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

Sparse matrix, memory address of any element of lower left triangular spars...

memory address of any element of lower left triangular sparse matrix

Discrete time simulation of a queue, In this project you will write a progr...

In this project you will write a program to produce a discrete time simulation of a queue as shown in Fig. 1. Time is slotted on the input and the output. Each input packet follows

Implement an algorithm to simulate car re-organizing, Design  and implement...

Design  and implement  an algorithm  to simulate car  re-organizing of the train at the railway switching junction. You can only use stacks as the data structure to represent the t

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.

Algorithm for finding a key by binary search technique, Q. Write down an al...

Q. Write down an algorithm for finding a key from a sorted list using the binary search technique or method.

Techniques of representing polynomials using arrays, Q. Explain any three m...

Q. Explain any three methods or techniques of representing polynomials using arrays. Write which method is most efficient or effective for representing the following polynomials.

Explain the term totalling, Explain the term totalling To add up a ser...

Explain the term totalling To add up a series numbers the subsequent type of statement must be used: Total = total + number  This literally means (new) total = (old) t

Red-black trees, A Red-Black Tree (RBT) is a type of Binary Search tree wit...

A Red-Black Tree (RBT) is a type of Binary Search tree with one extra bit of storage per node, i.e. its color that can either be red or black. Now the nodes can have any of the col

Storing a sparse matrix in memory, Explain an efficient method of storing a...

Explain an efficient method of storing a sparse matrix in memory. Write a module to find the transpose of the sparse matrix stored in this way. A matrix which contains number o

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