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

Simplifying assumptions of wire frame representation, Simplifying Assumptio...

Simplifying Assumptions of wire frame representation Neglect colour - consider Intensity: For now we shall forget about colour and restrict our discussion just to the intensi

Define chaining process of hashing, Chaining In this method, instead of...

Chaining In this method, instead of hashing function value as location we use it as an index into an array of pointers. Every pointer access a chain that holds the element havi

Insertion in list, In the array implementation of lists, elements are store...

In the array implementation of lists, elements are stored into continuous locations. In order to add an element into the list at the end, we can insert it without any problem. But,

Types of triangular matrices, Triangular Matrices Tiangular Matrices is...

Triangular Matrices Tiangular Matrices is of 2 types: a)  Lower triangular b)  Upper triangular

What are circular queues, What are circular queues?  Circular queue: St...

What are circular queues?  Circular queue: Static queues have a very large drawback that once the queue is FULL, even though we erase few elements from the "front" and relieve

State warnock algorithm, Warnock's Algorithm An interesting approach to...

Warnock's Algorithm An interesting approach to the hidden-surface problem was presented by Warnock. His method does not try to decide exactly what is happening in the scene but

Total impedent of the circuit, an electrical student designed a circuit in...

an electrical student designed a circuit in which the impedence in one part of a series circuit is 2+j8 ohms and the impedent is another part of the circuit is 4-j60 ohm mm program

Threaded binary tree, i need the full concept of it... please can anyone pr...

i need the full concept of it... please can anyone provide

Explain about greedy technique, Explain about greedy technique The  gre...

Explain about greedy technique The  greedy  method  suggests  constructing  a   solution  to  an  optimization  problem   by  a sequence of steps, every expanding a partially c

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