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

State flowchart that take temperature input using pseudocode, Write an algo...

Write an algorithm using pseudocode which takes temperatures input over a 100 day period (once per day) and output the number of days when the temperature was below 20C and the num

Stack, how we will make projects on stack in c?

how we will make projects on stack in c?

A sort which relatively passes by a list, A Sort which relatively passes by...

A Sort which relatively passes by a list to exchange the first element with any element less than it and then repeats with a new first element is called as      Quick sort.

Tradeoff between space and time complexity, We might sometimes seek a trade...

We might sometimes seek a tradeoff among space & time complexity. For instance, we may have to select a data structure which requires a lot of storage to reduce the computation tim

Explain graph traversal, Graph Traversal In many problems we wish to in...

Graph Traversal In many problems we wish to investigate all the vertices in a graph in some systematic order. In graph we often do not have any single vertex singled out as spe

Splaying procedure, For splaying, three trees are maintained, the central, ...

For splaying, three trees are maintained, the central, left & right sub trees. At first, the central subtree is the complete tree and left and right subtrees are empty. The target

Explain about the containers, Containers Introduction Simple abstr...

Containers Introduction Simple abstract data types are useful for manipulating simple sets of values, such as integers or real numbers however more complex abstract data t

Abstract data type-tree, Definition: A set of data values & related operati...

Definition: A set of data values & related operations that are accurately specified independent of any particular implementation. As the data values and operations are described

R. Studio, I need a person who has a good background in using R. Studio? I...

I need a person who has a good background in using R. Studio? In adition, a person who is good in using algorithms.

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