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 algorithms, After learning this, you will be able to: u...

After learning this, you will be able to: understand the concept of algorithm; understand mathematical foundation underlying the analysis of algorithm; to understand se

Explain thread, Thread By changing the NULL lines in a binary tree to ...

Thread By changing the NULL lines in a binary tree to special links known as threads, it is possible to perform traversal, insertion and deletion without using either a stack

Order of efficiency - linear search, Linear search employee an exhaustive m...

Linear search employee an exhaustive method of verified each element in the array against a key value. Whereas a match is found, the search halts. Will sorting the array before uti

What are the properties of colour, Properties of colour Colour descript...

Properties of colour Colour descriptions and specifications generally include three properties: hue; saturation and brightness. Hue associates a colour with some position in th

Define doubly linked list, A list item stores pointers and an element ...

A list item stores pointers and an element to predecessor and successor. We call a pointer to a list item a handle . This looks simple enough, but pointers are so powerful tha

Preliminaries, Think of a program you have used that is unacceptably slow. ...

Think of a program you have used that is unacceptably slow. Identify the specific operations that make the program slow. Identify other basic operations that the program performs q

State the complex reallocation procedure, State the complex reallocation pr...

State the complex reallocation procedure Some languages provide arrays whose sizes are established at run-time and can change during execution. These dynamic arrays have an in

Abstract Data Types, A useful tool which is used for specifying the logical...

A useful tool which is used for specifying the logical properties of a data type is called the abstract data type or ADT. The term "abstract data type" refers to the fundamental ma

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