one of the following four things for any weekend:   go shopping   watch a movie   play tennis   just

Algorithm for a function that takes in integer as argument, Write a detaile...

Write a detailed description of a function that takes in an integer as an argument, then prints out the squares of all positive integers whose squares are less than the input. (The

Algorithm to delete node from binary search tree, Normal 0 fals...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

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