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

Context sensitive f1 help on a field, In what ways we can get the context s...

In what ways we can get the context sensitive F1 help on a field?' Data element documentation. Data element additional text in screen painter. Using the process on help r

Which sorting algorithm is adaptable to singly linked list, Which sorting a...

Which sorting algorithm is easily adaptable to singly linked lists? Simple Insertion sor t is easily adabtable to singly linked list.

Describe commonly used asymptotic notations, Q.1 Compare two functions n 2 ...

Q.1 Compare two functions n 2 and 2 n for various values of n. Determine when second becomes larger than first. Q.2 Why do we use asymptotic notation in the study of algorit

Logic circuits, the voltage wave forms are applied at the inputs of an EX-O...

the voltage wave forms are applied at the inputs of an EX-OR gate. determine the output wave form

How do collisions happen during hashing, How do collisions happen during ha...

How do collisions happen during hashing? Usually the key space is much larger than the address space, thus, many keys are mapped to the same address. Assume that two keys K1 an

State a algorithm that inputs the heights of all 500 student, As part of an...

As part of an experiment, a school measured heights (in metres) of all its 500 students. Write an algorithm, using a flowchart that inputs the heights of all 500 students and ou

Collision resolution techniques, complete information about collision resol...

complete information about collision resolution techniques

Preorder traversal of a binary tree, Preorder traversal of a binary tree ...

Preorder traversal of a binary tree struct NODE { struct NODE *left; int value;     /* can take any data type */ struct NODE *right; };   preorder(struct N

Define an array, Define an array. Array is made up of same data structu...

Define an array. Array is made up of same data structure that exists in any language. Array is set of same data types. Array is the collection of same elements. These same elem

Splaying algorithm, Insertion & deletion of target key requires splaying of...

Insertion & deletion of target key requires splaying of the tree. In case of insertion, the tree is splayed to find the target. If, target key is found out, then we have a duplicat

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