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

Pre-order and post order traversal of a binary tree, The pre-order and post...

The pre-order and post order traversal of a Binary Tree generates the same output. The tree can have maximum One node

Quicksort and bubble sort algorithms, Task If quicksort is so quick, w...

Task If quicksort is so quick, why bother with anything else? If bubble sort is so bad, why even mention it? For that matter, why are there so many sorting algorithms? Your

Encryption the plain-text using the round keys, Encryption the plain-text u...

Encryption the plain-text using the round keys: 1. (Key schedule) Implement an algorithm that will take a 128 bit key and generate the round keys for the AES encryption/decryp

Explain backtracking, Explain Backtracking The  principal idea is to co...

Explain Backtracking The  principal idea is to construct solutions single component  at a time  and evaluate such  partially constructed candidates as follows. If a partiall

Operation of algorithm, Operation of Algorithm The following sequence o...

Operation of Algorithm The following sequence of diagrams shows the operation of Dijkstra's Algorithm. The bold vertices show the vertex to which shortest path has been find ou

Data structure- tree, Tree is dynamic data structures. Trees can expand & c...

Tree is dynamic data structures. Trees can expand & contract as the program executes and are implemented via pointers. A tree deallocates memory whereas an element is deleted.

Determine the complexity, 1)    The set of the algorithms whose order is O ...

1)    The set of the algorithms whose order is O (1) would run in the identical time.  True/False 2)    Determine the complexity of the following program into big O notation:

Algorithm for stack using array, write an algorithm for stack using array p...

write an algorithm for stack using array performing the operations as insertion ,deletion , display,isempty,isfull.

Need help with working out. I dont really get it, Suppose there are exactly...

Suppose there are exactly five packet switches (Figure 4) between a sending host and a receiving host connected by a virtual circuit line (shown as dotted line in figure 4). The tr

Travelling salesman problem, Example 3: Travelling Salesman problem G...

Example 3: Travelling Salesman problem Given: n associated cities and distances among them Find: tour of minimum length that visits all of city. Solutions: How several

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