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 prim''s minimum spanning tree algorithm, Question 1. Explai...

Question 1. Explain the different types of traversal on binary tree 2. Explain the Prim's minimum spanning tree algorithm 3. Differentiate fixed and variable storage allo

Explain about hidden-surface, Explain about Hidden-surface Hidden-line...

Explain about Hidden-surface Hidden-line removal refers to wire-frame diagrams without surface rendering and polygonal surfaces with straight edges. Hidden-surface removal ref

Write a procedure that produces independent stack, Write a procedure (make-...

Write a procedure (make-stack) that produces independent stack objects, using a message-passing style, e.g. (define stack1 (make-stack))  (define stack2 (make-stack)) W

Program of insertion of an element in list, Program will demonstrate the in...

Program will demonstrate the insertion of an element at desired position /* Inserting an element into contiguous list (Linear Array) at particular position */ /* contiguous_

Algorithms, 2. Write a note on i) devising ii) validating and...

2. Write a note on i) devising ii) validating and iii) testing of algorithms.

Deletion of any element from the queue, Program segment for the deletion of...

Program segment for the deletion of any element from the queue delmq(i)  /* Delete any element from queue i */ { int i,x; if ( front[i] == rear[i]) printf("Queue is

Determine the greatest common divisor, Determine the greatest common diviso...

Determine the greatest common divisor (GCD) of two integers, m & n. The algorithm for GCD might be defined as follows: While m is greater than zero: If n is greater than m, s

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

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