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

File organisation, File organisation might be described as a method of stor...

File organisation might be described as a method of storing records in file. Also, the subsequent implications approaching these records can be accessed. Given are the factors invo

What is assertions, What is Assertions Introduction At every point...

What is Assertions Introduction At every point in a program, there are generally constraints on the computational state that should hold for program to be correct. For ins

Logic circuits, the voltage wave forms are applied at the inputs of an EX-O...

the voltage wave forms are applied at the inputs of an EX-OR gate. determine the output wave form

Explain arrays, Arrays :- To execute a stack we need a variable called top,...

Arrays :- To execute a stack we need a variable called top, that holds the index of the top element of stack and an array to hold the part of the stack.

Procedures, what is far and near procedures in system programming?

what is far and near procedures in system programming?

Row major representation, Row Major Representation In memory the primar...

Row Major Representation In memory the primary method of representing two-dimensional array is the row major representation. Under this representation, the primary row of the a

Graphs, c program to represent a graph as an adjacency multilist form

c program to represent a graph as an adjacency multilist form

Enumerate about the carrier set members, Enumerate about the carrier set me...

Enumerate about the carrier set members Ruby is written in C, so carrier set members (which is, individual symbols) are implemented as fixed-size arrays of characters (which is

Sparse matrix, what are the disadvantages of sparse matrix?

what are the disadvantages of sparse matrix?

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