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

Stack, write pseudocode to implement a queue with two stacks

write pseudocode to implement a queue with two stacks

Basic concept of the primitive data structures, Q. Explain the basic concep...

Q. Explain the basic concept of the primitive data structures.                                             Ans. The concept of P r i m i t i ve Data

Steps of pre-order traversal, Pre-order Traversal The method of doing a...

Pre-order Traversal The method of doing a pre-order traversal iteratively then has the several steps(suppose that a stack is available to hold pointers to the appropriate nodes

Write an algorithm to display this repeated calculation, The following form...

The following formula is used to calculate n: n = x * x/(1 - x) . Value x = 0 is used to stop algorithm. Calculation is repeated using values of x until value x = 0 is input. There

Abstract data types, Abstract Data Types :- A useful tool for specifying th...

Abstract Data Types :- A useful tool for specifying the logical properties of a data type is the abstract data type or ADT. The term "abstract data type" refers to the basic mathem

Sorted list using binary search technique, Write an algorithm for searching...

Write an algorithm for searching a key from a sorted list using binary search technique 1.   if (low > high) 2.     return (-1) 3.    mid = (low +high)/2; 4    .if ( X

The complexity of searching an element, The complexity of searching an elem...

The complexity of searching an element from a set of n elements using Binary search algorithm is   O(log n)

Array implementation of a queue, Since the stack is list of elements, the q...

Since the stack is list of elements, the queue is also a list of elements. The stack & the queue differ just in the position where the elements may be added or deleted. Similar to

Design and implement a software system, In this assignment, you are invited...

In this assignment, you are invited to design and implement a software system for catalogue sale. A catalogue is organised in a tree structure. Each node of the catalogue tree repr

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